2017 parag s. raneufdcimages.uflib.ufl.edu/uf/e0/05/03/73/00001/rane_p.pdfeffect of microtubule...
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EFFECT OF MICROTUBULE MOTORS ON MICROTUBULE MECHANICS
By
PARAG S. RANE
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOLOF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
2017
© 2017 Parag S. Rane
I dedicate this to my family.
ACKNOWLEDGMENTS
I want to take this opportunity to thank all individuals who lead to the successful
completion of this work and made my life easier during this process. Firstly, I am indebted
to my advisors, Prof. Tony Ladd and Prof. Tanmay Lele for their limitless patience, invaluable
guidance, and unwavering support at all times with a much-needed room for growth. I would
like to thank Prof. Rich Dickinson for providing me his invaluable time particularly during
the summer of 2015 and for his lectures in biophysics which transformed my perspective
of this field. This work was enabled by the support of National Science Foundation (grant
no.1236616).
I would like to thank Dr. Ian Kent from Lele Lab who performed all the experiments
for the modeling project in chapter 2. My depth of knowledge in biology was improved
substantially because of the discussions with Samer Alam, Varun Agarwal and other members
in the Lele Lab group. I am thankful to Nandini Shekhar for answering the queries which
proved helpful in the completion of Chapter 4. I want to acknowledge my labmates, Dr. Virat
Upadhyay, Dr.Vitali Starchekno for making my workplace the place to be. I want to thank
Dr.Gaurav Mishra, who is a former student from Tony’s group for his helpful conversations
during my transition to the Ladd Lab.
It was a real treat and a valuable learning experience to be a teaching assistant for the
Chemical Reaction Engineering course taught by Prof. Jason Weaver and the Computer Model
Formulation course taught by Prof. Spyros Svoronos which has sparked my interest in teaching.
Shoutout to Sandaliya Sanbathula for the annual road trips where we explored this great and
diverse country. I will cherish my friendship with Mert Arca, Akshat Dimiri, Maxim Prokopenko
Rahul Rai, Varun Agarawal , Harsh Tanrang, and many others in times to come.
I would like to thank Shirley Kelly and other members of departmental staff for their kind
help. Thanks to Janis Mena for insightful discussions on nutrition. I am thankful to Janice
Ladd for her kindness and delicious thanksgiving dinners. I feel blessed to have my cousin
Sarang and his wife Yogini in my life, who made me feel at home during my visits to their
4
place. Lastly, I want to express my gratitude from the bottom my heart towards my parents,
Dr. Subhash Rane & Rekha Rane and my grandmother Kamlabai whose handvowen ”Godadi”
(blanket) has kept me warm during these years.
5
TABLE OF CONTENTS
page
ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
CHAPTER
1 INTRODUCTION AND BACKGROUND . . . . . . . . . . . . . . . . . . . . . . . 12
1.1 Contributions of this Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 131.2 Microtubule Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131.3 Force Acting on Microtubules . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2 MODELING AND SIMULATION METHODS . . . . . . . . . . . . . . . . . . . . . 18
2.1 Model for Microtubule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.1.1 Discretization of Microtubule Shape . . . . . . . . . . . . . . . . . . . 182.1.2 Dynamic Instability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.1.3 Internal Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2 Model for Motor Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.2.1 Continuous Motor Force Model for Dynein Forces . . . . . . . . . . . . 222.2.2 Discrete Motor Force Model for Dynein and Kinesin Forces . . . . . . . 24
2.2.2.1 Initialization and termination of motors . . . . . . . . . . . . 242.2.2.2 Linkage based force generation . . . . . . . . . . . . . . . . 26
2.2.3 Background Friction . . . . . . . . . . . . . . . . . . . . . . . . . . . 272.2.4 Pinning Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272.2.5 Equation of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3 A MECHANISM FOR BENDING MICROTUBULES . . . . . . . . . . . . . . . . . 32
3.1 Background Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.2 Equation of Motion and and Selection of Model Parameters . . . . . . . . . . 343.3 Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.3.1 Microtubules Bend against Transiently Immobilized Segments . . . . . 353.3.2 Dynein, but not Myosin is Involved in Formation of Local Bends under
Nucleus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.3.3 A Mechanism for Microtubule Bend Formation by Dynein-mediated
Transport towards a Pinning Point . . . . . . . . . . . . . . . . . . . . 373.3.4 Bending near the Microtubule Plus End Tip Leads to Tip Rotation . . . 38
3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
6
4 EXCESS LENGTH IN MICROTUBULES . . . . . . . . . . . . . . . . . . . . . . . 49
4.1 Objective and Background Information . . . . . . . . . . . . . . . . . . . . . 494.1.1 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494.1.2 Background Information . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.2 Data Analysis Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514.2.1 Fourier Mode Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 514.2.2 Variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524.3.1 A Putative Role for Plus End Motors in Generating Excess Length . . . 52
4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5 OUTLOOK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
BIOGRAPHICAL SKETCH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
7
LIST OF TABLES
Table page
3-1 Model Parameters: Microtubule, Continous Motor Model . . . . . . . . . . . . . . 48
4-1 Model Parameters: Microtubule, Discrete Motor Model . . . . . . . . . . . . . . . 63
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LIST OF FIGURES
Figure page
1-1 Microtubule Structure and Dynamic Instability. . . . . . . . . . . . . . . . . . . . . 16
1-2 Structure of Dynactin molecule. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2-1 Model points representing microtubules. . . . . . . . . . . . . . . . . . . . . . . . 29
2-2 Stresses within the microtubule. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2-3 Initial motor configuration leads to a shortlived compressive stress. . . . . . . . . . 31
3-1 Local bends develop by dynein-dependent translation of microtubule segments fromthe minus end. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3-2 Simulations of dynein mediated bend formation in microtubules. . . . . . . . . . . . 44
3-3 Rotation of the microtubule tip due to local bend formation. . . . . . . . . . . . . . 46
3-4 Effect of overhanging segment length on the rotation of the tip. . . . . . . . . . . . 47
4-1 Experimentally recorded tip trajectories of growing microtubules. . . . . . . . . . . 56
4-2 Microtubule straightening in absence of pinning under the action of dynein motor. . 56
4-3 Sine Waves corresponding to mode numbers in the Fourier mode spectrum. . . . . . 57
4-4 Simulations of growing microtubules subjected to motor forces. . . . . . . . . . . . 58
4-5 Motors binding near the tip change the orientation of the tip. . . . . . . . . . . . . 59
4-6 Comparison of Fourier modes of tip trajectories and simulated microtubules. . . . . 60
4-7 Average poly. speed estimated from tip trajectories of simulated microtubule. . . . . 61
4-8 Excess length in simulated microtubules. . . . . . . . . . . . . . . . . . . . . . . . 62
9
Abstract of Dissertation Presented to the Graduate Schoolof the University of Florida in Partial Fulfillment of theRequirements for the Degree of Doctor of Philosophy
EFFECT OF MICROTUBULE MOTORS ON MICROTUBULE MECHANICS
By
Parag S. Rane
May 2017
Chair: Anthony J.C. LaddCochair: Tanmay LeleMajor: Chemical Engineering
Microtubules (MTs) and microtubule associated proteins (MAP’s), particularly motor
proteins are being extensively researched for two specific reasons, viz. anomalies in MAP’s is
the leading cause in many neurodegenerative diseases and for its potential application in cancer
treatment as MT and MAP’s form the machinery to separate chromosomes during cell division.
Microtubules have a persistence length of the order of millimeters in vitro, but inside cells, they
bend over length scales of microns which suggest non-thermal forces at work.
We modeled microtubules as elastic rods and associated motor proteins as elastic linkages
which attach and detach along its length to study the shape dynamics of microtubules in-vivo.
Our collaborative work with Lele lab shows that a majority of microtubule bending, in the cell
interior away from the cell boundary is primarily caused by dynein-mediated transport of MT
length towards its plus end in presence of cross-linkers. In absence of such linkers, we found
that MT was being straightened by dynein which led to the further question, how a nucleating
MT could retain its curvature required for MT bending in presence of dynein. We investigate
this question in chapter 3. Additionally, in some cases bend formation near the tip altered its
direction. We systematically investigated this mechanism in presence of cross-linkers and found
that this mechanism could influence microtubule tips growing at a slower rate.
We show that an ensemble of plus end-directed motors acting on a MT generates
observed quantified deflections in MT tips (variance) on dynein inhibition. Further, our
simulations show that the curvature along the MT can be introduced by the action of opposing
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motor forces based on their distribution. This model allows a majority of MT to be under
tension with some of its sections under compression showing that centrosome centering
mechanism and microtubule bending away from periphery can co-exist together thereby tying
all the previous experimental observations in our group.
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CHAPTER 1INTRODUCTION AND BACKGROUND
The eukaryotic cytoskeleton consists of three types of proteinaceous filaments- F-actin,
intermediate filaments and microtubules found in the cytoplasm. Polymerizing F-actin
filaments grow to push the cell membrane outward during cell motility and enable cell crawling.
Intermediate filaments are structurally stable networks, which provide shape stability to cells,
and also form the nuclear lamina which maintains a mechanically stable nucleus. Microtubules
are hollow biopolymers that participate in cell division, serve as traffic highways along which
motor proteins transport organelles, and generate mechanical forces to position the nucleus.
Given the mechanical functions of these three cytoskeletal structures in enabling cell motility,
intracellular transport, pulling chromatids apart during anaphase and maintaining cell shape in
homeostasis, there has been much interest in understanding the mechanical properties of these
cytoskeletal elements. This thesis focuses on the mechanical forces on interphase microtubules
generated by motor proteins in the cytoplasm.
When isolated in vitro, the microtubule has a persistence length of the order of millimeters
indicating that it is stiff to thermal fluctuations [1]. In comparison, F-actin has a persistence
of a few microns [1], while that of DNA is 30-50 nanometers [2]. Despite its stiffness, the
microtubule is bent with wavelengths of a few microns in cells [3–6]. Microtubules are also
dynamic in that they grow and shrink continuously in cells by cycles of polymerization and
depolymerization. This phenomenon is known as dynamic instability [7]. In cells, microtubules
are shown to deviate from their initial direction of growth [8]. Wavy shapes of microtubules
and dynamic polymerization and depolymerization are thought to allow sampling of cellular
space efficiently compared with a straight, static polymer. This has the benefit of efficient
sampling of cytoplasmic space [9], which is crucial for efficient transport of organelles.
What is the explanation for the bent shapes of microtubules? This question has been
of interest in the recent literature [3–5, 10]. The commonly accepted explanation is that
a growing microtubule pushing against an immobile barrier will bend by Euler buckling (or
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modified Euler buckling if the microtubule is ’reinforced by connections with the cytoplasm
[4]). However, this explanation is challenged by experiments with laser ablation [11] in which
increased bending of severed microtubule fragments were observed instead of relaxation
of bending as would be predicted for a microtubule under compression. The laser ablation
experiments instead suggest that microtubules may be under tension along their lengths (this
does not argue against local compressive forces at a growing tip).
1.1 Contributions of this Thesis
In this thesis, we performed computational simulations to explain the mechanical behavior
of static and growing microtubules in living cells. By comparing results of simulations and
experimental observations made in the Lele lab, we explain how bends develop in microtubules
in living cells in Chapter 2. In Chapter 3, we explain how microtubules bend during growth,
again through a comparison between simulation results and experimental observations.
1.2 Microtubule Structure
We now discuss microtubule structure, which is important to understand microtubule
mechanics. A single microtubule consists of 13 proto-filaments [12] that are parallel to one
another and arranged circumferentially, forming a hollow tube with an inner diameter of 12 nm
and outer diameter of 24 nm 1.3. Each protofilament is a polymer of a dimer of proteins, α
and β tubulin, each of which has a molecular mass of 50 kilo Dalton (kDa). The monomers
associate in a −(α − β)n− like configuration that induces polarity in the MT. The number
of protofilaments that make up the microtubule are determined by γ tubulin ring complex
(γ − TuRC). The ring complex acts as a scaffold for assembly for tubulin dimers and speeds
up the nucleation process. Most microtubules in interphase cells are anchored in this complex,
which forms the core functional unit of the structure known as centrosome. In a interphase,
most microtubules radiate out ward from centrosome. This network topology is peculiar to
microtubules.
The end of the microtubule that terminates in the γ − TuRC is called the minus
end while the other end which undergoes polymerization and depolymerization constantly
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in cells is known as the plus end of the MT. The MT plus end cycles through phases of
polymerization and depolymerization and this phenomenon is termed as dynamic instability
[7]. In order to polymerize, tubulin needs to bind to GTP [13]. Upon binding in the cytoplasm,
the tubulin-GTP complex is stable [14, 15]. When GTP-tubulin subunits are incorporated
into an MT, the rate of hydrolysis of exposed GTP on β-tubulin increases significantly [16].
