Microtubule dynamicsMicrotubule dynamics

Vladimir Rodionov

The goal of this project is to develop a The goal of this project is to develop a comprehensive computational tool for modeling comprehensive computational tool for modeling cytoskeletal dynamics using two cytoskeletal dynamics using two complementary approaches: detailed discrete complementary approaches: detailed discrete modeling and coarse-grain continuous modeling and coarse-grain continuous approximation. approximation.

The biological problem of regulation of The biological problem of regulation of intracellular transport by dynamics of the intracellular transport by dynamics of the cytoskeleton is being used as a test bed for cytoskeleton is being used as a test bed for validation of this computational tool. validation of this computational tool.

Melanosomes are captured by growing MT plus-ends during aggregation

Stabilization of microtubules inhibits pigment aggregation

Aggregation

Low cAMPActin Filaments

Granule

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CLIP-170

Aggregation

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CLIP-170

Computational model for pigment aggregation

Model includes dynamically unstable microtubules (MTs) interacting with melanosomes.

Microtubules:

MTs are modeled as radial lines with minus ends fixed at the cell center and dynamic plus ends extended to the periphery .

Plus end can either move towards the periphery with velocity v+, (MT growth, state M+), toward the center wth velocity v- (MT

shortening, state M-), or pause (state M0) .

Binding of melanosomes to MTs occur at a short distance (3 m or less) from the tip.

Melanosomes:

A melanosome either undergoes actin-dependent random walks (state G), or is bound to MT.

The MT-bound states of a melanosome include plus-end runs (G+), minus-end runs (G-), and pauses (G0).

Wiring diagram:

Wiring diagram for MT states with rates q1 – q6 (left) is coupled to melanosome transitions with rates k1 – k6 (right) through

the collision-controlled binding of the melanosome to a growing MT tip.

All rates are found from experimental data.

Parameters used in the computational model for pigment aggregation

Notation

Values

GFP TaxolEB3-GFP

GFP-CLIP tail

GFP-CLIP head

GFP-Lis1

Cell radius (μm) R 20

Diffusion of unbound melanosome (μm2/s) D 4x10-3

Melanosome radius (μm) Rg 0.25

MT cross-section (μm) δ 0.025

Nucleus radius (μm) a 4

Rate constant for M - → M + (s-1

) q2 0.052 0.043 0.05 0.028 0.042 0.065

Rate constant for M - → M 0 (s-1

) q3 0.008 0.192 0.008 0.003 0.005 0.009

Rate constant for M + → M 0 (s-1

) q5 0.012 0.206 0.009 0.009 0.007 0.013

Rate constant for M 0 → M - (s-1

) q4 0.09 0.034 0.096 0.057 0.085 0.079

Rate constant for M 0 → M + (s-1

) q6 0.161 0.053 0.142 0.247 0.157 0.15

Rate constant for M+ → M - (s-1

) q1 0.044 0.029 0.039 0.023 0.033 0.053

Rate constants for G - → G + (s-1

) k2 0.587 0.587 0.623 0.988 0.554 0.703

Rate constants for G - → G 0 (s-1

) k3 0.374 0.374 0.278 0.382 0.286 0.299

Rate constants for G + → G 0 (s-1

) k5 0.274 0.274 0.163 0.268 0.197 0.151

Rate constants for G 0 → G - (s-1

) k4 0.8 0.8 0.965 0.763 0.909 0.917

Rate constants for G 0 → G + (s-1

) k6 0.176 0.176 0.159 0.237 0.167 0.149

Rate constants for G+ → G- (s-1

) k1 1.948 1.948 2.218 2.232 2.076 2.185

Simulation time step (s) t 10-3

Total number of melanosomes Ng 770

Total number of MTs Nm 370

Velocity of melanosome minus-end runs (μm/s) 0.344 0.344 0.382 0.351 0.343 0.376

Velocity of melanosome plus-end runs (μm/s) 0.345 0.345 0.342 0.323 0.327 0.354

Velocity of MT growth (μm/s) 0.167 0.059 0.171 0.225 0.293 0.153

Velocity of MT shortening (μm/s) 0.185 0.058 0.188 0.269 0.336 0.175

Spatial stochastic simulations of MT dynamics and intracellular transport

Dynamic MTs (control) Stabilized MTs (taxol treatment )

The results of spatial stochastic simulations agree with experimental data

Granule aggregation signals change major parameters of MT dynamic instability, and these changes accelerate pigment

aggregation

Dynamic parametersDispersed

stateAggregated

state

Growth duration (s) 27.34 17.99

Growth length (μm) 6.13 2.59

Growth rate (μm/s) 0.23 0.16

Shortening duration (s) 24.55 11.86

Shortening length (μm) 7.72 2.06

Shortening rate (μm/s) 0.25 0.18

Catastrophe frequency (s-1)0.03 0.04

Rescue frequency (s-1) 0.046 0.085

Pause duration (s) 3.45 4.42

Number of analyzed MTs 40 60

Number of analyzed cells 8 13

Conclusion

We have developed stochastic model for microtubule dynamics, and validated the model in an experiment.

Lomakin, A., Semenova, I., Zalyapin, I., Kraikivski, P., Nadezhdina, E., Slepchenko, B.M., Akhmanova, A., and

Rodionov. V. (2009). CLIP-170-dependent capture of membrane organelles by microtubules initiates minus-

end directed transport. Dev. Cell 17, 323-333.

Plans for the next year

Discrete and coarse-grain stochastic approaches for modeling dynamics of actin filaments and microtubules will be further developed.

Dispersion

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Dispersion

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