Samik Ghosh

Channel Assignment Strategies for Multiradio Wireless Mesh Networks: Issues and Solutions

Next-generation wireless mobile communications will be driven by converged networks that integrate disparate technologies and services. The wireless mesh network is envisaged to be one of the key components in the converged networks of the future, providing flexible high- bandwidth wireless backhaul over large geographical areas. While single radio mesh nodes operating on a single channel suffer from capacity constraints, equipping mesh routers with multiple radios using multiple nonoverlap- ping channels can significantly alleviate the capacity problem and increase the aggregate bandwidth available to the network. However, the assignment of channels to the radio interfaces poses significant challenges. The goal of channel assignment algorithms in multiradio mesh networks is to minimize interference while improving the aggregate network capacity and maintaining the connectivity of the network. In this article we examine the unique constraints of channel assignment in wireless mesh networks and identify the key factors governing assignment schemes, with particular reference to interference, traffic patterns, and multipath connectivity. After presenting a taxonomy of existing channel assignment algorithms for WMNs, we describe a new channel assignment scheme called MesTiC, which incorporates the mesh traffic pattern together with connectivity issues in order to minimize interference in multi- radio mesh networks.

GaMa: an evolutionary algorithmic approach for the design of mesh-based radio access networks

Wireless mesh based access networks are destined to play a pivotal role in next generation broadband systems. With the proliferation of mesh networks, a key issue for network designers is the design of an optimal mesh topology which minimizes cost while maintaining carrier-class features. In this paper, we formulate the design of an optimal mesh, taking network deployment cost, topological properties and carrier-grade reliability into account. Next, we present a genetic algorithm based algorithm (GaMa) for mesh topology design. We show that GaMa is capable of determining a generic mesh topology with carrier-class network features. The performance of the algorithm is compared with existing mesh topologies and gives improved results without the constraints of maintaining a regular topology

iSimBioSys: a discrete event simulation platform for 'in silico' study of biological systems

With the availability of huge databases cataloguing the various molecular parts of complex biological systems, researchers from multiple disciplines have focused on developing modeling and simulation tools for studying the variability of cellular behavior at a system level - encompassing the dynamics arising from many species of interacting molecules. In this work, we present a system engineering approach to model biological processes. In this approach, a biological process is modeled as a collection of interacting functions driven in time by a set of discrete events. We focus on the discrete event simulation platform, called iSimBioSys, which we have developed for studying the dynamics of cellular processes in silico. As a test-bed for studying our approach we model the two component PhoPQ system, responsible for the expression of several virulence genes in Salmonella Typhimurium. We analyzed the effect of extra cellular magnesium on the behavioral dynamics of this pathway using our framework and compared the results with an experimental system. We also analyze the performance of iSimBioSys, based on the model biological system, in terms of system usage and response.

An analytical model to estimate the time taken for cytoplasmic reactions for stochastic simulation of complex biological systems

The complexity of biological systems motivates the use of a computer or in silico stochastic event based modeling approach to better identify the dynamic interactions of different processes in the system. This requires the computation of the time taken by different events in the system based on their biological functions and corresponding environment. One such important event is the reactions between the molecules inside the cytoplasm of a cell where the reaction environment is highly chaotic. We present a mathematical formulation for the estimation of the reaction time between two molecules within a cell based on the system state assuming that the reactant molecules enter the system one at a time to initiate reactions. We derive expressions for the average and second moment of the time for reaction to be used by our stochastic event-based simulation. Unlike rate equations, the proposed model does not require the assumption of concentration stability for multiple molecule reactions. The reaction time estimate is considered to be a random variable that suits the stochastic event based simulation method.

Modeling the Stochastic Dynamics of Gene Expression in Single Cells: A Birth and Death Markov Chain Analysis

Fluctuations in protein number (noise) caused by the stochasticity in gene expression plays a central role in the dynamic behavior of cellular pathways. Deterministic models capture average cell population behavior and are limited in their relevance in modeling stochastic deviations of gene expression in single cells. In this paper, we develop a birth and death Markov chain model to capture the discrete molecular events of transcription and translation in prokaryotic cells. We derive mathematical models for the expression `burst frequency distribution as well as the number of protein molecules per burst. We validate our stochastic models with recent single cell experiments on the lacZ gene in Escherichia Coli. Further, we build a discrete-event stochastic simulation system to study the transient dynamics of lacZ gene expression, quantifying the role of promoters in controlling the `burstiness of protein synthesis.

Stochastic modeling of cytoplasmic reactions in complex biological systems

The use of “in silico” stochastic event based modeling can identify the dynamic interactions of different processes in a complex biological system. This requires the computation of the time taken by different events in the system based on their biological functions. One such important event is the reactions between the molecules inside the cytoplasm of a cell. We present a mathematical formulation for the estimation of the reaction time between two molecules within a cell based on the system state. We derive expressions for the average and second moment of the time for reaction to be used by our stochastic event-based simulation. Unlike rate equations, the proposed model does not require the assumption of concentration stability for multiple molecule reactions.