The GTP-tubulin hydrolyzes to GDP-tubulin and the resulting energy is stored within the
protofilament tube-like structure of the microtubule. This energy is available to do work during
depolymerization and is used to pull chromatids apart during anaphase [17]. Depolymerization
is triggered when there is a loss of GTP-tubulin at the plus end- GTP-tubulin on the plus end
is referred to as the GTP-cap. GTP-tubulin restricts the backward coiling of GDP-tubulin
protofilaments. GTP on the MT is continuously hydrolyzed but new GTP tubulin is added at
the tip maintaining the GTP cap. When the rate of GTP hydrolysis exceeds the recruitment of
GTP tubulin, depolymerization (also called catastrophe) takes place [18]. Additionally, evidence
has been found to support the presence of unhydrolyzed regions of GTP-tubulin away from the
plus end, which are likely to aid in rescue of polymerization following catastrophe [19–22].
1.3 Force Acting on Microtubules
When the plus end of a growing microtubule encounters a barrier, it may continue to
add monomer sub-units which allows the microtubule to push against the barrier [23, 24].
These polymerization forces are known to cause local buckling of the microtubule close to
the periphery [10, 25, 26]. Compressive forces generated by pushing against the barrier are
implicated in centering of the MTOC and spindle bodies [27–29] demonstrated in in-vitro
experiments [30, 31]. However, this mechanism seems viable in cells with small size as the
critical buckling force (F) for a microtubule of length (L) scales as F ∝ L−2 . Additionally, this
mechanism seem to function better in square shaped micro-fabricated chambers which is not a
typical geometry of a cell. Microtubule depolymerization releases energy stored in microtubule
lattice. This energy is stored in lattice due to hydrolysis of incorporated GTP tubulin units and
is used to generate forces on sister chromatids to pull them apart [32–37].
14
Of particular interest in this thesis the action of microtubule motors dynein and kinesin
family which processively walk along microtubules. Dynein walks toward the minus end of
microtubules while kinesin walks toward the plus end. These motors convert the energy of
ATP hydrolysis to motor along the microtubule, and are able to perform work by moving
organelles anchored to the other end of the motors in the crowded, viscous cytoplasm. Dynein
and kinesin may exert significant forces on the microtubule when they continue to motor
while their other end is bound to immobile objects [11]. For example, dynein can bind to
the nuclear surface [38–43]. The nucleus is a large object, and a single dynein motor that
is bound to the nucleus on one end and lengthens as it walks on the microtubule on the
other end will pull on the nucleus and on the microtubule. In the same way, dynein may walk
on microtubules in the cytoplasm, while being connected at the other end with dynactin.
Dynactin is a multisubunit protein complex found in eukarytoic cells that is required to
activate dynein[44, 45]. Dynactin increases the processivity of dynein, and allows a dynein
molecule to travel a larger distance on the microtubule contour [46–49]. The dynactin molecule
is 40 nm in length and 15 nm in height. Morphologically, dynactin can be divided into two
domains viz. Arp1 (Actin Related Protein 1) rod and the shoulder domain [50, 51]. Figure 1-2
shows a schematic representation of dynactin with various domains, including the p150Glued
which is located at the end of the shoulder domain. While dynein binds to the p150Glued
subunit of dynactin (corresponding to AA 217-548 of p150Glued), kinesin-2 binds to AA
600-811 of p150Glued. Schematic descriptions for dynein is included in Chapter 3.
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Figure 1-1. Microtubule Structure and Dynamic Instability.(a) Microtubules are composed of stable / -tubulin heterodimers that are aligned ina polar head-to-tail fashion to form protofilaments. (b) The cylindrical and helicalmicrotubule wall typically comprises 13 parallel protofilaments in vivo. The 12-nmhelical pitch in combination with the 8-nm longitudinal repeat between / -tubulinsubunits along a protofilament generates the lattice seam (red dashed line). (c)Assemblypolymerization and disassemblydepolymerization of microtubules is drivenby the binding, hydrolysis and exchange of a guanine nucleotide on the -tubulinmonomer (GTP bound to tubulin is non-exchangeable and is never hydrolysed).GTP hydrolysis is not required for microtubule assembly per se but is necessary forswitching between catastrophe and rescue. (Adapted by permission from MacmillanPublishers Ltd: Nature Reviews Molecular Cell Biology, Anna Akhmanova andMichel O. Steinmetz. Tracking the ends: a dynamic protein network controls thefate of microtubule tips, 9(4):309322, 2008)[52]
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Figure 1-2. Structure of Dynactin molecule.The p150glued arm has sites for attachment for microtubules as well as motors likedynein and heterotrimeric kinesin-2. The Arp1 rod provides binding for coupling ofthe complex with various cargoes,membranes, etc . We hypothesize that dynactinability to attach to immobile elements allows dynein to spend longer duration in itsstalled state. The Figure was taken from
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CHAPTER 2MODELING AND SIMULATION METHODS
The objective of this work is to investigate the effect of motor forces on microtubule. In
Chapter 3, we show how microtubule bends illustrated in Figure 3-2 can result from motor
activity while in Chapter 4 we investigate how these forces can affect growing microtubules.
2.1 Model for Microtubule
A microtubule is modeled as infinitely thin linear object that is expected to behave like an
elastic, non-extensible rod. Typically a thin rod of finite thickness has 6 degrees of freedom.
Assuming the rod to be infinitely thin allows us to remove 2 degrees of freedom pertaining
to shear within the rod body and 1 degree of freedom pertaining to twisting motion. In most
experiments we observed the inplane motion of microtubule. As a result, we can neglect
out of plane bending of the microtubule. Thus, for our model we have 2 degrees of freedom
corresponding to the in-plane bending of the microtubule and motion of points along the
tangent direction due to compression/extensional forces, which is kept small by selecting a high
extensional modulus to mimic the non-extensible rod. The first step in the simulation is to
initialize the input shape which is described in the section below.
2.1.1 Discretization of Microtubule Shape
The initial microtubule shape is represented by N + 1 equidistant nodal points, mi where,
i = [0, 1, · · ·,N]. The distance between nodal points, referred to as segment length h and is
calculated as,
h =L
N + 1 + 0.5α(2–1)
where, the paramater α is the function of boundary conditions. The parameter α is given by,
α = O1 +O2 − 2 (2–2)
where, O1 and O2 determine the offsets that best account for boundary condition at the plus
and the minus end of the filament respectively. For instance, O1 is equal to 1, 0, -2 for free,
hinged and clamped boundary conditions respectively which is based on 2nd order convergence
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of shapes and forces. The expected segment length h is determined during the initialization
step and we keep h constant for the rest of the entire simulation duration.
If the input shape is specified using a discrete set of co-ordinates (xinput , yinput) (not
necessarily equally spaced), we fix the origin at the minus end of the filament and orient it
along the x-axis. Cubic splines were used to store these co-ordinates as the function of s which
is the distance along the filament arc. The set of co-ordinates that defines the discretized input
shape are generated by reverse mapping at the points si along the microtubule contour.
si = (i + 0.5O1)h, i = [0, 1, 2, .., ·N]. (2–3)
Note that for a clamped boundary condition, s0 takes the value of -1 and the corresponding
co-ordinates are set to (−h, 0). This is shown in figure 2-1A This marks the completion of
the initialization step and we are ready to begin the simulation. The position vectors for mi
are denoted as ri . The bond vectors ri+1 − ri are denoted as ri ,i+1. Usually microtubule has N
segments including the ones that are part of the boundary condition. However when boundary
condition is free at both ends there are N + 1 segments.
2.1.2 Dynamic Instability
Microtubule length can change due to polymerization or depolymerization at the plus
end which differentiates one end from the other.The co-ordinate of the microtubule’s plus
end is mn. The instantaneous length of the microtubule Lt+δt is tracked independently and is
the updated at the end of each simulation step. For instance, for a microtubule undergoing
polymerization with velocity vpol ,
Lt+δt = Lt + vpolδt (2–4)
Additional nodal points are added or subtracted from plus end if,
|Lt+δt − Lt | >h
2. (2–5)
The co-ordinates for new nodal point/s are obtained by extrapolating past mn in
increments of h along the along rN−1,N which represents the direction of the tip. There is
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a provision in the model for switching a polymerizing state to a depolymerizing one, with
probabilities derived form the rates of switching from polymerization to depolymerization
(catastrophe) and back again (recovery).
2.1.3 Internal Forces
The cellular environment is viscous and the inertial forces on the microtubule are
insignificant [53]. Internal forces arise the deviation of the microtubule shape from its stress
free state and the magnitude can be estimated from the resulting strain. The stresses in the
rod are assumed to be linear in the deviations in the strain fields. Note that the resulting stress
associated with extension Γ (s) and due to bending Ω(s) are independent, which is shown in
Figure 2-2. The symbol s is the distance along the filament arc. Thus the internal energy U
for the microtubule can be written as,
U = UΓ + UΩ. (2–6)
The extensional strain energy within the elastic filament of length L is given by line integral of
the strain within the filament.
UΓ =E
2
∫ L
0
Γ 2(s)ds, (2–7)
where, E is the extensional modulus of elasticity per micrometer. This equation can be written
in terms of position vectors for a discretized filament of segment length h,
UΓ =
N−1∑i=0
E
2
1
h
√(ri+1 − ri).(ri+1 − ri)− h)2. (2–8)
The corresponding force on each nodal point can be obtained by differentiating the above
equation,
F Γi = −∂UΓ
∂ ri. (2–9)
Note that every term except for the end points will have two terms, because they have they
have two neighbors.
20
The bending strain energy in a bent elastic filament of length L in absence of an external
couple can be written as a line integral of mean-square curvature [54].
UΩ =B
2
∫ L
0
C 2(s)ds (2–10)
where B is flexural rigidity per micrometer. The flexural rigidity B = EI , where I is the
moment of inertia along the filament axis. The equation can be discretized for a filament
composed of N equal segments of length h [55, 56].
UΩ =Bh
2
1
h2
N−1∑1
C 2
i . (2–11)
The curvature Ci is related to the angle between the adjacent segments and is given by
the formula,
C 2
i = 2(ri−1,i .ri−1,i − ri−1,i .ri ,i+1)/h4 (2–12)
The discrete approximation of UΩ can then be differentiated to find the elastic bending
force on each nodal point of the filament.
FΩi = −∂UΩ
∂ ri(2–13)
2.2 Model for Motor Forces
The motor body consists of 3 core structures, the cargo binding domain which connects
the motor to the cargo, the microtuble binding domain through which motor binds to a
microtubule segment and the linker domain which connects these two domains. A typical
microtubule-motor interaction can be broken down into 3 events. First, a motor binds to a
microtubule then it walks along the microtubule and at some point in time it unbinds. During
this interaction period, motor exerts force on the microtubule. For instance, consider the cargo
binding domain of a motor anchored to a relatively immobile surface like nucleus. As the motor
walks along the microtubule the force within the linkage increases and begins to exert tension.
This force is transferred to cargo end and the microtubule via linakge. In order to estimate the
motor force, we considered two different motor models in this work. In Chapter 3, we used the
21
model[11, 57] for dynein motors which computes the force exerted by a motor averaged over
all binding times. This is what we call as a continuous motor model. While in Chapter 4, we
simulated individual motors to determine to compute the motor force. This model is referred to
as a discrete motor model.
2.2.1 Continuous Motor Force Model for Dynein Forces
The speed of a dynein motor v−m attached to a microtubule under a linkage force f is [58],
v−m
v−max
= 1− t .f
f −max
(2–14)
where, v−max is the speed of the motor in a stress free state, f −max is the magnitude of the force
in the linkage along tangential direction when motor cannot walk any further which is known as
stall force and t is the unit tangent vector along the microtubule and directed towards the plus
end. Note that as t .f → f −max , vm → 0. The force on the linkage increases as dynein translates
with velocity vm inducing tension, where
vm = v−m (−t) (2–15)
We modeled the linkage as a spring with stiffness κ. If microtubule segment to which motor is
attached moves with a velocity v relative to the anchor point, the net rate of increase in the
linkage force is,
df
dt= −κ(v + vm), (2–16)
Substituting vm from Eq. 2–14 into Eq. 2–16,
df
dt= −κv + κv−
max t − κv−max(
t .f
f −max
)t (2–17)
Note that the equation needs to be integrated separately in the tangential and the normal
direction as the variable on the LHS is f while on the RHS is t .f . Assuming that linkage is in a
stress free state when motor binds to microtubule i.e. f (0) = 0, the time-dependent force f (t)
22
from a single motor obtained by integrating Eq. 2–17 is,
f (t) = f −max(1−v .t
v−max
)(1− e−t/τ )t − κv .(1− t t)t (2–18)
Linkages are assumed to dissociate with a first order rate constant ko (s−1)such that the
probability of a linkage existing at time t after its attachment,
Pb(t) = e−ko t . (2–19)
The mean force over the bond lifetime η is,
< f >=
∫ ∞
0
f (η)dPb(η) = f0(1−t.v
v−max
)t − κ
ko(1− t t)v (2–20)
where 1 denotes the unit tensor,
f0 = f −max/(f −maxko
κv−max
+ 1) (2–21)
is the average tangential force exerted by a dynein molecule on a stationary microtubule.
