Introduction to Systems Biology - Lecture Notes | CSE 60531, Study notes of Computer Science

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Computational Biophysics and

Systems Biology

Introduction to Systems Biology

Prof. Jesús A. Izaguirre

Overview

• Stochastic vs. deterministic models:

• Example: simple model of circadian cycle
• Reference: Vilar JMG, Kueh HY, Barkai N, Leibler S ,

Mechanisms of noise-resistance in genetic

oscillators ,

PNAS April 30, 2002 vol. 99 no. 9 5988-

• Stochastic vs. deterministic differential

equations:

• Explicit solvent vs. implicit solvent molecular

dynamics simulations

Original set of equations

Comparison of results

Deterministic equations Stochastic equations

Model simplification

Steady state vs. oscillation

Biological model databases

• We will find this model in

www.biomodels.net

Concise notation x

collection of positions

~r i

M

diagonal matrix of masses,

v

collection of velocities,

p

M v

collection of momenta,

F

x

U

x

collection of forces.

Equations are a Hamiltonian system,

d d t x

t

M

− 1 p

t

d d t p

t

F

x

t

with Hamiltonian

H

x, p

1 2 p T

M

− 1 p

U

x

NSF Summer School on Theoretical and Computational Biophysics – p.

Implicit solvent

Dynamical equations are those of Langevin dynamics:

d d t x

t

v

t

M

d d t v

t

U

x

t

k B

T D

x

t

− 1 v

t

k B

T D

1 / 2

x

t

− T d d t

W

t

where

U

x

includes a Poisson-Boltzmann solution,

D

D

1 / 2

D

T 1 / 2

is a diffusion tensor, and

d d t

W

t

is standard white noise,

i. e.,

W

t

is Gaussian

with

E

W

t

and

E

W

i

s

W

j

t ) = min

s, t

δ ij

Implicit solvent deviates from explicit solventunless four layers of explicit solvent are included.Cheaper and less accurate is a generalized Born potential.

NSF Summer School on Theoretical and Computational Biophysics – p.