A Stochastic model to estimate the time taken for Protein-Ligand Docking

Quantum mechanics and molecular dynamic simulation provide important insights into structural configurations and molecular interaction data today. To extend this atomic/molecular level capability to system level understanding, we propose an in silico stochastic event based simulation technique. This simulation characterizes the time domain events as random variables represented by probabilities. This random variable is called the execution time and is different for different biological functions (e.g. the protein-ligand docking time). The simulation model requires fast computational speed and we need a simple transformation of the energy plane dynamics of the molecular behavior to the information plane. We use a variation of the collision theory model to get this transformation. The velocity distribution and energy threshold are the two parameters that capture the effects of the energy dynamics within the cell in our model. We use this technique to approximately determine the time required for the ligand-protein docking event. The model is parametric and uses the structural configurations of the ligands, proteins and the binding mechanism. The numerical results for the first moment show good correspondence with experimental results and demonstrate the efficacy of our model. The model is fast in computing and is less dependent on experimental data like rate constants

Discrete diffusion models to study the effects of Mg2+ concentration on the PhoPQ signal transduction system.

BackgroundThe challenge today is to develop a modeling and simulation paradigm that integrates structural, molecular and genetic data for a quantitative understanding of physiology and behavior of biological processes at multiple scales. This modeling method requires techniques that maintain a reasonable accuracy of the biological process and also reduces the computational overhead. This objective motivates the use of new methods that can transform the problem from energy and affinity based modeling to information theory based modeling. To achieve this, we transform all dynamics within the cell into a random event time, which is specified through an information domain measure like probability distribution. This allows us to use the “in silico” stochastic event based modeling approach to find the molecular dynamics of the system.ResultsIn this paper, we present the discrete event simulation concept using the example of the signal transduction cascade triggered by extra-cellular Mg2+ concentration in the two component PhoPQ regulatory system of Salmonella Typhimurium. We also present a model to compute the information domain measure of the molecular transport process by estimating the statistical parameters of inter-arrival time between molecules/ions coming to a cell receptor as external signal. This model transforms the diffusion process into the information theory measure of stochastic event completion time to get the distribution of the Mg2+ departure events. Using these molecular transport models, we next study the in-silico effects of this external trigger on the PhoPQ system.ConclusionsOur results illustrate the accuracy of the proposed diffusion models in explaining the molecular/ionic transport processes inside the cell. Also, the proposed simulation framework can incorporate the stochasticity in cellular environments to a certain degree of accuracy. We expect that this scalable simulation platform will be able to model more complex biological systems with reasonable accuracy to understand their temporal dynamics.

Holding time estimation for reactions in stochastic event-based simulation of complex biological systems

Abstract The complexity of biological systems motivate the use of an “in silico” stochastic discrete event simulation methodology. This method can incorporate the effects of the recently identified stochastic resonance of a biological system and is computationally capable to process the dynamic interactions of different pathways in the cell. The main requirement for this technique is the event time models for the discrete events of the biological system. Currently such models do not exist for biological functions and this paper proposes one such event model – the biochemical reactions between the molecules inside the cytoplasm of a cell where the reaction environment is highly chaotic. We present a mathematical formulation for the estimation of the reaction time between two molecules within a cell based on the discrete system states. In particular, we propose two models: (1) The reactant molecules enter the system one at a time to initiate reactions, and (2) The reactant molecules arrive in batches of a certain size. We derive expressions for the average and second moment of the time for reaction. This random time is used by our stochastic event-based simulation. Unlike rate equations, the proposed model does not require the assumption of concentration stability for multiple molecule reactions. Also the models incorporate many structural and functional parameters of the biological function, that are lacking in the currently used rate equation model. The parametric nature of the model makes it generic and useful for diverse studies.

Modeling protein-DNA binding time in Stochastic Discrete Event Simulation of Biological Processes

This paper presents a parametric model to estimate the DNA-protein binding time using the DNA and protein structures and details of the binding site. To understand the stochastic behavior of biological systems, we propose an in silico stochastic event based simulation that determines the temporal dynamics of different molecules. This paper presents a parametric model to determine the execution time of one biological function (i.e. simulation event): protein-DNA binding by abstracting the function as a stochastic process of microlevel biological events using probability measure. This probability is coarse grained to estimate the stochastic behavior of the biological function. Our model considers the structural configurations of the DNA, proteins and the actual binding mechanism. We use a collision theory based approach to transform the thermal and concentration gradients of this biological process into the probability measure of DNA-protein binding event. This information theoretic approach significantly removes the complexity of the classical protein sliding along the DNA model, improves the speed of computation and can bypass the speed-stability paradox. This model can produce acceptable estimates of DNA-protein binding time to be used by our event-based stochastic system simulator where the higher order (more than second order statistics) uncertainties can be ignored. The results show good correspondence with available experimental estimates. The model depends very little on experimentally generated rate constants