The expression for force per unit length exerted by dynein motors on the microtubule can be
obtained by multiplying eq. 2–20 with the dynein density per unit length, ρ.
K = ρf0(1−t.v
v−max
)t − ρκ
ko(1− t t)v (2–22)
Eq. 2–22 can be rewritten as,
K = ρf0t − ξ∥(v .t )t − ξ⊥(v .n)n (2–23)
where n is the unit normal vector. The coefficients ξ∥ and ξ⊥ represent the friction coefficients
in tangential and normal direction which resist the microtubule motion and are given by,
ξ∥ =ρf0vmax
(2–24)
ξ∥ =ρκ
ko(2–25)
23
The frictional nature arises from the transient nature of the linkages and is well known as
protein friction. The velocity of microtubule v can be obtained by solving the equation of
motion which is described in subsequent sections. We used this model to study small length
scale high amplitude transient bends observed in the area under the nucleus.
2.2.2 Discrete Motor Force Model for Dynein and Kinesin Forces
We model two families of microtubule motors that are likely to generate force on growing
microtubules. Motors that walk towards the minus end represent cytoplasmic dynein and the
ones that walk towards the plus end collectively represent members from kinesin family. Both
motor families operate similarly with individual set of specified parameters listed in Table XX.
Motor forces are included as linkages distributed along the length of the microtubule, as
shown in Figure 2-4. The linkages are modeled as springs with stiffness κ.
2.2.2.1 Initialization and termination of motors
We imagine that a particular segment of the microtubule is occasionally captured by a
motor attached to the background cytoskeleton and is bound for the times of the order of ko
where we take the motor off-rate to be of the order of 1 s−1 [57] for both motors. A motor
appears on a segment length h in a time step δt with a probability,
p = nmh ∗ (1− e−ko δt) (2–26)
where, nm is the combined linear density of both motor families. The number of motors Nb
that appear on the microtubule of length Lt at time t during the time step δt is determined by
drawing a sample from Possion distribution with mean µ = p ∗ Lt/h,
Nb = ⌊P(µ)⌋ (2–27)
Note that this also adds variability to number of motors that appear during every simulation
step. The initial assignment of parameters for each motor includes the position along the
microtubule contour Si(0), the microtubule-cytomatrix linkage bi(0) and the motor type
identifier Idxi . If Idxi = −1 then the motor then the motor is classified as dynein, if Idxi = +1
24
then the motor is classified as kinesin. The value is assigned using a random number X where,
X ∼ U[0, 1), (2–28)
via the formula,
Idxi = 2
⌊1− (nm − n+)
nm+ X
⌋− 1, (2–29)
where n+ is the density of the kinesin motors. Note that the resulting distribution is skewed
by the factor (nm − n+)/nm to obtain the desired motor densities. On average the binding
and unbinding rates will balance at the desired motor densities if each bound motor unbinds
with a probability (1 − e−ko δt). On an average it takes 1-2 seconds to saturate the long
initialized microtubule shape after the simulation begins. For instance, if relaxation of a
microtubule shape needs to be observed, the background friction is assigned a high value 100
Pa.S to keep the shape intact during this period saturation period. The position vector for a
motor xi(t = 0) is determined by interpolating the nodal vectors for the microtubule rj , rj+1
corresponding to Si(0). The initial distribution of directions of the linkage is isotropic. The
position vector for anchor point is initialized as, ai(0) = xi + bi(0). We model linkages as
springs with stiffness κ and assume that during the time of attachment the linkage is in a
stress-free state with rest linkage length lm.
|bi(0)| = lm (2–30)
κ and lm are kept identical for both motors for the sake of simplicity.
Motors are added and removed during the before executing the equation of motion during
each simulation step. Motors located on the microtubule in the previous step are assigned a
random number X which is then compared with unbinding probability 1 − e−ko δt . The motor
stays on the microtubule for the next simulation step if,
X > 1− e−ko δt (2–31)
25
Motors are also removed if they walk off the microtubule i.e,
Si(t) /∈ [0,Lt ] (2–32)
The motor model resembles that proposed by Nedelec and Foethke [59] The major
difference lies in our implementation where the motors only exist while they are bound to the
microtubule instead of being permanently bound to random positions in the cytoskeleton at all
times.
2.2.2.2 Linkage based force generation
A dynein motor walks towards the minus end with velocity vm,i 2–15 until the force within
the linkage reaches stall force or it unbinds. The equivalent expression for kinesin motors is,
vm,i = (v+max(1 +t.fif +max
))t (2–33)
where,f +max and v+max represent the stall force and stress free motor speed for kinesin motors.
Force can develop in the linkage due to change in position vector of the motor (point of motor
attachment to microtubule) and due to motion of anchor points. The position vector of motor
changes due its motion along the microtubule and the motion of microtubule itself.
xi(0) = xi(t) +
∫ t
0
(v+m,i + v)t (2–34)
The motor position Si(t) is updated in increments of vm,iδt at the end of every simulation
step corresponding to a small time δt and the position vectors are determined by interpolating
from the neighboring nodes. The velocity of the segment is found by interpolating the nodal
velocities which described in the next section. The position vector of the anchor points are
updated at the end of every simulation step,
ai(t + δt) = va,iδt + ai(t) (2–35)
where va,i is the velocity motor anchor points. This is added to model the motion background
cytoskelton which can result from actomyosin contractions within the cytoskeleton,retrograde
26
actin flow,etc. Note that va,i is significantly smaller than free motor velocity of myosin motors
because the cross linked network is expected to move slower than individual motors. In order to
compute the nodal velocities we need to compute the force exerted by the motor linkage/s on
the microtuble nodes. The force fi based on the extension in a linkage bi(t), where
bi(t) = ai(t)− xi(t) (2–36)
is
fi = max
(κ
(1− |bi0|
|bit|
), bi(t), 0
)(2–37)
This modification to the force eq. 2–37 is made to avoid motor exerting compressive elastic
force during initial stages of the walk due to its initial orientation see Figure 2-3. Such a state
is short lived and the motor will eventually walk to a position such that |bit| > |bi0|. This
is because one would expect the linear chains to buckle rather than compress under those
circumstances.
2.2.3 Background Friction
A substantial amount of background friction was observed by Wu et. al. [11] in cells
despite inhibiting dynein. This can possibly come from kinesins or other proteins that interact
with microtubules in cells. Wu et. al [11] observed straightening of microtubule near minus
end on laser ablation in dynein inhibited cells. However, this interaction is complicated by the
fact that tangential pulling from kinesin can straightens microtubules at the minus end despite
of lateral protein friction arising from linkages. As a result, we used the value of 10 Pa.S as
background friction which is lower than motor friction.
2.2.4 Pinning Points
Pinning points model the immobile sections observed in experiments listed in Chapter
3. The microtubule node closer the to the location of pinning point/s along the microtubule
contour is assigned a zero velocity in order to mimic the effect of pinning in simulations. The
list of nodes are stored in the list Pl .
27
2.2.5 Equation of Motion
The force balance on the microtubule in the overdamped limit where hamiltonian H ≈
U(internal energy)
− ∂H
∂ rn+ nhK + γbgvnh = 0; (vn = 0 for vn ∈ Pl , ) (2–38)
where K is the total motor force which takes nature of viscosity in continuous motor model
and γbg is the background friction. We do not require background friction in continuous motor
model because we get nodal velocity terms in the expression for average motor force. However,
we require in case of discrete motors. The difference in relaxation is insignificant because
typically motor friction is significantly higher in the magnitude.
28
The minus end has a clamped boundary condition i.e. the v0 and v1= 0. The plus end has
free boundary condition.
Figure 2-1. Stresses within the microtubule.A) A microtubule filament of length 0.15µm represented by 3 model points forvarious boundary conditions. The solid blue line represents the free filament lengthwhile the red dots represent the model points that model that free length by takingboundary condition into consideration. The blue line is not the part of freemicrotubule length. We do not use the model point that is not the part of freelength for estimating the properties of microtubule. B) The figure illustrates theprocess of adding nodal points for the polymerizing at 0.4µm.−1. Additional nodalpoints are added when the actual microtubule length and the representedmicrotubule length is more than half the segment length. The solid blue lineindicates the section of microtubule that constitutes the free length of themicrotubule.
29
Figure 2-2. Stresses within the microtubule.A) The figure shows the filament with no strains. The bond length for vectorsr0,1andr1,2 is equal to the segment length h. As a result, there is extenional strainwithin the microtubule. The bond vectors are parallel to one another as result thecurvature C = 0. Thus there is no bending strain this configuration. B) Thebond-vectors deviate from its rest length as a result there is extensional strainenergy associated with the configuration. Since, C = 0 there is no bending strainwithin the filament. C) The filament has no extensional strain but it has non-zerobending strain as the adjacent bond vectors are not parallel to one another.
30
Figure 2-3. Initial motor configuration leads to a shortlived compressive stress..The minus end is on the left and and + end is on the right which are marked intop most figure. A typical dynein linkage with a plausible initial configuration isshown here. Initially motors appears on the microtubule in a stress free state attime t=0 shown by the green color for the linkage. A plus end directed motorundergoes a shortlived state where the linkage is under compression due to itsinitial configuration. Motor does not produce any force on microtubule during thisstate because we assume that linkage chains would rather buckle and the resultingforce would be small. At time t=0.3 s motor linkage is under extension indicatedby red color. The motor is exerting some force on microtubule at this time.
31
CHAPTER 3A MECHANISM FOR BENDING MICROTUBULES
3.1 Background Information
Microtubules play critical roles in cell functions such as mitosis, intracellular transport, and
motility. They are the most rigid of the three cytoskeletal elements (microtubules, intermediate
filaments, and F-actin [53], and isolated microtubules are straight over length scales of
millimeters [1]. Microtubules can buckle by polymerizing against obstacles [4, 26, 31], and
their bent appearance in cells [6, 60, 61] is suggestive of a mechanical role in which they bear
compressive loads [62, 63]. In this way, microtubules may help stabilize and maintain cell shape
[64, 65].
However, microtubule bending does not only derive from polymerization against a barrier,
because local bends also develop when the tips are polymerizing freely. By freely polymerizing,
we mean that the microtubule tip moves to accommodate the additional length, which is
distinct from the situation when the polymerizing tip is immobilized by the cell periphery or
other obstacle. Moreover, polymerization forces cannot explain wavy microtubule growth from
the centrosome, which is observed in tip-tracking experiments [8, 66]. Bicek et al. [3] have
hypothesized that tangential forces generated by molecular motors can bend a microtubule by
transporting portions of it (referred to as segments from now on) toward an immobile point
on its contour. However, such pinning points have not been observed during the bending of
freely growing microtubules, nor have the motors that might push the segments towards these
pinning points been identified.
In vitro experiments with reconstituted microtubules have shown the feasibility of
microtubule bend formation due to the activity of myosin motors [5]; retrograde flow of
0 Reprinted under the Creative Commons Attribution (CC BY) license(http://creativecommons.org/licenses/by/4.0/) with changes to formatting from: KentIA, Rane PS, Dickinson RB, Ladd AJ, & Lele TP (2016) Transient Pinning and Pulling: AMechanism for Bending Microtubules. PLoS One 11(3):e0151322. Ian Kent and Tanmay Leleare credited with experiments.
32
actomyosin can also cause microtubule buckling [67, 68]. However, Bicek et al. [3] have
argued against a role for actomyosin contraction in driving anterograde flow of microtubule
bends, at least in LLC-PK1 epithelial cells [3]. Microtubule motors like kinesin [69] may
drive microtubule bending but others have suggested that dynein is the dominant motor
pulling along microtubule lengths [3, 11]. Thus the mechanisms for bend formation away
from the cell periphery remain unclear. Forces generated by dynein, kinesin, and actomyosin
suggest different outcomes for the direction of microtubule-segment transport during the
development of a bend. Dynein would be expected to translate segments from the minus end
to the plus end, while kinesin would translate segments from the plus end to the minus end
[3, 11]. Actomyosin contraction would bring in segments from both minus and plus ends. We
hypothesized that determining the predominant direction of microtubule motion during bend
formation, specifically the frequency of bends created by minus-end directed versus plus-end
directed transport, could help identify the motors and mechanisms responsible for the shapes of
microtubules in cells.
