Zero-order reaction (Gillespie/stochastic simulation)

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Sebastián

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Apr 30, 2025, 9:32:23 PMApr 30
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Hi,

I'm interested in simulating a chemical reaction network in which some reactions are assumed to follow zero-order kinetics rather than the usual mass-action form. For example, a degradation reaction like:

A →

would proceed at a constant rate k, independent of the concentration of A (i.e., rate = k, not k·[A]). Of course, I can define the rate in COPASI as zero-order, but I have a related question:

From a theoretical perspective, is a zero-order reaction compatible with the assumptions underlying the Gillespie’s stochastic simulation algorithm?

Thanks in advance for you insights.

Sebastian

Matthias König

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May 1, 2025, 5:47:06 AMMay 1
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Hi Sebastian,

I'm not an expert on the Gillespie algorithm, but from what I understand, this approach should be compatible.

The main issue with using constant rates is the risk of numerical instability during integration. You need to ensure that there's always a sufficient amount of substrate A available to support the reaction rate over a given time step (Δt); otherwise, you may end up with negative concentrations.

Moreover, systems without saturation mechanisms can easily become unstable, diverging towards ±∞ under certain conditions. To avoid this, I often model reactions with saturation kinetics using very low values. This effectively yields zero-order kinetics—since the system is nearly always saturated—while maintaining stability even when A is depleted.

Best regards,
Matthias


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Hoops, Stefan (sh9cq)

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May 1, 2025, 9:42:25 AMMay 1
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Hello Sebastian,

Zero order (constant) reaction kinetics can be used in COPASI with
stochastic algorithm. In fact all types of kinetics may be used.

However as Matthias pointed out you must assure that the substrate may
never be depleted. Which you cannot guarantee in a stochastic
simulation. Thus any reaction with substrate(s) should not use constant
rate.

However -> A is perfectly fine.

Thanks,
Stefan
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Stefan Hoops, Ph.D.
Research Associate Professor
Biocomplexity Institute & Initiative
University of Virginia
995 Research Park Boulevard
Charlottesville, VA 22911

Phone: +1 540 570 1301
Email: sho...@virginia.edu
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