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The relationship between stochastic and deterministic quasi-steady state approximations.

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Area of Science:

  • Biochemical Systems Analysis
  • Computational Biology
  • Systems Biology

Background:

  • The quasi steady-state approximation (QSSA) is widely used to simplify complex biochemical network models.
  • Reduced models often employ non-elementary reaction functions (e.g., Hill functions).
  • The validity of stochastic models based on deterministic QSSA reductions is not well-established.

Purpose of the Study:

  • To investigate the accuracy of stochastic QSSA reductions in biochemical models.
  • To identify conditions under which stochastic QSSA provides reliable results.
  • To establish a method for validating stochastic QSSA accuracy.

Main Methods:

  • Analysis of a two-state promoter model.
  • Numerical simulations of various biochemical models.
  • Comparison of deterministic and stochastic QSSA accuracy across different initial conditions.

Main Results:

  • Discrepancies between deterministic and stochastic QSSA accuracy were explained.
  • A direct relationship between deterministic and stochastic QSSA accuracy was demonstrated.
  • Stochastic QSSA accuracy correlates with deterministic approximation accuracy over relevant initial condition ranges.

Conclusions:

  • The accuracy of stochastic QSSA is linked to the accuracy of its deterministic counterpart.
  • A computationally inexpensive method to test stochastic QSSA validity using deterministic simulations is proposed.
  • This provides a concrete approach to determine when non-elementary rate functions are suitable for stochastic simulations.