To detect the direction of transport of microtubule segments, photobleaching was used
to create fiduciary markers along the microtubule length (all experiments listed in this thesis
were performed by Dr. Ian Kent in the Lele laboratory), which could then be used to follow
individual segments as they reptate along the microtubule contour. We tracked the positions of
these markers in LLCPK-1 cells, porcine kidney epithelial cells stably expressing GFP--tubulin.
We observed that bends form primarily by plus-end directed transport of microtubule segments
toward stationary segments along the microtubule. These pinning points were found to be
transient, with a typical lifetime of less than 1 minute. When the pinning points released, the
stationary segments started to move and the bends relaxed. Dynein inhibition eliminated the
directional bias of microtubule transport and reduced the incidence of bend formation. We
propose a model based on these observations, which involves dynein motor forces pushing
segments towards a point. Simulations of the development of microtubule bends correlate well
33
with experimentally observed shapes and time scales. The model explains how bends forming
near a growing microtubule tip can cause changes in direction of the growing microtubule.
3.2 Equation of Motion and and Selection of Model Parameters
The detailed derivation for dynein mediated forces used in this section is included in
Chapter 2,2.2.1 [11, 57]. The force exerted by dynein per K is given by,
K = ρf0(1−t.v
v−max
)t − ρκ
ko(1− t t)v (3–1)
where v is the velocity of the segment the motor is bound to, t is the local tangent to the
microtubule contour, and 1 denotes the unit tensor. There are three parameters in this model
(Table 3-1): the maximum pulling (or stall) force of the motor f −max , the velocity of a force-free
dynein motor walking along the microtubule v−max , and the lateral friction from motor binding
and unbinding γ. Two of these parameters have established values in the literature: f −max = 8
pN and v−max = 0.8 µms−1 [58, 70]. The motor friction for nuclear-bound dynein motors, γ =
56 pNsµm−1 was determined by fitting to data on nuclear rotation rates [57]. Note that the
dynamics of bend relaxation in this model do not change significantly if we neglect background
friction as motor friction is substantially higher in the magnitude.
Microtubule dynamics was simulated by incorporating the model for dynein forces with
a standard model for the bending of an elastic filament [55, 56]. The details for estimating
internal forces can be found in in Chapter 2 2.1 In the over-damped limit, the model point
velocities vi are obtained from the balance between elastic and motor forces:
− ∂H
∂ ri+ nhKi = 0 (3–2)
where Ki is the motor force on model point mi , and n is the density of cytoskeletal-bound
dynein motors; as in previous work [11, 57], we take n = 2µm−1.
34
3.3 Result
3.3.1 Microtubules Bend against Transiently Immobilized Segments
Microtubules commonly form local bends, even when the microtubule plus end is freely
polymerizing (Figure 3-1A). Thus, polymerization against an obstruction such as the cell
membrane is not necessary for formation of local bends. The bends have a characteristic oxbow
shape in which the curvature changes sign twice. We observed the direction of tangential
motion of microtubules during bend formation by photo-bleaching fiduciary markers onto
microtubules under the nucleus. Before photobleaching fiduciary markers, cells were imaged to
select growing microtubules. This procedure allowed for an unambiguous identification of the
growing plus end, because free minus ends never polymerize in cells [61, 71–75]. The nuclear
region was selected because it offered a dark background against which the microtubules were
clearly visible and was far from the cell periphery (Materials and Methods and Figure 3-1B).
During bend formation, the bleached microtubule segments were consistently observed to
transport towards the bend from only one side (kymograph in Figure 3-1C), while remaining
stationary on the other side. Hence, translation of the microtubule towards a stationary region,
or pinning point, appeared to be a consistent characteristic of local bend formation. After some
time the bend relaxed, either through motion of the pinning point (Figure 3-1C) or motion of
the bend while the pinning point itself remained stationary (Figure 3-1D).
Having established that tangential motion toward stationary segments produces bends
in microtubules, we counted the frequency of bends formed by translation toward the plus
end and by translation toward the minus end. The majority of bends under the nucleus
(87.54.8%SE) were formed by translation of microtubule length from the minus end rather
than from the plus end (Figure 3-1E). This argues against kinesin and myosin as dominant
drivers of local bend formation in these cells and supports the hypothesis that dynein is
involved in bend formation. It also implies that the additional microtubule length required to
form bends does not come from plus-end polymerization.
35
3.3.2 Dynein, but not Myosin is Involved in Formation of Local Bends underNucleus
To determine whether dynein is involved in local bend formation under the nucleus,
we inhibited dynein activity by over-expression of the fluorescently tagged CC1 domain of
p150 (Glued), which is the dynein-binding domain of the dynactin complex [11, 47, 76–
79]. Inhibition of dynein activity was validated by dispersion of the Golgi apparatus (S1
Fig). In cells expressing DsRed-CC1, the percentage of bends caused by translation of the
microtubule from the minus end was reduced significantly, to 55.2 9.2% (2 = 10.16, p =
0.001; Figure 3-1E). Therefore, the bias in the direction of microtubule translation is due to
dynein force generation. Inhibiting myosin activity by treating cells with Y-27632, a Rho kinase
inhibitor [80], had no effect on the directional bias of microtubule translation (Figure 3-1E),
in agreement with previously reported results in this cell type that argue against a role for
actomyosin contraction in bend formation [3].
To determine the effect of dynein inhibition on the probability of bend formation, the area
under the nucleus was bleached, and microtubules growing back into the area were observed
over 3 minutes. New segments of microtubule that polymerized to a length of at least 5 m
under the nucleus over the observation period exhibited a reduced frequency of bend formation
in dynein-inhibited cells compared to control cells, from 36.5 3.7% in control to 17.9 4.7%
in CC1-expressing cells (2 = 7.72; p = 0.005; Figure 3-1F). This result adds support to the
idea that dynein is acting to form bends from translation of microtubule segments from the
minus end rather than to inhibit bend formation from translation of segments from the plus
end. Inhibiting dynein not only equalized the probability of bending in the anterograde and
retrograde directions, but also decreased the overall probability that a microtubule will bend.
On the other hand, treating cells with Y-27 to disrupt myosin contractility did not decrease the
frequency of bend formation, consistent with myosin activity not being a major cause of local
bending (Figure 3-1F).
36
3.3.3 A Mechanism for Microtubule Bend Formation by Dynein-mediated Transporttowards a Pinning Point
We applied a mathematical model [11, 57] for dynein force generation on microtubules
(Figure 3-2A) to explain bend formation near a pinning point. In this model, an ensemble of
dynein motors linking the microtubule to the surrounding cytoplasmic structures [11] or to the
nucleus [57] exert a tangential force directed towards the plus end of the microtubule. The
microtubule is modeled as an elastic filament subjected to tangential pulling forces from the
dynein motors, and a lateral viscous force due to protein friction arising from transient dynein
linkages [11].Figure 3-2B shows results of a simulation in which the microtubule is pinned
at the minus end (green circle) and also pinned (red circle) at a significant distance (8µm)
from the free plus end. This configuration represents a centrosome-bound microtubule with
a (transient) pinning point at a distance from the growing tip. The microtubule to the right
of the purple line represents the region lying within the field of view of the microscope. We
assume there must be sufficient curvature to provide the necessary excess length (the difference
between the contour length of the microtubule and the linear distance between the endpoints)
to form a bend, since the minus end is anchored at the centrosome and microtubules are
essentially inextensible.
Initially (t = 0), the microtubule in view appears straight, but as tangential dynein forces
drive the excess length into the region of view, a bend begins to form near the pinning point
(Figure 3-2B ). Using the estimated motor friction for nuclear-bound dynein [57] simulations
predict that bends are formed in about 5-10 s, which is consistent with the timescales of the
experimental observations.
Simulations support the conclusion that bends are formed when the transport of excess
length by dynein from the minus end direction is halted by stationary (pinned) segments. The
resulting bend shapes depend on the amount of excess length, but are insensitive to the shape
of the microtubule segments acting as the source of excess length (i.e. the region to the left of
37
the field of view in Figure 3-2B ). Typical microtubule bends arising from various excess lengths
are shown in Figure 3-2C; these are similar to shapes observed experimentally (Figure 3-2E).
Microtubule bends formed in the simulations are not static but undergo limit cycles
consisting of slow oscillations between different bend orientations (Figure 3-2D). The cycle
time varies inversely with excess length; from tens of seconds for large excess lengths (> 3µm)
to several minutes for small excess lengths (< 1µm). Although bends in experiments were
sometimes observed to change orientation, we did not observe limit cycles with multiple periods
because pinning points were too short-lived.
3.3.4 Bending near the Microtubule Plus End Tip Leads to Tip Rotation
When local bends form far from the microtubule tip, the shape changes did not propagate
very far from the bend. For example, Figure 3-3A shows a typical experiment when a bend
formed far from the tip. The bend formed and relaxed over a period of about 25 s, but the
microtubule shape and position on either side of the bend remained nearly the same, and the
initial shape was restored after the bend relaxed. However, when a bend formed near the tip
of a growing microtubule (Figure 3-3B), the direction of polymerization changed and the new
direction persisted even after the bend relaxed.
Bend formation generates a bending moment at the pinning point, as illustrated in Figure
3-4A. When the segment on the plus-end side of the pinning point is sufficiently short, the
resulting moment causes the tip to rotate to a new direction for subsequent growth. However,
when the segment is long, the large lateral friction prevents rotation and the initial orientation
is preserved. These qualitative insights are confirmed by numerical simulations, illustrated in
Figure 3-3C and Figure 3-3D, where the motion of growing microtubules with either a long or a
short segment past the pinning point were tracked through a cycle of pinning and release. The
time evolution of the microtubule shape and tip orientation closely resembles the corresponding
dynamics observed experimentally. The microtubule pinned far from the tip (Figure 3-3C)
continues growing in the same direction after release, whereas the one pinned near the tip
changes its direction of growth. Thus, our model for dynein force generation accounts for the
38
observed correlation between the formation of bends and a sharp change in the direction of a
growing microtubule tip; furthermore it explains why the bend must be close to the growing tip
in order to cause a change of direction.
We repeated the simulations shown in Figure 3-3C and Figure 3-3D with different
segment lengths between the pinning point and the tip, which we refer to as the overhang.
The resulting tip orientations are plotted versus time in Figure 3-4B. When the distance
between the pinning point and the tip is small (blue line) the tip rotates rapidly as the bend
forms. However, after pinning, the overhang acquires additional frictional resistance because of
polymerization, which opposes the relaxation in orientation after the pinning point is released.
This leads to a substantial rotation of the tip, even 25 s or more after the pinning point is
released, but when the pinning is more than about 1 µm from the microtubule tip (green and
red lines), there is no significant change of direction.
When the overhang is small (< 1µm), microtubule polymerization contributes significantly
to the net rotation of the tip. In Figure 3-4C the rotation of the tip of non-polymerizing
microtubules is shown. Here the short (0.5µm) overhang rotates rapidly after pinning, but
when the bend relaxes it tends to return to its initial direction because the friction remains
small. The longer (1.5µm) overhang now rotates significantly (because its friction remains
constant during bend formation) but it also relaxes once the pinning point it released, although
more slowly than the 0.5µm overhang. The longest overhang has sufficient friction that it
scarcely rotates, even when the tip is not growing.
3.4 Discussion
Polymerization forces from a growing microtubule can cause compressive buckling
if the tip is pinned at the cell periphery, but it is difficult to see how this mechanism can
generate local bends far from the tip or how they can propagate back from the periphery. In
addition, such a model cannot explain how local bends form when the microtubule tips are
free. However, tangential force generation by molecular motors can transport curved segments
towards any stationary point (including the cell periphery). In this paper we focused on bends
39
that develop under the nucleus, where individual microtubules could be easily seen and where
they were far from the cell periphery. Tracking of fiduciary markers along the microtubule
length showed that transport of length during the formation of a bend occurs primarily from
the minus-end direction; the bend develops because excess length is transported toward pinned
microtubule segments; and dynein activity increases the frequency of bend formation and helps
drive excess length preferentially from the minus end. Simulations that account for dynein
activity and microtubule mechanics correctly predict the observed shapes and time scales of
bend formation, supporting our physical explanation for how dynein generates local bends in
microtubules. Dynein activity also explains previously reported transport of microtubule bends
toward the cell periphery [3].
While bends occur primarily by translation of microtubule segments from the minus
end direction, in a small but significant fraction of the observed bend formations, the bends
developed by transport from the plus end direction. In dynein-inhibited cells, the overall
frequency of bending decreased and the probability of bending in either direction was equalized.
This suggests that other mechanisms exist by which microtubule bends can form, potentially
including kinesin motoring [69] and actomyosin contraction [4, 5].While we do not rule out
these other mechanisms contributing to the bending, the primary mechanism in LLC-PK1 cells
appears to be dynein mediated forces.
