Flux Analysis in Process Models via Causality

We present an approach for flux analysis in process algebra models of biological systems. We perceive flux as the flow of resources in stochastic simulations. We resort to an established correspondence between event structures, a broadly recognised model of concurrency, and state transitions of process models, seen as Petri nets. We show that we can this way extract the causal resource dependencies in simulations between individual state transitions as partial orders of events. We propose transformations on the partial orders that provide means for further analysis, and introduce a software tool, which implements these ideas. By means of an example of a published model of the Rho GTP-binding proteins, we argue that this approach can provide the substitute for flux analysis techniques on ordinary differential equation models within the stochastic setting of process algebras

The correlation between gemcitabine efficacy and the ratio of dCK and RR.

<p>The correlation between gemcitabine efficacy, measured as and the ratio of dCK and RR concentrations, given with , with respect to the experiments reported in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0050176#pone.0050176-Giovannetti2" target="_blank">[27]</a>.</p

Gemcitabine biochemical machinery.

<p>The biotransformation and pharmacologic action of dFdC and its metabolites. The different arrows, with respect to the legend on the right, are () transport into cell (by a nucleoside transporter hENT1); () enzymatic reaction (where dCK is the enzyme); () inhibition (of dCK by binding with dCTP); () synthesis (of CDP); () DNA incorporation (of dFdC-TP). See the text for or a more detailed description.</p

Intracellular concentration of observed metabolites.

<p>The values have been taken from the concentration profiles reported in [?], where the units are given in pico-moles/mg of cellular protein.</p

Estimated parameters.

<p>Estimated parameters.</p

Sensitivity to dCK, dCMPD and RR inhibitions.

<p>The plots displaying the area under the curve (AUC) for dFdC-TP (top row) and dCTP (bottom row) that result from the simulations with respect to different rate values. At every column, there are plots for different RR inhibition association rates, varied from to with an order of magnitude at each step. In each plot, the association rates of the dCK and dCMPD inhibitions are varied from to , given in logarithmic scale. The dissociation rates are set to . A scaling factor of is used for intrinsic noise, which is observed at the dCTP plots where RR inhibition rate values are less than .</p

The correlation between gemcitabine efficacy and the ratio of dCK and RR in the simulations.

<p>The correlation between gemcitabine efficacy measured as and the ratio of dCK and RR, given with with respect to simulations with our model.</p

Observed number of molecules of intracellular metabolites.

<p>Number of molecule obtained by a conversion of the concentration values given in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0050176#pone-0050176-t001" target="_blank">Table 1</a>.</p

Sensitivity to paired inhibitions.

<p>The plots displaying the area under the curve (AUC) for dFdC-TP that result from the simulations where the association rates of the inhibitions are varied from to , given in logarithmic scale. The dissociation rates for the inhibitions are set to . At the simulations for the plot on the left, dCMPD inhibition rate is set to zero, and the dCK and RR are varied. At the middle plot, dCK inhibition rate is set to zero, and at the plot on the right RR inhibition rate is set to zero.</p