A fine-grain time-sharing Time Warp system

Although Parallel Discrete Event Simulation (PDES) platforms relying on the Time Warp (optimistic) synchronization protocol already allow for exploiting parallelism, several techniques have been proposed to further favor performance. Among them we can mention optimized approaches for state restore, as well as techniques for load balancing or (dynamically) controlling the speculation degree, the latter being specifically targeted at reducing the incidence of causality errors leading to waste of computation. However, in state of the art Time Warp systems, events’ processing is not preemptable, which may prevent the possibility to promptly react to the injection of higher priority (say lower timestamp) events. Delaying the processing of these events may, in turn, give rise to higher incidence of incorrect speculation. In this article we present the design and realization of a fine-grain time-sharing Time Warp system, to be run on multi-core Linux machines, which makes systematic use of event preemption in order to dynamically reassign the CPU to higher priority events/tasks. Our proposal is based on a truly dual mode execution, application vs platform, which includes a timer-interrupt based support for bringing control back to platform mode for possible CPU reassignment according to very fine grain periods. The latter facility is offered by an ad-hoc timer-interrupt management module for Linux, which we release, together with the overall time-sharing support, within the open source ROOT-Sim platform. An experimental assessment based on the classical PHOLD benchmark and two real world models is presented, which shows how our proposal effectively leads to the reduction of the incidence of causality errors, as compared to traditional Time Warp, especially when running with higher degrees of parallelism

An ultrasensitive sorting mechanism for EGF receptor endocytosis

Background The EGF receptor has been shown to internalize via clathrin-independent endocytosis (CIE) in a ligand concentration dependent manner. From a modeling point of view, this resembles an ultrasensitive response, which is the ability of signaling networks to suppress a response for low input values and to increase to a pre-defined level for inputs exceeding a certain threshold. Several mechanisms to generate this behaviour have been described theoretically, the underlying assumptions of which, however, have not been experimentally demonstrated for the EGF receptor internalization network. Results Here, we present a mathematical model of receptor sorting into alternative pathways that explains the EGF-concentration dependent response of CIE. The described mechanism involves a saturation effect of the dominant clathrin-dependent endocytosis pathway and implies distinct steady-states into which the system is forced for low vs high EGF stimulations. The model is minimal since no experimentally unjustified reactions or parameter assumptions are imposed. We demonstrate the robustness of the sorting effect for large parameter variations and give an analytic derivation for alternative steady-states that are reached. Further, we describe extensibility of the model to more than two pathways which might play a role in contexts other than receptor internalization. Conclusions Our main result is that a scenario where different endocytosis routes consume the same form of receptor corroborates the observation of a clear-cut, stimulus dependent sorting. This is especially important since a receptor modification discriminating between the pathways has not been found. The model is not restricted to EGF receptor internalization and might account for ultrasensitivity in other cellular contexts

Modeling recursive RNA interference.

An important application of the RNA interference (RNAi) pathway is its use as a small RNA-based regulatory system commonly exploited to suppress expression of target genes to test their function in vivo. In several published experiments, RNAi has been used to inactivate components of the RNAi pathway itself, a procedure termed recursive RNAi in this report. The theoretical basis of recursive RNAi is unclear since the procedure could potentially be self-defeating, and in practice the effectiveness of recursive RNAi in published experiments is highly variable. A mathematical model for recursive RNAi was developed and used to investigate the range of conditions under which the procedure should be effective. The model predicts that the effectiveness of recursive RNAi is strongly dependent on the efficacy of RNAi at knocking down target gene expression. This efficacy is known to vary highly between different cell types, and comparison of the model predictions to published experimental data suggests that variation in RNAi efficacy may be the main cause of discrepancies between published recursive RNAi experiments in different organisms. The model suggests potential ways to optimize the effectiveness of recursive RNAi both for screening of RNAi components as well as for improved temporal control of gene expression in switch off-switch on experiments

Switching and diffusion models for gene regulation networks

We analyze a hierarchy of three regimes for modeling gene regulation. The most complete model is a continuous time, discrete state space, Markov jump process. An intermediate 'switch plus diffusion' model takes the form of a stochastic differential equation driven by an independent continuous time Markov switch. In the third 'switch plus ODE' model the switch remains but the diffusion is removed. The latter two models allow for multi-scale simulation where, for the sake of computational efficiency, system components are treated differently according to their abundance. The 'switch plus ODE' regime was proposed by Paszek (Modeling stochasticity in gene regulation: characterization in the terms of the underlying distribution function, Bulletin of Mathematical Biology, 2007), who analyzed the steady state behavior, showing that the mean was preserved but the variance only approximated that of the full model. Here, we show that the tools of stochastic calculus can be used to analyze first and second moments for all time. A technical issue to be addressed is that the state space for the discrete-valued switch is infinite. We show that the new 'switch plus diffusion' regime preserves the biologically relevant measures of mean and variance, whereas the 'switch plus ODE' model uniformly underestimates the variance in the protein level. We also show that, for biologically relevant parameters, the transient behaviour can differ significantly from the steady state, justifying our time-dependent analysis. Extra computational results are also given for a protein dimerization model that is beyond the scope of the current analysis