Our simulations show that tangential forces pushing mobile microtubule segments against
stationary pinning points are mechanically sufficient to give rise to the bends observed in
experiments. The time scale of bend formation depends on the lateral friction from transient
motor linkages. The fact that the timescales of bend formation can be predicted with the same
motor parameters that were estimated from a separate study on nuclear rotation [57] increases
our confidence in the proposed model.
Microtubules in cells do not grow in straight lines [66]. In previous experiments, we have
shown that the waviness in microtubule growth is primarily due to dynein activity [8]. Tip
rotation due to bend formation may be a means whereby a growing microtubule amplifies
40
existing excess length through a succession of pinning and unpinning events. A pinning event
near the tip, together with bend formation, causes a change in the direction of growth and
therefore generates additional excess length because the microtubule is following a wavier path.
This would appear as random fluctuations in a tip-tracking experiment, because the developing
bend behind the tip remains unobserved. We note that this mechanism requires preexisting
excess length, but its origin remains unclear because microtubules can grow along wavy paths
even when dynein, myosin, or kinesin are inhibited [8].
In summary, the experimental results and simulations presented here support the existence
of two related mechanisms of microtubule bending by dynein: bend formation near pinning
points and resulting reorientation of the direction of polymerization. These findings continue to
point to the critical role of motor forces and protein friction in governing microtubule bending
dynamics in vivo.
41
Figure 3-1. Local bends develop by dynein-dependent translation of microtubule segments fromthe minus end. Figure description is on the next page.
42
(A) Image sequence shows bending of a freely growing microtubule, demonstrating thatpinning of the plus end is not required for bends to develop. (B) Experimental Technique.Fluorescent microtubules under the cell nucleus are photobleached to allow for easier analysis ofindividual microtubules. Only newly polymerized segments of microtubules are fluorescent afterbleaching. Microtubule plus ends are identified by their polymerization, since minus ends donot polymerize in cells. Once new microtubules grow to a sufficient length, fiduciary markersare bleached onto them so we may observe the lengthwise translation of different regions alongtheir length. (C) The top panel shows a microtubule that polymerizes to the right over thecourse of 31 seconds and is bleached with a pattern of dashes at 66 seconds. A local bendthen forms (white frames in bottom panel). During development of the bend, the minus end(left) side of the microtubule moves towards the plus end, and buckles against a stationarymicrotubule region, indicating pinning. The local bend then maintains its shape for some time(yellow frame) before relaxing. Bend relaxation (cyan frames) occurs by movement of thepreviously stationary right side toward the plus end, indicating unpinning of the microtubule,while the left side is stationary. Vertical white lines are provided to help visualize the movementof fiduciary markers. A cartoon trace of the microtubules shape evolution is provided below,in which the pinning point is marked with an x and translation of different regions of themicrotubule during development and relaxation of the local bend is marked with red andcyan arrows, respectively. (D) The top panel shows that the microtubule polymerizes to theright over the course of 28 seconds and is then pattern bleached. A local bend develops bytranslation of the plus end (right) side of the microtubule toward the minus end, the oppositeof what occurs in C. Also different from the microtubule in C, the bend relaxes away fromthe pinning point (in this case back toward the plus end), with the pinning point stayingintact throughout. All colors and symbols are the same as in part C. (E) Plot showing thepercentage of bends that formed by microtubule translation towards the plus and minus ends incontrol (n = 48 bends from 21 cells), dynein inhibited (CC1; n = 29 bends from 16 cells), andmyosin-inhibited (Y-27; n = 45 bends from 18 cells) cells. Error bars indicate standard error.(F) Proportion of visible microtubules that bent in three minutes following photobleaching ofthe area under the nucleus in control (n = 167 microtubules from 9 cells), dynein inhibited(CC1; n = 67 microtubules from 6 cells), and myosin-inhibited (Y-27; n = 83 microtubulesfrom 7 cells) cells. Error bars indicate standard error.
43
Figure 3-2. Simulations of dynein mediated bend formation in microtubules. Proceedto next page for figure description
44
A) The cartoon illustrates a model for the dynein-generated force on a microtubule. Anet tangential force is experienced by the microtubule due to collective motor activity. B)Simulated bend development by tangential forces using the model represented in A. Thered dot is the location of the pinning site, the green dot indicates the minus end of themicrotubule, and the blue dot is a point that marks the beginning of the microtubule segmentthat would be observed in a typical experiment. The magenta colored line marks initial positionof the blue dot. The figure shows microtubule translation due to cytoskeletal dynein motors.The excess length behind the blue marker translates into the viewing window by motor activity,leading to a pronounced bend on the minus side of the pinning point. The excess length isequal to the maximum displacement of the blue marker from its original position. C) Simulatedshapes from varying excess lengths, generated after 10 seconds. D) Snapshots of a segment ofa microtubule at different times, showing how different shapes can develop if the microtubuleis pinned for a long time (excess length of 2.5 µm). E) Microtubule shapes observed in livingcells.
45
Figure 3-3. Rotation of the microtubule tip due to local bend formation.A) Images show that the microtubule shape on either side of the bend remainedalmost the same, and the initial shape was ultimately restored after the bendrelaxed (initial and final shapes marked in red). B) An example of a microtubulethat changes direction of polymerization due to a local bend near the tip. Initiallythe filament is aligned at an angle of roughly 30 degrees to the horizontal (markedby red dash), but as soon as the bend starts to form, the tip starts to rotatetoward the horizontal direction. The plus end continues to grow as the benddevelops over the course of about three seconds. The bend relaxes after about 10seconds, but the tip keeps growing in the newly acquired direction (marked inyellow). C) Simulation of local bend formation when the pinning point is far fromthe tip (as in the experiment shown in panel A). The red dot indicates the pinningsite which is initially at a distance of 8 µm from the tip. A bend forms within thefirst 5 seconds, after which the pinning point is released. The segment on the plusside of the pinning point does not rotate because of the large lateral friction alongits length. As a result, the direction of microtubule growth remains unchanged. D)Local bend formation when the pinning point is close (0.5 µm) to the tip (as in theexperiment shown in panel B). The short microtubule segment to the plus side ofthe pinning point changes direction during bend formation, but microtubule growthduring the pinning event increases the lateral friction and prevents the tip relaxingback to its original direction after the pinning point is released. There is a netchange in the tip direction even after 30 seconds.
46
Figure 3-4. Effect of overhanging segment length on the rotation of the tip.A) The sketch shows how a local increase in curvature during bend formationdrives tip rotation. A local bend (a) generates a bending moment across thepinning point (b). Motion of the overhanging segment is opposed by friction, butgiven enough time, the tip rotates to straighten the segment (c). B) Orientation ofa growing microtubule tip as a function of time. The microtubule is initially pinnedat different distances from the tip: 0.5 µm (blue), 1.5 µm (green) and 2.5 µm(red) and unpinned after 15 seconds (black dot). C) Orientation of anon-polymerizing microtubule tip as a function of time. The microtubule is initiallypinned at different distances from the tip: 0.5 µm (blue), 1.5 µm (green) and 2.5µm (red) and unpinned after 15 seconds (black dot).
47
Table 3-1. Model Parameters: Microtubule and Dynein Motors
Parameter Symbol ValueModulus of Elasticity E 1.75 ∗ 104 pN.µm−2
Flexural Rigidity B 25 pN.µm2
Polymerization Velocity vpol 0.1µ.s−1
Number of motors ρ 2µ−1
Dynein Stall force f −max 8 pNDynein stress free speed vmax
− 8µm.s−1
Lateral friction coefficient γ 56 pN.s.µm−1
48
CHAPTER 4EXCESS LENGTH IN MICROTUBULES
4.1 Objective and Background Information
4.1.1 Objective
While Chapter 3 showed that microtubule bends develop by transport of contour length
of initially curved microtubules, it did not address the origin of this initial curved shape. Here
we explore how this contour length- the length which is ’excess’ over the shortest line segment
joining two end points on the microtubule- could arise. Quantifying this length in microtubules
from experimental images is a daunting task because microtubules frequently overlap with each
other and other structures, which makes it difficult to trace a complete microtubule in the cell.
Since, this question is not easily addressed experimentally, we chose to explore this question
with computations.
4.1.2 Background Information
As shown in the Chapter 3, microtubule segments are transported toward the plus end
of microtubules, which give rise to local, dynamic bends in the microtubule. Naturally, this
transport cannot occur if the microtubule is straight to begin with as microtubule behaves
like a non-extensible rod. We term the length along the curved microtubule contour which
is available for transport and results in local bends, ’excess’ length. Shekhar et al. [8] and
Brangwynne et al. [66] have previously shown that microtubules do not grow along straight
paths. Rather, as the microtubule tip moves outward from the centrosome due to microtubule
polymerization, it deviates from its initial trajectory. Shekhar et al. [8] quantified this deviation
by measuring the motion of the microtubule tips labeled with GFP-EB1 (green fluorescent
protein that labels End Binding protein-1). They plotted the tip trajectories such that
the initial orientation of all tip trajectories was along the positive x-axis. As expected, the
trajectories deviated from the x-axis, resulting in a plot like Figure 4-1.
As seen in Figure 4-1B, Shekhar et al. [8] further showed that inhibiting dynein reduced
the spread of the trajectories. They also reported that inhibiting myosin had only a modest
49
effect, while kinesin-1 inhibition did not affect the spread. These results implicated dynein as
the major motor protein involved in deviating microtubule tips from their original directions.
Yet, simulations of growing microtubules under dynein-forces tangential to the contour using a
model similar to the one in Chapter 3 do not predict such a spread. Rather dynein forces are
predicted to straighten out any curvature in the growing microtubules, because dynein pulls
toward the plus end which generates tension in the centrosome bound microtubules. This can
be seen in Figure 4-2.
To explain how dynein could potentially deviate tips from their straight path, Shekhar
et al. [8] explored the possibility that single dynein motors binding at random angles to the
microtubule contour could exert lateral (normal) force on it. In addition, the anchor point
to which the dynein is bound could move in a random direction due to local actomyosin
contraction in the cytoplasm [81], exerting further lateral forces on the microtubule.
This model successfully predicted the experimentally observed spread in tip trajectories
(more specifically the amplification of the spread by dynein) for anchor-point speeds that were
closer to lower end for myosin walking speeds as crosslinked cytoskelton is hypothesized to
move slower that individual motors pulling on it. While the previously proposed explanation [8]
is plausible, it suffers from the obvious weakness that it cannot explain the experimentally
observed variance of tip trajectories in dynein inhibited cells [8]. In these experiments,
dynein was inhibited by over expression of the CC1-domain (coiled coil 1) of dynactin, which
competitively binds to dynein and disengages it from the dynactin complex. Therefore, no
lateral force is expected due to dynein, yet there is a significant spread observed in microtubule
trajectories, far in excess of that expected by thermal forces. It would appear that a mechanism
separate from dynein operates in cells to impose deviations in tip growth. Another weakness
of the model by Shekhar et al. [8] is that there is no direct evidence that dynein anchor points
move and thereby exert lateral forces on microtubules.
50
4.2 Data Analysis Methods
4.2.1 Fourier Mode Analysis
Fourier mode analysis was performed to quantitatively investigate the extent of bending
in the simulated microtubules. Figure 4-1 shows that the ensemble of microtubules span into
a divergent V shape with the tip of V locate at origin. Keeping this geometry in mind we
characterized the shape of the microtubule as sum of sine waves of imaginary frequency. We
computed frequencies corresponding to quarter waves and the half waves.
θ(s) =
√2
L
∞∑n=1
ansin
(2πns
4L
)(4–1)
The shapes for sin waves are for n=1,2..7, are show shown in Figure 4-3 with a fix
amplitude A=0.25 units for demonstrative purpose. The amplitude for actual modes goes down
as n increases. From a set of N coordinates (xk , yk) of a trajectory, the length ∆sk and the
angles k for (N − 1) segments that connect these co-ordinates was calculated.
∆sk = [(xk+1 − xk)2 + (yk+1 − yk)
2]1
2 (4–2)
θk = tan−1[yk+1 − yk
xk+1 − xk
](4–3)
The amplitudes computed by taking the Fourier inverse of eq. 4–1,
an =
√2
L
N−1∑k=1
θk∆sksin(2πnsmid
k
L) (4–4)
where,
L =
N−1∑k=1
∆sk (4–5)
and
smidk = ∆s1 +∆s2 + ....∆sk−1 +
1
2∆sk (4–6)
4.2.2 Variance
Simulated trajectories are oriented along the x-axis to begin with. We recorded the
co-ordinates for the last node that represents the microtubule contour as the position of the
51
tip. Length dependent variance was estimated for the simulated tip trajectories at points along
the trajectory contour (s) corresponding to the ones reported experimentally. The variance is
computed as y(s)2.
