The relationship between art and science and its implications for design education

<p><b>Left</b>: Plots for Clb2. The distribution density error is 4%. <b>Right</b>: Plots for Z. The distribution density error is 3.3%.</p

The Abridgment and Relaxation Time for a Linear Multi-Scale Model Based on Multiple Site Phosphorylation

<div><p>Random effect in cellular systems is an important topic in systems biology and often simulated with Gillespie’s stochastic simulation algorithm (SSA). Abridgment refers to model reduction that approximates a group of reactions by a smaller group with fewer species and reactions. This paper presents a theoretical analysis, based on comparison of the first exit time, for the abridgment on a linear chain reaction model motivated by systems with multiple phosphorylation sites. The analysis shows that if the relaxation time of the fast subsystem is much smaller than the mean firing time of the slow reactions, the abridgment can be applied with little error. This analysis is further verified with numerical experiments for models of bistable switch and oscillations in which linear chain system plays a critical role.</p></div

Motif of oscillation model one.

<p>In this motif, Clb2 and Cdh1 form a positive feedback loop and Clb2 and Z construct a negative feedback loop.</p

Distributions of Clb2 time fraction from original model and reduced model.

<p>(A)<i>k</i> = 5 and the distribution density error is 4.53%. (B)<i>k</i> = 0.5 and the distribution density error is 7.81%. (C)<i>k</i> = 0.05 and the distribution density error is 51.7%. (D)<i>k</i> = 0.01 and the distribution density error is 147%.</p

Motif of oscillation model two.

<p>In this motif, Clb2 and Cdh1 form a positive feedback loop. Cdh1, Clb2 and Z construct a negative feedback loop.</p

A bistable switch converted from the model in Fig 1 based on multiple site phosphorylation.

<p>Cdh1 is assumed to have 11 phosphorylation levels, as described as Cdh1 (the unphosphorylated form) and Cdh1P through Cdh1P₁₀.</p

An example of bistable switch in the cell cycle model.

<p>Each dashed line indicates the enzyme species on one enzyme-substrate reaction.</p

CPU time comparison on the bistable switch model.

<p>CPU time comparison on the bistable switch model.</p

Relaxation time of the chain reaction system.

<p>Relaxation time and time interval between two slow reaction events are computed with different parameters of <i>k</i> and molecule numbers of Clb2.</p

Deterministic and stochastic simulation results of oscillation model one.

<p>Phase property of oscillations in stochastic simulation consists of what shows in deterministic simulation. Amplitude of Clb2 is enlarged due to stochastic noise compared with amplitude in deterministic simulation. <b>Left</b>: Deterministic simulation results. <b>Right</b>: Stochastic simulation results.</p