02. dynamic systems in molecular & cell biology
DESCRIPTION
Cell Biology. Dynamic SystemsTRANSCRIPT
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Dynamic Systems in Molecular & Cell Biology
Olaf Wolkenhauer
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Cell Functions
Growth Proliferation
ApoptosisDifferentiation
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Key cellular processes and the network concept
Metabolism Cell signallingGene expression
Pathway, Network
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Examples of signaling pathways
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0 2 4 6 80
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time t
R(t)
0 5 10 150
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time t
R(t)
0 5 10 15 20 250
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time t
R(t)
S=8S=14
0 2 4 6 80
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time t
R(t)
0 5 10 15 20 250
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time t
R(t)
S=8S=14
Biological Complexity: Nonlinear Dynamics
0 5 10 150
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time t
R(t)
Signal S
Resp
onse
RSS
Scrit
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How do I model and simulate a system?
▪ Statistics and Probability Theory
▪ Machine-learning ▪ Clustering and Classification
▪ Dynamical Systems Theory
▪ ODE-based mechanistic modeling
▪ Stochastic modeling & simulation
▪ Simulation/Agent-based modeling
▪ Logical Representations
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Kinds of Modeling
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Kinds of modeling (cont’d)
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Mechanistic Modeling
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There is nothing more practical than a good theory!
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Why model?
▪ Explain (very distinct from predict!) ▪ Guide data collection ▪ Illuminate core dynamics ▪ Suggest dynamical analogies ▪ Discover new questions ▪ Promote scientific habit of mind ▪ Bound outcomes to plausible ranges ▪ Illuminate core uncertainties ▪ Formulate hypotheses ▪ Reveal simplicity in complexity
cf. JM Epstein JASSS 11 (4) 2008
René Magritte: La Clairvoyance, 1936
Modelling is a means for theorizing: We construct and analyse models in order to formulate hypotheses about general “law-like” (organising) principles.
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Interaction networks - Biochemical Reaction Networks
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Enzymatic Reaction as a Template:
SBGN:
Biochemical equation:
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Enzyme Kinetic Reactions
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Enzymatic Reaction as a Template:
Kinetic Rate Equations:
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Elementary Reactions
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Monomolecular Reaction:
Bimolecular Reaction:
Reversible Reaction:
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Enzyme Kinetic Reactions
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Enzymatic Reaction as a Template:
Kinetic Rate Equations:
Conservation laws:
Quasi steady state assumption:
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Derivation of the Michaelis-Menten Equation
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Quasi steady state assumption:
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Deriving the Michaelis-Menten Equation
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Michaelis-‐Menten Equation:
Limiting Rate:
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Deriving the Michaelis-Menten Equation
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Michaelis-‐Menten Equation:
Dimensionless Representation (Activity):
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From reactions to networks
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A generic signaling network
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A generic signaling network
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The Systems (Biology) Approach
Observa(ons+Experiments+ Modeling+ Explana(on+
Claim+
Hypothesis+Simula(on+
Predic'ons+
Contextual*Assump/ons**
Narra/ve*
Understanding+
Rebu>al+
Analyses+Concepts+
!!
dRdt
= k0E*(R)+k1S −k2R
t+
S+
S+
Rss+
e.g.+Feedback+regula(on,+Bistability+
R+
S+
E*+ E+
R"
R"
freq
uency)
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Learning Outcomes
● Cellular functions (cell growth, proliferation, differentiation and apoptosis are dynamical systems.
● The notion of a pathway/network is used to represent intracellular interactions.● The mechanisms, feedback loops in particular, determine the dynamic behavior of
the system.● Interaction networks can be modeled as biochemical reaction networks.● Ordinary differential equations are frequently employed to simulate such networks.● More complex networks can be broken down into basic elements, modeled in terms
of elementary reactions.● The vast majority of cellular reactions can be represented as a kind of “enzyme
kinetic reaction” (facilitated reaction)● The prototype enzymatic reactions can be modelled with four ODEs.● Conservation laws and steady-state assumptions allow us to simplify these equations
into the Michaelis-Menten equation.● When modelling and simulating cellular processes, we must be aware of the
assumptions we make.● Modeling and simulation serves several purposes (see list).
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