4.3 Results
4.3.1 A Putative Role for Plus End Motors in Generating Excess Length
Recent literature suggests that kinesin can generate opposing forces to dynein, resulting in
a ’tug-of-war’ between the two motors [82–87]. The ’tug-of-war’ is commonly associated with
organelle transport. Here we expand this idea from the perspective of the force balance on the
microtubule and its consequence on deviation of microtubule tips and excess length within the
microtubule.
While Shekhar et al. [8] ruled out kinesin-1 as being involved in deviating tips, there are
other kinesins (such as kinesin-2) that they did not explore experimentally. We reasoned that
plus-end directed motors like those belonging to the kinesin family could potentially generate
tangential forces on interphase microtubules directed toward the minus end. It is intuitively
obvious that such forces could bend an initially straight microtubule anchored at its minus
end, and thereby introduce a curvature in the microtubule. A strong case can be made for
heterotrimeric kinesin-2 given its ability to bind to dynactin and its expression in the NIH3T3
cells used in experiments conducted by Shekhar et al. [8]. Dynactin is shown to be necessary
for dynein function.
We therefore performed computations of growing microtubules under the action of
plus-end directed motors. Microtubules were nucleated with a polymerization velocity of 0.4
µm.s−1 [8]. Motors were allowed to bind to the growing microtubule at random locations
and orientations consistent with a specified motor density (e.g. 1.5 µm−1), and allowed to
motor toward the plus end. Motor force was chosen to be 5 pN (similar to force generated by
heterotrimeric kinesin-2) [88]. Details for the model are listed in section 2.2.2 of Chapter 2.
Shown in Figure 4-4 are results of simulations first with + end motors alone (Figure
4-4B) and then with both + and - end motors (Figure 4-4C). In Figure 4-4B, we computed
52
variances in an ensemble of growing microtubules at different densities. As seen in Figure
4-4B, the computed variances compare reasonably well with experimental measurements of
variances of tip trajectories in dynein-inhibited cells (blue squares in Figure 4-4B). As + end
motors were able to produce the variance in dynein inhibited cells in the above calculations, we
next examined if the action of minus-ended motors could amplify this ’background’ variance
produced by plus-end motors. To do this, we performed simulations that incorporated both
plus-end and minus-end directed motors, and calculated the spread in tip trajectories. We
chose 1.5 µm−1 as the density for + end motors because it appeared to closely match the length-
depedent variance in dynein inhibited cells. As seen in Figure 4-4C, including both - end and + end
motors in the simulation adequately predicts variance in tip trajectories for a density of 3 µm−1 and
1.5 µm−1 respectively.
The deflection of the tip is influenced by motors binding close to the tip. This can be seen in
Figure 4-5 where individual motor bound near the tip is able to change the orientation of the tip.
We see that both plus and minus end motor are capable of deflecting tips.The length of
microtubule is kept short because another linkage would appear considering the combined linear
density on the actual microtubule that would offer resistance to motion. We can expect a slight
higher deflection as the resisting motor may act more like a hinge than a clamped boundary
condition for the microtubule here. We computed Fourier modes for an ensemble of 8 µm long
simulated microtubules (+ end motor density 1.5 µm−1) and compated it with the tip trajectories
in dynein inhibited cells. The fourier modes agree remarkably for this case which can be seen in
Figure 4-6A. Later we compared the Fourier modes for control cells with microtubules subjected to
+ and - end motors with density 1.5 and 3 µm−1 respectively. We did get find that 1st 3 modes
were in close agreement with experiment (see Figure 4-6B).
At this length microtubule shapes are fairly similar to their tip trajectories. Fourier modes
for simulated trajectories with + end motor density of 1.5 µm−1 agree remarkably with the
experiments. The case corresponding to control cells i.e with plus and minus end directed motors
were in agrement with the experiment. It is only in the case of longer microtubules
53
in kinesin only case (dynein inhibited case) they differ significantly because motor force from
kinesin alone tends to buckle the microtubules.
Additionally, we found that the mean polymerization speed estimated from tip trajectories
was lower in case where microtubules were sujected to plus end motors only in comparison
microtubules subjected to plus and minus end motors despite of the fact that the polymerization
velocities are identical in simulations seen in Figure 4-7. This is also reported in Shekhar et al.
This apparent lowering is observed because as microtubules become longer they tend to buckle
when only kinesin. As a result tip appears to move slower. It is a minor observation that this
model is able to explain based on the microtubule force balance.
4.4 Discussion
Here we presented a simulation study of a growing microtubule under forces generated
by stochastically binding plus and minus-ended motors binding along the length of the
microtubule. We showed that plus ended motors deflect the microtubule tip as it grows.
We tuned the parameters such that the variance of the growing tip is similar to experimental
measurements in dynein-inhibited cells. Addition of minus ended motors to the growing
microtubule amplified the variance, similar to experimental observations. By qualitative
comparison with experimental measurements of variance, we estimated the density of plus
ended motors at 1.5 µm−1m, and the density of minus-ended motors at 3 µm−1. The average
net force of 17.5 pN.µ−1
n+f+
max − n−f−max = 17.5pN.µm−1 (4–7)
toward the plus end. This force is consistent with the net force per micron of the microtubule
estimated in Wu et al.[11]. There, a force of 16 pNµm−1 was shown to predict the increased
bending of minus ended microtubule fragments that were created by laser severing. A force
of 16 pNµm−1 was also found necessary to predict the timescales of centrosome centering
[11]. This consistency in parameter estimates which were deduced from disparate experimental
observations- variance of growing tips, time scales of microtubule bending in laser severing
experiments, and centrosome centering time scales- increase our confidence in the model.
54
In the model, because motors bind stochastically, it can happen that parts of the
microtubule are under tension and parts of the microtubule are under compression as motors
work against each other. At the same time, we predict the average force on the microtubule
to be tensile with a magnitude of roughly 17.5 pNµm−1. Experiments that inhibit kinesin-2 or
other kinesin motors, and quantify the spread in microtubule trajectories will be necessary to
test our model. The list of all parameters can be found in Table 4-1.
The mechanism by which dynein amplifies the spread in microtubule tip trajectories
created by plus end motors is similar to that proposed by Sekhar et al. [8]. That is, the binding
of dynein at random angles and extensions and subsequent walking and finally stalling, exerts a
lateral force on the microtubule. This force ensures a spread despite the tendency for tangential
dynein forces to straighten out bends. Such a mechanism is able to explain the accumulation of
contour length in the microtubule as shown in Figure 4-8. The curved contour of microtubules
created by this mechanism results in occasional transport of curved lengths next to pinned
regions, which gives rise to dynamic bends in the microtubule as shown in Chapter 2. As
argued in Chapter 2, it is also possible that pinning by itself could give rise to a spread in
the microtubules, but we found that speed of microtubule growth and our preliminary studies
suggest that pinning under the action of dynein motors can amplify the excess length but fails
to nucleate and sustain the excess length within the microtubule.
55
Figure 4-1. Experimentally recorded tip trajectories of growing microtubules.An ensemble of microtubule tip trajectories recorded in control cells. A) and indynein inhibited cells. B) Tip trajectories were oriented to have the same initialdirection.
Figure 4-2. Microtubule straightening in absence of pinning under the action of dynein motor.The black dot represents the centrosome. The microtuble has an excess length of 1µm at 0 sec and it is subjected to dynein forces using the continuous motor modelfrom Chapter 2. Tangential dynein forces transport microtubule length lengthtowards plus end as seen from microtubule shape at 3 sec and and 6 sec. Thisresults into a straight microtubule in absence of pinning.
56
Figure 4-3. Sine Waves corresponding to mode numbers in the Fourier mode spectrum.Sine waves were used for calculating the amplitudes of fourier modes based on theboundary conditions. The tip trajectories spread around its initial direction in a ’V’shape with tip at origin. Wave shapes corresponding to the modes are plotted witha constant amplitude of 0.25 units for demonstrative purpose as the spectrum iscombination of quarter waves ad half waves.
57
Figure 4-4. Simulations of growing microtubules subjected to motor forces.A) Simulated microtubules that grew to about 8 µm length is shown here. Duringthe entire duration of growth it was subjected to randomly binding + end motors. The density of motors along its length is 1.5 µm−1 on average. As seen, the microtubule bends significantly during growth. B) Variance calculated from tip trajectories of an ensemble of growing microtubules a different motor densities. 0.5 to 2 µm−1 densities are reasonable in predicting the variance in dynein inhibited cells (blue squares, experimental data). We chose a density of 1.5 µm−1 as an optimal density. C) Using 1.5 µm−1 as the density for +end motors, we simulated growth, but now under different densities of - end motors. As seen, + and - end motors collectively predict the variance appropriately. Simulated trajectories with minus end directed motor density of 3 µm−1 in addition to plus end directed motors was found to be in close agreement with experimentally measured values as seen in Figure 4-4C.
58
Figure 4-5. Motors binding near the tip change the orientation of the tip.A) A typical kinesin motor appears on the MT at 0.9 L and starts walking towardsthe plus end thereby changing the orientation of the tip. B) Direction of tip altered by - end directed motor dynein. The extent of change in tip orientation will be higher than what is observed her because of the small lenght of the microtubule with clamped boundary condition. A small length of microtubule is selcted to account for motors that would actually be present on a typical microtubule. However, those motors are expected to impose a hinge like boundary condition than the clamped one.
59
Figure 4-6. Comparison of Fourier modes of tip trajectories and simulated microtubules.Fourier modes for 8 µm long simulated microtubules (circle) and 8 µm long tip trajectories (squares) were calculated using the method described in the earlier section on page 57. A) Fourier modes for simulated microtubules grown with stochastically binding + end directed motors with linear density of 1.5 µm−1 are compared with tip trajectories in dynein inhibited cells. Apart from the 2nd Fourier mode corresponding to half sine wavelength they match remarkably with one another. B) Simulated microtubules experienced + and - end directed motors with linear density of 3 µm−1 and 1.5 µm−1 respectively. First 2 Fourier modes show reasonable agreement with the experiments, however the 4th Fourier mode for simulated trajectories corresponding to a complete sine wave is significantly lower ( 0.03 µm) and shows poor agreement with the experiment.
60
Figure 4-7. Average poly. speed estimated from tip trajectories of simulated microtubule.The actual polymerization speed for both cases is 0.4µm.s−1. Microtubules buckle under the action of plus end motors alone. This leads to lower measured speed. Sections of microtubules buckle in when + and - end motors but buckling is transient and not persistent due to the dynein dominated force balance. Hence the value for estimated polymerization speed when + and - end motors are active is close to actual polymerization velocity.
61
Figure 4-8. Excess length in simulated microtubules.An ensemble of 100 microtubules was simulated for calculation of excess lengthdistribution in the histogram above. The histogram data is collected by selection ofthe maximum excess length for a given microtubules during the entire simulation.About 25% of them have excess length more than 0.5 µm. Figure 3-2C in Chapter3 has an example of microtubule with 0.5 µm that generates a small length highcurvature bend.
62
Table 4-1. Model Parameters: Microtubule, + and - End Directed Motors
Parameter Symbol ValueModulus of Elasticity E 1.75 ∗ 104 pN.µm−2
Flexural Rigidity B 25 pN.µm2
Polymerization Velocity vpol 0.4µ.s−1
- end motor stall force f −max 8 pN+ end motor stall force f +max 5 pN
- end motor stress free speed vmax− 8µm.s−1
+ end motor stress free speed vmax+ 0.5µm.s−1
- end motor density n− 3µ−1
+ end motor density n+ 1.5µ−1
motor off-rate ko 1 s−1
motor spring constant κ 1000 pN.µm−1
Background Friction γbg 10Pa.s
63
CHAPTER 5OUTLOOK
In this thesis, we explained how microtubules undergo local bending in the cytoplasm. In
Chapter 2, we showed that microtubule bending occurs by the plus-end-directed transport of
microtubule segments toward stationary microtubule segments termed pinning points. This
transport causes the microtubule to display local oxbow type bent shapes. Such shapes have
been posited to be caused by lateral forces due to myosin activity. But such forces cannot
explain the directional bias in bending. We solved a computational model that incorporates
tangential forces generated by dynein, frictional forces due to dynein dissociation, and frictional
forces due to cytoplasmic background. We showed how local bends develop in microtubules on
time scales similar to those observed in experiments.
A corollary of Chapter 2 was to explain how dynein forces can cause lateral deviation of
growing microtubule tips. Dynein inhibition has been experimentally shown in the Lele lab to
decrease the spread of growing microtubules. However, as we showed in Chapter 3, dynein
activity is expected to straighten out bends in a short growing microtubule, not increase them.
Moreover, dynein inhibition in experiments does not eliminate variance in tip trajectories. Using
a stochastic model of motor binding and dissociation, we computationally showed in Chapter
3 that the action of plus-ended directed motors can produce bends in a growing microtubule.
Adding dynein motors to this model amplifies variance. Our computational model explains how
dynein amplifies variance, and how excess length is generated by plus-end directed motors.
