Gradient descent optimization in gene regulatory pathways

A model of an integrated immune system pathway in Homo sapiens and its interaction with superantigen producing expression regulatory pathway in Staphylococcus aureus: comparing behavior of pathogen perturbed and unperturbed pathway

Response of an immune system to a pathogen attack depends on the balance between the host immune defense and the virulence of the pathogen. Investigation of molecular interactions between the proteins of a host and a pathogen helps in identifying the pathogenic proteins. It is necessary to understand the dynamics of a normally behaved host system to evaluate the capacity of its immune system upon pathogen attack. In this study, we have compared the behavior of an unperturbed and pathogen perturbed host system. Moreover, we have developed a formalism under Flux Balance Analysis (FBA) for the optimization of conflicting objective functions. We have constructed an integrated pathway system, which includes Staphylococcal Superantigen (SAg) expression regulatory pathway and TCR signaling pathway of Homo sapiens. We have implemented the method on this pathway system and observed the behavior of host signaling molecules upon pathogen attack. The entire study has been divided into six different cases, based on the perturbed/unperturbed conditions. In other words, we have investigated unperturbed and pathogen perturbed human TCR signaling pathway, with different combinations of optimization of concentrations of regulatory and signaling molecules. One of these cases has aimed at finding out whether minimization of the toxin production in a pathogen leads to the change in the concentration levels of the proteins coded by TCR signaling pathway genes in the infected host. Based on the computed results, we have hypothesized that the balance between TCR signaling inhibitory and stimulatory molecules can keep TCR signaling system into resting/stimulating state, depending upon the perturbation. The proposed integrated host-pathogen interaction pathway model has accurately reflected the experimental evidences, which we have used for validation purpose. The significance of this kind of investigation lies in revealing the susceptible interaction points that can take back the Staphylococcal Enterotoxin (SE)-challenged system within the range of normal behavior.

Second order optimization for the inference of gene regulatory pathways

With the increasing availability of experimental data on gene interactions, modeling of gene regulatory pathways has gained special attention. Gradient descent algorithms have been widely used for regression and classification applications. Unfortunately, results obtained after training a model by gradient descent are often highly variable. In this paper, we present a new second order learning rule based on the Newton's method for inferring optimal gene regulatory pathways. Unlike the gradient descent method, the proposed optimization rule is independent of the learning parameter. The flow vectors are estimated based on biomass conservation. A set of constraints is formulated incorporating weighting coefficients. The method calculates the maximal expression of the target gene starting from a given initial gene through these weighting coefficients. Our algorithm has been benchmarked and validated on certain types of functions and on some gene regulatory networks, gathered from literature. The proposed method has been found to perform better than the gradient descent learning. Extensive performance comparison with the extreme pathway analysis method has underlined the effectiveness of our proposed methodology.

An evolutionary firefly algorithm for the estimation of nonlinear biological model parameters

The development of accurate computational models of biological processes is fundamental to computational systems biology. These models are usually represented by mathematical expressions that rely heavily on the system parameters. The measurement of these parameters is often difficult. Therefore, they are commonly estimated by fitting the predicted model to the experimental data using optimization methods. The complexity and nonlinearity of the biological processes pose a significant challenge, however, to the development of accurate and fast optimization methods. We introduce a new hybrid optimization method incorporating the Firefly Algorithm and the evolutionary operation of the Differential Evolution method. The proposed method improves solutions by neighbourhood search using evolutionary procedures. Testing our method on models for the arginine catabolism and the negative feedback loop of the p53 signalling pathway, we found that it estimated the parameters with high accuracy and within a reasonable computation time compared to well-known approaches, including Particle Swarm Optimization, Nelder-Mead, and Firefly Algorithm. We have also verified the reliability of the parameters estimated by the method using an a posteriori practical identifiability test.

Modeling the optimal central carbon metabolic pathways under feedback inhibition using flux balance analysis

Metabolism is a complex process for energy production for cellular activity. It consists of a cascade of reactions that form a highly branched network in which the product of one reaction is the reactant of the next reaction. Metabolic pathways efficiently produce maximal amount of biomass while maintaining a steady-state behavior. The steady-state activity of such biochemical pathways necessarily incorporates feedback inhibition of the enzymes. This observation motivates us to incorporate feedback inhibition for modeling the optimal activity of metabolic pathways using flux balance analysis (FBA). We demonstrate the effectiveness of the methodology on a synthetic pathway with and without feedback inhibition. Similarly, for the first time, the Central Carbon Metabolic (CCM) pathways of Saccharomyces cerevisiae and Homo sapiens have been modeled and compared based on the above understanding. The optimal pathway, which maximizes the amount of the target product(s), is selected from all those obtained by the proposed method. For this, we have observed the concentration of the product inhibited enzymes of CCM pathway and its influence on its corresponding metabolite/substrate. We have also studied the concentration of the enzymes which are responsible for the synthesis of target products. We further hypothesize that an optimal pathway would opt for higher flux rate reactions. In light of these observations, we can say that an optimal pathway should have lower enzyme concentration and higher flux rates. Finally, we demonstrate the superiority of the proposed method by comparing it with the extreme pathway analysis.

Systems biology data analysis methodology in pharmacogenomics

Pharmacogenetics aims to elucidate the genetic factors underlying the individual's response to pharmacotherapy. Coupled with the recent (and ongoing) progress in high-throughput genotyping, sequencing and other genomic technologies, pharmacogenetics is rapidly transforming into pharmacogenomics, while pursuing the primary goals of identifying and studying the genetic contribution to drug therapy response and adverse effects, and existing drug characterization and new drug discovery. Accomplishment of both of these goals hinges on gaining a better understanding of the underlying biological systems; however, reverse-engineering biological system models from the massive datasets generated by the large-scale genetic epidemiology studies presents a formidable data analysis challenge. In this article, we review the recent progress made in developing such data analysis methodology within the paradigm of systems biology research that broadly aims to gain a 'holistic', or 'mechanistic' understanding of biological systems by attempting to capture the entirety of interactions between the components (genetic and otherwise) of the system.