Statistical ensemble analysis for simulating extrinsic noise-driven response in NF-κB signaling networks.

BACKGROUND: Gene expression profiles and protein dynamics in single cells have a large cell-to-cell variability due to intracellular noise. Intracellular fluctuations originate from two sources: intrinsic noise due to the probabilistic nature of biochemical reactions and extrinsic noise due to randomized interactions of the cell with other cellular systems or its environment. Presently, there is no systematic parameterization and modeling scheme to simulate cellular response at the single cell level in the presence of extrinsic noise. RESULTS: In this paper, we propose a novel statistical ensemble method to simulate the distribution of heterogeneous cellular responses in single cells. We capture the effects of extrinsic noise by randomizing values of the model parameters. In this context, a statistical ensemble is a large number of system replicates, each with randomly sampled model parameters from biologically feasible intervals. We apply this statistical ensemble approach to the well-studied NF-κB signaling system. We predict several characteristic dynamic features of NF-κB response distributions; one of them is the dosage-dependent distribution of the first translocation time of NF-κB. CONCLUSION: The distributions of heterogeneous cellular responses that our statistical ensemble formulation generates reveal the effect of different cellular conditions, e.g., effects due to wild type versus mutant cells or between different dosages of external stimulants. Distributions generated in the presence of extrinsic noise yield valuable insight into underlying regulatory mechanisms, which are sometimes otherwise hidden.

Understanding virulence mechanisms in M. tuberculosis infection via a circuit-based simulation framework.

Tuberculosis (TB), caused by the bacterium Mycobacterium tuberculosis (Mtb), is a growing international health crisis. Mtb is able to persist in host tissues in a non-replicating persistent (NRP) or latent state. This presents a challenge in the treatment of TB. Latent TB can re-activate in 10% of individuals with normal immune systems, higher for those with compromised immune systems. A quantitative understanding of latency-associated virulence mechanisms may help researchers develop more effective methods to battle the spread and reduce TB associated fatalities. Leveraging BioXyce's ability to simulate whole-cell and multi-cellular systems we are developing a circuit-based framework to investigate the impact of pathogenicity-associated pathways on the latency/reactivation phase of tuberculosis infection. We discuss efforts to simulate metabolic pathways that potentially impact the ability of Mtb to persist within host immune cells. We demonstrate how simulation studies can provide insight regarding the efficacy of potential anti-TB agents on biological networks critical to Mtb pathogenicity using a systems chemical biology approach.

Sensitivity analysis of a computational model of the IKK NF-kappaB IkappaBalpha A20 signal transduction network.

The NF-kappaB signaling network plays an important role in many different compartments of the immune system during immune activation. Using a computational model of the NF-kappaB signaling network involving two negative regulators, IkappaBalpha and A20, we performed sensitivity analyses with three different sampling methods and present a ranking of the kinetic rate variables by the strength of their influence on the NF-kappaB signaling response. We also present a classification of temporal-response profiles of nuclear NF-kappaB concentration into six clusters, which can be regrouped to three biologically relevant clusters. Last, we constructed a reduced network of the IKK-NF-kappaB-IkappaBalpha-A20 signal transduction based on the ranking.

Bacteriophage-mediated competition in Bordetella bacteria.

Apparent competition between species is believed to be one of the principal driving forces that structure ecological communities, although the precise mechanisms have yet to be characterized. Here we develop a model system that isolates phage-mediated interactions by neutralizing resource competition with a large excess of nutrients, and consists of two genetically identical Bordetella strains that differ only in that one is the carrier of phage and the other is susceptible to the phage. We observe and quantify the competitive advantage of the bacterial strain bearing the prophage in both invading and in resisting invasion by the bacterial strain sensitive to the phage, and use our experimental measurements to develop a mathematical model of phage-mediated competition. The model predicts, and experimental evidence confirms, that the competitive advantage conferred by the lysogenic phage depends only on the phage pathology on the sensitive bacterial strain and is independent of other phage and host parameters, such as the infection-causing contact rate, the spontaneous and infection-induced lysis rates and the phage burst size. This work combines experimental and mathematical approaches to the study of phage-driven competition, and provides an experimentally tested framework for evaluation of the effects of pathogens/parasites on interspecific competition.

Population dynamics in spatially heterogeneous systems with drift: The generalized contact process.

We investigate the time evolution and stationary states of a stochastic, spatially discrete, population model (contact process) with spatial heterogeneity and imposed drift (wind) in one and two dimensions. We consider in particular a situation in which space is divided into two regions: an oasis and a desert (low and high death rates). Carrying out computer simulations we find that the population in the (quasi) stationary state will be zero, localized, or delocalized, depending on the values of the drift and other parameters. The phase diagram is similar to that obtained by Nelson and coworkers from a deterministic, spatially continuous model of a bacterial population undergoing convection in a heterogeneous medium.

Pair approximation of the stochastic susceptible-infected-recovered-susceptible epidemic model on the hypercubic lattice.

We investigate the time evolution and steady states of the stochastic susceptible-infected-recovered-susceptible (SIRS) epidemic model on one- and two-dimensional lattices. We compare the behavior of this system, obtained from computer simulations, with those obtained from the mean-field approximation (MFA) and pair approximation (PA). The former (latter) approximates higher-order moments in terms of first- (second-) order ones. We find that the PA gives consistently better results than the MFA. In one dimension, the improvement is even qualitative.

Behavior of susceptible-infected-susceptible epidemics on heterogeneous networks with saturation.

We investigate saturation effects in susceptible-infected-susceptible models of the spread of epidemics in heterogeneous populations. The structure of interactions in the population is represented by networks with connectivity distribution P(k), including scale-free (SF) networks with power law distributions P(k) approximately k(-gamma). Considering cases where the transmission of infection between nodes depends on their connectivity, we introduce a saturation function C(k) which reduces the infection transmission rate lambda across an edge going from a node with high connectivity k. A mean-field approximation with the neglect of degree-degree correlation then leads to a finite threshold lambda(c) >0 for SF networks with 2