Collectively, this thesis has brought clarity to the mechanisms by which microtubules bend
along their lengths, and the mechanism by which the microtubule deviates from originally
straight trajectories.
Our thesis is significant because there is little appreciation in the literature of the fact that
tensile forces can be generated by motor forces along the lengths of microtubules in interphase
cells. Most researchers assume that microtubules exist under simple compression due to
immobile but growing tips. Tensile forces are thought to exist on microtubules only in mitosis
64
when chromosomes separate due to microtubules that shorten at their kinetochore-bound
ends. That dynein can generate tension on microtubules has largely escaped attention in the
literature. Yet, such tensile forces are primarily responsible for centering the centrosomal array
of microtubules, and therefore crucial in the establishment of cell polarity, a function critical for
processes like wound healing and development.
Looking to the future, many questions remain which will need to be answered by a similar
cross-talk between experimental and computational efforts. First, what is the mechanism by
which the microtubule gets pinned at pinning points? We hypothesize that molecular motors
like dynein or kinesin may pin the microtubule if they lose their ability to process (i.e. dead
motors). Other possibilities include protein complexes at the growing tip which might connect
microtubules to dynactin or other complexes.
Second, what is the functional significance of microtubule bending? The dynamic bending
of microtubules, and its growth in wavy paths in cells is a fascinating feature of microtubules,
yet this phenomenon largely lacks a (known) function. Does random microtubule bending
allow efficient sampling of the neighborhood? Is this perhaps for transport of cargo to a larger
space than possible by a straight microtubule? These questions could potentially be explored
computationally, but perhaps also experimentally. Alternatively, microtubule bending and
bending during growth might just be an intrinsic property of thermally driven motor driven
bending of randomly growing, stiff microtubules.
Our computational model suggests that plus-ended motors might be important in
the mechanical behavior of growing microtubules. This prediction awaits experimental
confirmation. If it is found that kinesin plays no role in bending microtubules, then the
question of how the spread in the tips of growing microtubules develops will need to be
tackled. As we have mentioned in Chapter 3, an alternative hypothesis is that anchor points of
dynein motors move due to random dipoles in the cytoplasm generated by actomyosin forces.
Experimentally testing this hypothesis requires the imaging of the anchor points of individual
dynein proteins. While this may be experimentally challenging, it also represents an exciting
65
opportunity to understand how dynein motors function in the complex environment of the cell
cytoplasm, and impact microtubule behavior.
Also important in testing the predictions of our model will be to experimentally measure
the density of dynein and kinesin molecules as they walk along microtubules. In particular, our
model requires estimates of these proteins while they are bound to relatively immobile objects
(i.e. not that fraction of motors that transport organelles). It is when the anchor points are
bound to immobile objects that the motors are predicted to generate measureable forces on the
microtubule. Admittedly, such an experiment will be greatly challenging. In particular, if force
sensors are developed that can measure the force on a microtubule as the dynein motor walks,
that would be the ultimate test of the mechanical models in this thesis.
66
REFERENCES
[1] Gittes F, Mickey B, Nettleton J, Howard J. Flexural rigidity of microtubules and actinfilaments measured from thermal fluctuations in shape. J Cell Biol. 1993;120(4):923–934.
[2] Brinkers S, Dietrich HRC, de Groote FH, Young IT, Rieger B. The persistence length ofdouble stranded DNA determined using dark field tethered particle motion. The Journal ofChemical Physics. 2009;130(21):215105. doi:http://dx.doi.org/10.1063/1.3142699.
[3] Bicek AD, Tuzel E, Demtchouk A, Uppalapati P, Hancock WO, Krol DM,et al. Anterograde Microtubule Transport Drives Microtubule Bending inLLC-PK1 Epithelial Cells. Molecular Biology of the Cell. 2009;20(12):2943–2953.doi:10.1091/mbc.E08-09-0909.
[4] Brangwynne CP, MacKintosh FC, Kumar S, Geisse NA, Talbot J, Mahadevan L, et al.Microtubules can bear enhanced compressive loads in living cells because of lateralreinforcement. J Cell Biol. 2006;173(5):733–741. doi:10.1083/jcb.200601060.
[5] Brangwynne CP, Koenderink GH, MacKintosh FC, Weitz DA. NonequilibriumMicrotubule Fluctuations in a Model Cytoskeleton. Phys Rev Lett. 2008;100(11).doi:http://dx.doi.org/10.1103/PhysRevLett.100.118104.
[6] Odde DJ, Ma L, Briggs AH, DeMarco A, Kirschner MW. Microtubule bending andbreaking in living fibroblast cells. J Cell Sci. 1999;112 ( Pt 19):3283–3288.
[7] Mitchison T, Kirschner M. Dynamic instability of microtubule growth. Nature.1984;312(5991):237–242. doi:doi:10.1038/312237a0.
[8] Shekhar N, Neelam S, Wu J, Ladd AJC, Dickinson RB, Lele TP. Fluctuating Motor ForcesBend Growing Microtubules. Cellular and Molecular Bioengineering. 2013;6(2):120–129.doi:10.1007/s12195-013-0281-z.
[9] Holy TE, Leibler S. Dynamic instability of microtubules as an efficient way to search inspace. Proc Natl Acad Sci USA. 1994;91(12):5682–5685.
[10] Janson ME, Dogterom M. A Bending Mode Analysis for Growing Microtubules:Evidence for a Velocity-Dependent Rigidity. Biophysical Journal. 2004;87(4):2723–2736.doi:http://dx.doi.org/10.1529/biophysj.103.038877.
[11] Wu J, Misra G, Russell RJ, Ladd AJC, Lele TP, Dickinson RB. Effects of dynein onmicrotubule mechanics and centrosome positioning. Molecular Biology of the Cell.2011;22(24):4834–4841. doi:10.1091/mbc.E11-07-0611.
[12] Ledbetter MC, Porter KR. Morphology of Microtubules of Plant Cell. Science.1964;144(3620):872–874. doi:10.1126/science.144.3620.872.
[13] Sept D. Microtubule Polymerization: One Step at a Time. Current Biology.2007;17(17):R764–R766. doi:10.1016/j.cub.2007.07.002.
67
[14] Caplow M, Shanks J. Mechanism for oscillatory assembly of microtubules. Journal ofBiological Chemistry. 1990;265(3):1414–8.
[15] David-Pfeuty T, Erickson HP, Pantaloni D. Guanosinetriphosphatase activity of tubulinassociated with microtubule assembly. Proceedings of the National Academy of Sciences.1977;74(12):5372–5376.
[16] Desai A, Mitchison TJ. MICROTUBULE POLYMERIZATION DYNAMICS.Annual Review of Cell and Developmental Biology. 1997;13(1):83–117.doi:10.1146/annurev.cellbio.13.1.83.
[17] Lodish H. Molecular Cell Biology. W.H. Freeman and Co; 2008.
[18] Alushin GM, Lander GC, Kellogg EH, Zhang R, Baker D, Nogales E. High-ResolutionMicrotubule Structures Reveal the Structural Transitions in Tubulin upon GTP Hydrolysis.Cell. 2014;157(5):1117–1129. doi:10.1016/j.cell.2014.03.053.
[19] Akhmanova A, Steinmetz MO. Control of microtubule organization and dynamics: twoends in the limelight. Nature Reviews Molecular Cell Biology. 2015;16(12):711–726.doi:10.1038/nrm4084.
[20] Cassimeris L. Microtubule Assembly: Lattice GTP to the Rescue. Current Biology.2009;19(4):R174–R176. doi:10.1016/j.cub.2008.12.035.
[21] Dimitrov A, Quesnoit M, Moutel S, Cantaloube I, Pous C, Perez F. Detection ofGTP-Tubulin Conformation in Vivo Reveals a Role for GTP Remnants in MicrotubuleRescues. Science. 2008;322(5906):1353–1356. doi:10.1126/science.1165401.
[22] Tropini C, Roth EA, Zanic M, Gardner MK, Howard J. Islands Containing SlowlyHydrolyzable GTP Analogs Promote Microtubule Rescues. PLoS ONE. 2012;7(1):e30103.doi:http://dx.doi.org/10.1371/journal.pone.0030103.
[23] Mogilner A, Oster G. The polymerization ratchet model explains the force-velocityrelation for growing microtubules. European Biophysics Journal. 1999;28(3):235–242.doi:10.1007/s002490050204.
[24] Peskin CS, Odell GM, Oster GF. Cellular motions and thermal fluctuations:the Brownian ratchet. Biophysical Journal. 1993;65(1):316–324.doi:doi:10.1016/S0006-3495(93)81035-X.
[25] Dogterom M, Yurke B. Measurement of the force-velocity relation for growingmicrotubules. Science. 1997;278(5339):856–860.
[26] Dogterom M, Kerssemakers JW, Romet-Lemonne G, Janson ME. Force generationby dynamic microtubules. Current Opinion in Cell Biology. 2005;17(1):67–74.doi:10.1016/j.ceb.2004.12.011.
[27] Howard J. Elastic and damping forces generated by confined arrays of dynamicmicrotubules. Physical Biology. 2006;3(1):54–66. doi:10.1088/1478-3975/3/1/006.
68
[28] Inoue S, Salmon ED. Force generation by microtubule assembly/disassembly in mitosisand related movements. Mol Biol Cell. 1995;6(12):1619–1640.
[29] Tran PT, Marsh L, Doye V, Inoue S, Chang F. A mechanism for nuclear positioning infission yeast based on microtubule pushing. J Cell Biol. 2001;153(2):397–411.
[30] Faivre-Moskalenko C, Dogterom M. Dynamics of microtubule asters in microfabricatedchambers: The role of catastrophes. Proceedings of the National Academy of Sciences.2002;99(26):16788–16793. doi:10.1073/pnas.252407099.
[31] Holy TE, Dogterom M, Yurke B, Leibler S. Assembly and positioning of microtubuleasters in microfabricated chambers. Proc Natl Acad Sci USA. 1997;94(12):6228–6231.
[32] Asbury CL, Gestaut DR, Powers AF, Franck AD, Davis TN. The Dam1 kinetochorecomplex harnesses microtubule dynamics to produce force and movement.Proceedings of the National Academy of Sciences. 2006;103(26):9873–9878.doi:10.1073/pnas.0602249103.
[33] Grishchuk EL, Efremov AK, Volkov VA, Spiridonov IS, Gudimchuk N, Westermann S,et al. The Dam1 ring binds microtubules strongly enough to be a processive as well asenergy-efficient coupler for chromosome motion. Proceedings of the National Academy ofSciences. 2008;105(40):15423–15428. doi:10.1073/pnas.0807859105.
[34] Koshland DE, Mitchison TJ, Kirschner MW. Polewards chromosome movementdriven by microtubule depolymerization in vitro. Nature. 1988;331(6156):499–504.doi:10.1038/331499a0.
[35] Molodtsov MI, Grishchuk EL, Efremov AK, McIntosh JR, Ataullakhanov FI. Forceproduction by depolymerizing microtubules: A theoretical study. Proceedings of theNational Academy of Sciences. 2005;102(12):4353–4358. doi:10.1073/pnas.0501142102.
[36] Oguchi Y, Uchimura S, Ohki T, Mikhailenko SV, Ishiwata S. The bidirectionaldepolymerizer MCAK generates force by disassembling both microtubule ends. Nature CellBiology. 2011;13(7):846–852. doi:10.1038/ncb2256.
[37] Volkov VA, Zaytsev AV, Gudimchuk N, Grissom PM, Gintsburg AL, AtaullakhanovFI, et al. Long tethers provide high-force coupling of the Dam1 ring to shorteningmicrotubules. Proceedings of the National Academy of Sciences. 2013;110(19):7708–7713.doi:10.1073/pnas.1305821110.
[38] Fridolfsson HN, Ly N, Meyerzon M, Starr DA. UNC-83 coordinates kinesin-1 and dyneinactivities at the nuclear envelope during nuclear migration. Developmental Biology.2010;338(2):237–250. doi:10.1016/j.ydbio.2009.12.004.
[39] Levy JR, Holzbaur ELF. Dynein drives nuclear rotation during forward progressionof motile fibroblasts. Journal of Cell Science. 2008;121(19):3187–3195.doi:10.1242/jcs.033878.
69
[40] Salina D, Bodoor K, Eckley DM, Schroer TA, Rattner JB, Burke B. Cytoplasmic dyneinas a facilitator of nuclear envelope breakdown. Cell. 2002;108(1):97–107.
[41] Vogel SK, Pavin N, Maghelli N, Jlicher F, Tolic-Nørrelykke IM. Self-Organization ofDynein Motors Generates Meiotic Nuclear Oscillations. PLoS Biology. 2009;7(4):e1000087.doi:10.1371/journal.pbio.1000087.
