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COPASI®: Introduction

Stefan HoopsCOPASI User Workshop July 2014

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Overview

►Biochemical Reaction Network►Deterministic Simulation►Stochastic Simulation►COPASI Model►Model Translation►Steady State

Biological Process

What is a biological process?Participants:

molecules, genes, proteins, complexes, drugs, etc.

Participant Roles: input, output , modifiers

Happens with a speed, propability, or frequency

Process Examples

Chemical Reaction:2 * H2 + O2 -> 2 * H2O

Complex Formation:

Protein A + Protein B = Complex

Process Examples

Translation:

-> Protein; RNA

Note: RNA is not consumed

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Biochemical Reaction Network

A B

C + D E

B + 2 F G +H

Genome

Metabolome

Proteome

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Deterministic Simulation

-1 0 01 0 -10 -1 00 -1 0 0 1 00 0 -20 0 10 0 1

ABCDEFGH

.

.

.

.

.

.

.

.

=v 1 (A, B, H)v 2 (B, C, D, E)v 3 (B, E, F, G, H)

x = N v with:.

v =

v 1

v 2

…

v m

x =

x 1

x 2

…

x n

ODE System:

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Stochastic Simulation

Initialize system

Calculate: Reaction probabilities

Generate random numbers to determine:

• time of next reaction• which reaction happens

Update the system the system

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Stochastic Simulation

►Reactions are discrete events.►Reaction events fire with a probability

P = k * S1* S

2*

…

depending on the reaction substrates Si.

►Reactions are irreversible

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COPASI Model

►COPASI models are reaction networks.►The tool “Convert to Irreversible” helps the user to

convert each reversible reactions into 2 irreversible reactions.

►Kinetic laws may be interpreted as reaction velocities or as reaction probabilities through a user settable flag.

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Hybrid Methods

►Switching between stochastic and deterministic integration depending on the smallest particle number (min(PN)) currently present in the model.►Start with stochastic simulation.►If (min(PN) < Lower Bound) switch to stochastic

simulation.►If (min(PN) > Upper Bound) switch to deterministic

simulation.

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Hybrid Methods

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Translating Kinetic Laws

2 A2 + B

2 -> 2 A

2B with Mass Action Kinetics

deterministic:

2 A2 + B

2 -> 2 A

2B with positive kinetics f([A

2], [B

2])

deterministic:

stochastic:

stochastic:

p=f [A2] , [B2]A2 A2−1 B2

[A2] [A2] [B2]

p=k A2 A2−1 B2

v=f [A2] , [B2]

v=k [A2] [A2] [B2]

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Steady-State

x = N v = 0 with:.

v =

v 1

v 2

…

v m

x =

x 1

x 2

…

x n

Condition:Condition:

Method: Damped NewtonForward IntegrationBackward Integration