[42] Zhou K, Rolls MM, Hall DH, Malone CJ, Hanna-Rose W. A ZYG-12–dynein interaction atthe nuclear envelope defines cytoskeletal architecture in the C. elegans gonad. J Cell Biol.2009;186(2):229–241. doi:10.1083/jcb.200902101.
[43] Payne C. Preferentially localized dynein and perinuclear dynactin associate with nuclearpore complex proteins to mediate genomic union during mammalian fertilization. Journalof Cell Science. 2003;116(23):4727–4738. doi:10.1242/jcs.00784.
[44] Gill SR. Dynactin, a conserved, ubiquitously expressed component of an activatorof vesicle motility mediated by cytoplasmic dynein. The Journal of Cell Biology.1991;115(6):1639–1650. doi:10.1083/jcb.115.6.1639.
[45] Schroer TA. Two activators of microtubule-based vesicle transport. The Journal of CellBiology. 1991;115(5):1309–1318. doi:10.1083/jcb.115.5.1309.
[46] Culver–Hanlon TL, Lex SA, Stephens AD, Quintyne NJ, King SJ. A microtubule-bindingdomain in dynactin increases dynein processivity by skating along microtubules. NatureCell Biology. 2006;8(3):264–270. doi:10.1038/ncb1370.
[47] Kardon JR, Reck-Peterson SL, Vale RD. Regulation of the processivity and intracellularlocalization of Saccharomyces cerevisiae dynein by dynactin. Proceedings of the NationalAcademy of Sciences. 2009;106(14):5669–5674. doi:10.1073/pnas.0900976106.
[48] Ross JL, Wallace K, Shuman H, Goldman YE, Holzbaur ELF. Processive bidirectionalmotion of dynein–dynactin complexes in vitro. Nature Cell Biology. 2006;8(6):562–570.doi:10.1038/ncb1421.
[49] Schroer TA, King SJ. Dynactin increases the processivity of the cytoplasmic dynein motor.Nature Cell Biology. 1999;2(1):20–24. doi:10.1038/71338.
[50] Eckley DM, Gill SR, Melkonian KA, Bingham JB, Goodson HV, Heuser JE, et al.Analysis of Dynactin Subcomplexes Reveals a Novel Actin-Related Protein Associatedwith the Arp1 Minifilament Pointed End. J Cell Biol. 1999;147(2):307–320.doi:10.1083/jcb.147.2.307.
[51] Schafer DA. Ultrastructural analysis of the dynactin complex: an actin-related proteinis a component of a filament that resembles F-actin. The Journal of Cell Biology.1994;126(2):403–412. doi:10.1083/jcb.126.2.403.
[52] Akhmanova A, Steinmetz MO. Tracking the ends: a dynamic protein network controlsthe fate of microtubule tips. Nature Reviews Molecular Cell Biology. 2008;9(4):309–322.doi:doi:10.1038/nrm2369.
70
[53] Howard J. Mechanics of Motor Proteins and the Cytoskeleton. Sinauer Associates; 2001.
[54] Landau LD, Lifshitz EM. Theory of Elasticity. Oxford: Elsevier; 1976.
[55] Llopis I, Pagonabarraga I, Lagomarsino MC, Lowe CP. Sedimentation of pairs ofhydrodynamically interacting semiflexible filaments. Physical Review E. 2007;76(6).doi:http://dx.doi.org/10.1103/PhysRevE.76.061901.
[56] Llopis I, Lagomarsino MC, Pagonabarraga I, Lowe CP. Cooperativity and hydrodynamicinteractions in externally driven semiflexible filaments. Computer Physics Communications.2008;179(1-3):150–154. doi:http://dx.doi.org/10.1016/j.cpc.2008.01.014.
[57] Wu J, Lee KC, Dickinson RB, Lele TP. How dynein and microtubules rotate the nucleus.J Cell Physiol. 2011;226(10):2666–2674. doi:10.1002/jcp.22616.
[58] Toba S, Watanabe LY T M andOkimoto, oyoshima YY, Higuchi H. Overlappinghand-over-hand mechanism of single molecular motility of cytoplasmic dynein.Proceedings of the National Academy of Sciences. 2006;103(15):5741–5745.doi:10.1073/pnas.0508511103.
[59] Nedelec F, Foethke D. Collective Langevin dynamics of flexible cytoskeletal fibers. NewJournal of Physics. 2007;9(11):427.
[60] Sammak PJ, Borisy GG. Direct observation of microtubule dynamics in living cells.Nature. 1988;332(6166):724–726. doi:10.1038/332724a0.
[61] Schulze E, Kirschner M. New features of microtubule behaviour observed in vivo. Nature.1988;334(6180):356–359. doi:10.1038/334356a0.
[62] Ingber DE, Ingber DE. Tensegrity I. Cell structure and hierarchical systems biology. J CellSci. 2003;116(Pt 7):1157–1173.
[63] Stamenovic D, Mijailovich SM, Tolic-Norrelykke IM, Chen J, Wang N. Cell prestress.II. Contribution of microtubules. AJP: Cell Physiology. 2001;282(3):C617–C624.doi:10.1152/ajpcell.00271.2001.
[64] Ingber DE, Ingber DE. Opposing views on tensegrity as a structural framework forunderstanding cell mechanics. J Appl Physiol. 2000;89(4):1663–1670.
[65] Wang N, Naruse K, Stamenovic D, Fredberg JJ, Mijailovich SM, Tolic-NorrelykkeIM, et al. Mechanical behavior in living cells consistent with the tensegritymodel. Proceedings of the National Academy of Sciences. 2001;98(14):7765–7770.doi:10.1073/pnas.141199598.
[66] Brangwynne CP, MacKintosh FC, Weitz DA. Force fluctuations and polymerizationdynamics of intracellular microtubules. Proceedings of the National Academy of Sciences.2007;104(41):16128–16133. doi:10.1073/pnas.0703094104.
71
[67] Gupton SL, Salmon WC, Waterman-Storer CM. Converging populations of f-actinpromote breakage of associated microtubules to spatially regulate microtubule turnover inmigrating cells. Curr Biol. 2002;12(22):1891–1899.
[68] Waterman-Storer CM, Salmon ED. Actomyosin-based Retrograde Flow of Microtubulesin the Lamella of Migrating Epithelial Cells Influences Microtubule Dynamic Instabilityand Turnover and Is Associated with Microtubule Breakage and Treadmilling. J Cell Biol.1997;139(2):417–434. doi:10.1083/jcb.139.2.417.
[69] Jolly AL, Gelfand VI. Cytoplasmic microtubule sliding. Communicative & IntegrativeBiology. 2010;3(6):589–591. doi:10.4161/cib.3.6.13212.
[70] Gennerich A, Carter AP, Reck-Peterson SL, Vale RD. Force-Induced Bidirectional Steppingof Cytoplasmic Dynein. Cell. 2007;131(5):952–965. doi:10.1016/j.cell.2007.10.016.
[71] Dammermann A, Desai A, Oegema K. The minus end in sight. Current Biology.2003;13(15):R614–R624. doi:10.1016/s0960-9822(03)00530-x.
[72] Komarova YA, Vorobjev IA, Borisy GG. Life cycle of MTs: persistent growth in the cellinterior, asymmetric transition frequencies and effects of the cell boundary. J Cell Sci.2002;115(Pt 17):3527–3539.
[73] Rodionov V, Nadezhdina E, Borisy G. Centrosomal control of microtubuledynamics. Proceedings of the National Academy of Sciences. 1999;96(1):115–120.doi:10.1073/pnas.96.1.115.
[74] Vorobjev IA, Svitkina TM, Borisy GG. Cytoplasmic assembly of microtubules in culturedcells. J Cell Sci. 1997;110 ( Pt 21):2635–2645.
[75] Yvon AM, Wadsworth P. Non-centrosomal microtubule formation and measurement ofminus end microtubule dynamics in A498 cells. J Cell Sci. 1997;110 ( Pt 19):2391–2401.
[76] Abal M. Microtubule release from the centrosome in migrating cells. The Journal of CellBiology. 2002;159(5):731–737. doi:10.1083/jcb.200207076.
[77] Gaetz J, Kapoor TM. Dynein/dynactin regulate metaphase spindle length bytargeting depolymerizing activities to spindle poles. J Cell Biol. 2004;166(4):465–471.doi:10.1083/jcb.200404015.
[78] King SJ. Analysis of the Dynein-Dynactin Interaction In Vitro and In Vivo. MolecularBiology of the Cell. 2003;14(12):5089–5097. doi:10.1091/mbc.E03-01-0025.
[79] Quintyne NJ, Gill SR, Eckley DM, Crego CL, Compton DA, Schroer TA. Dynactin IsRequired for Microtubule Anchoring at Centrosomes. J Cell Biol. 1999;147(2):321–334.doi:10.1083/jcb.147.2.321.
72
[80] Kumar S, Maxwell IZ, Heisterkamp A, Polte TR, Lele TP, Salanga M, et al.Viscoelastic Retraction of Single Living Stress Fibers and Its Impact on Cell Shape,Cytoskeletal Organization, and Extracellular Matrix Mechanics. Biophysical Journal.2006;90(10):3762–3773. doi:10.1529/biophysj.105.071506.
[81] Verkhovsky AB, Svitkina TM, Borisy GG. Myosin II filament assemblies in the activelamella of fibroblasts: their morphogenesis and role in the formation of actin filamentbundles. J Cell Biol. 1995;131(4):989–1002.
[82] Ally S, Larson AG, Barlan K, Rice SE, Gelfand VI. Opposite-polarity motors activateone another to trigger cargo transport in live cells. J Cell Biol. 2009;187(7):1071–1082.doi:10.1083/jcb.200908075.
[83] Gross SP, Welte MA, Block SM, Wieschaus EF. Coordination of opposite-polaritymicrotubule motors. J Cell Biol. 2002;156(4):715–724. doi:10.1083/jcb.200109047.
[84] Hendricks AG, Perlson E, Ross JL, Schroeder HW, Tokito M, Holzbaur ELF. MotorCoordination via a Tug-of-War Mechanism Drives Bidirectional Vesicle Transport. CurrentBiology. 2010;20(8):697–702. doi:10.1016/j.cub.2010.02.058.
[85] Jolly AL, Gelfand VI. Bidirectional intracellular transport: utility and mechanism: Figure1. Biochm Soc Trans. 2011;39(5):1126–1130. doi:10.1042/BST0391126.
[86] Muller MJI, Klumpp S, Lipowsky R. Tug-of-war as a cooperative mechanism forbidirectional cargo transport by molecular motors. Proceedings of the National Academyof Sciences. 2008;105(12):4609–4614. doi:10.1073/pnas.0706825105.
[87] Soppina V, Rai AK, Ramaiya AJ, Barak P, Mallik R. Tug-of-war between dissimilarteams of microtubule motors regulates transport and fission of endosomes.Proceedings of the National Academy of Sciences. 2009;106(46):19381–19386.doi:10.1073/pnas.0906524106.
[88] Schroeder HW, Hendricks AG, Ikeda K, Shuman H, Rodionov V, Ikebe M,et al. Force-Dependent Detachment of Kinesin-2 Biases Track Switching atCytoskeletal Filament Intersections. Biophysical Journal. 2012;103(1):48–58.doi:10.1016/j.bpj.2012.05.037.
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BIOGRAPHICAL SKETCH
Born and raised in the town of Jalgaon, in India Parag Rane is the son of Subhash Rane
and Rekha Rane. From his childhood, his parents nurtured his curiosity by providing him with
ample books and visits to various places like Nehru planetarium at Mumbai, botanical gardens
at Bangalore and Singadh fort in Pune to name a few. This played a vital part is his strong
inclination towards STEM fields.
For his undergraduate education, Parag landed at Institute of Chemical Technology (ICT),
Mumbai in fall of 2007 where he earned his Bachelor of Chemical Engineering (B.Chem Engg.)
degree in spring of 2011. During this time he was thankful for having the opportunity to lead
the undergraduate technical festival at the institute. He interned at Vega Chemicals. Ltd.
during summer of 2010. He is grateful for Prof.V.G. Gaiker, Prof.S.D. Samant and his parents
who played a vital role in his decision to persue higher education. He joined University of
Florida in fall of 2011 for doctorate studies and was fortunate enough to find a chance to work
with Prof. Tony Ladd, Prof. Rich Dickinson and Prof. Tanmay Lele. They refined Parag’s
sense of science, how it is done at the highest level and how it must be communicated in its
simplest form. He feels lucky to have a very strong PhD committee with whom he was able to
interact with quite frequently.
In his leisure time, Parag likes to sing, run and play computer games on his system which
he assembled during Christmas in 2012. He has keen interest in machine learning, physics,
and American politics. He is looking forward to make his transition to the field of data science
which he not only finds fascinating but it also compliments his skill set that he has developed
during the doctoral program.
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