Reaction-Diffusion Modeling ERK- and STAT-Interaction Dynamics

<p/> <p>The modeling of the dynamics of interaction between ERK and STAT signaling pathways in the cell needs to establish the biochemical diagram of the corresponding proteins interactions as well as the corresponding reaction-diffusion scheme. Starting from the verbal description available in the literature of the cross talk between the two pathways, a simple diagram of interaction between ERK and STAT5a proteins is chosen to write corresponding kinetic equations. The dynamics of interaction is modeled in a form of two-dimensional nonlinear dynamical system for ERK&#8212;and STAT5a &#8212;protein concentrations. Then the spatial modeling of the interaction is accomplished by introducing an appropriate diffusion-reaction scheme. The obtained system of partial differential equations is analyzed and it is argued that the possibility of Turing bifurcation is presented by loss of stability of the homogeneous steady state and forms dissipative structures in the ERK and STAT interaction process. In these terms, a possible scaffolding effect in the protein interaction is related to the process of stabilization and destabilization of the dissipative structures (pattern formation) inherent to the model of ERK and STAT cross talk.</p

Qualitative Modelling of Quasi-homogeneous Effects in ERK and STAT Interaction Dynamics

On the basis of qualitative analysis of author's model published in previous paper, the stability and temporal behaviour of quasi-homogeneous distributions of ERK-protein concentrations are analyzed in terms of corresponding reaction-diffusion problem. The stable quasi-homogeneous distributions are treated as a dynamical basis of pathway compartmentalization. It is also shown, that a crowding effect exists in the form of loss of pathway stability. An experimentally verifiable issue for possible existence of protein scaffolding mechanism is derived on the basis of its qualitative correspondence with the pattern formation and molecular crowding effects inherent to the considered model. Moreover, it is demonstrated, that the predicted ERK and STAT pathway instability can be interpreted as traveling wave propagation of molecular concentration drop and jump from the nucleus membrane to the cell one and vice versa

Modeling Cell-to-Cell Communication Networks Using Response-Time Distributions.

Cell-to-cell communication networks have critical roles in coordinating diverse organismal processes,&nbsp;such as tissue development or immune cell response. However, compared with intracellular signal transduction networks, the function and engineering principles of cell-to-cell communication networks are far less understood. Major complications include: cells are themselves regulated by complex intracellular signaling networks; individual cells are heterogeneous; and output of any one cell can recursively become an additional input signal to other cells. Here, we make use of a framework that treats intracellular signal transduction networks as "black boxes" with characterized input-to-output response relationships. We study simple cell-to-cell communication circuit motifs and find conditions that generate bimodal responses in time, as well as mechanisms for independently controlling synchronization and delay of cell-population responses. We apply our modeling approach to explain otherwise puzzling data on cytokine secretion onset times in T&nbsp;cells. Our approach can be used to predict communication network structure using experimentally accessible input-to-output measurements and without detailed knowledge of intermediate steps

Spots & stripes: pleomorphic patterning of stem cells via p-ERK-depenendent cell chemotaxis shown by feather morphogenesis & mathematical simulation

A key issue in stem cell biology is the differentiation of homogeneous stem cells towards different fates which are also organized into desired configurations. Little is known about the mechanisms underlying the process of periodic patterning. Feather explants offer a fundamental and testable model in which multi-potential cells are organized into hexagonally arranged primordia and the spacing between primordia. Previous work explored roles of a Turing reaction–diffusion mechanism in establishing chemical patterns. Here we show that a continuum of feather patterns, ranging from stripes to spots, can be obtained when the level of p-ERK activity is adjusted with chemical inhibitors. The patterns are dose-dependent, tissue stage-dependent, and irreversible. Analyses show that ERK activity-dependent mesenchymal cell chemotaxis is essential for converting micro-signaling centers into stable feather primordia. A mathematical model based on short-range activation, long-range inhibition, and cell chemotaxis is developed and shown to simulate observed experimental results. This generic cell behavior model can be applied to model stem cell patterning behavior at large

Extended Kalman Filter for Estimation of Parameters in Nonlinear State-Space Models of Biochemical Networks

It is system dynamics that determines the function of cells, tissues and organisms. To develop mathematical models and estimate their parameters are an essential issue for studying dynamic behaviors of biological systems which include metabolic networks, genetic regulatory networks and signal transduction pathways, under perturbation of external stimuli. In general, biological dynamic systems are partially observed. Therefore, a natural way to model dynamic biological systems is to employ nonlinear state-space equations. Although statistical methods for parameter estimation of linear models in biological dynamic systems have been developed intensively in the recent years, the estimation of both states and parameters of nonlinear dynamic systems remains a challenging task. In this report, we apply extended Kalman Filter (EKF) to the estimation of both states and parameters of nonlinear state-space models. To evaluate the performance of the EKF for parameter estimation, we apply the EKF to a simulation dataset and two real datasets: JAK-STAT signal transduction pathway and Ras/Raf/MEK/ERK signaling transduction pathways datasets. The preliminary results show that EKF can accurately estimate the parameters and predict states in nonlinear state-space equations for modeling dynamic biochemical networks

A Heterogeneous And Multiscale Modeling Framework To Develop Patient-Specific Pharmacodynamic Systems Models In Cancer

Systems models of key signaling pathways in cancer have been extensively used to under- stand and explore the mechanisms of action of drugs and growth factors on cancer cell signaling. In general, such models predict the effect of environmental stimuli (both chemical such as for e.g., growth factor and drugs as well as mechanical such as matrix stiffness) in terms of activities of proteins such as ERK or AKT which are important regulators of cell fate decisions. Although such models have helped uncover important emergent properties of signaling networks such as ultrasensitivity, bistability, and oscillations, they miss many key features that would make them useful in a clinical setting. 1) The predictions of activity of proteins such as ERK or AKT cannot be directly translated into a clinically useful parameter such as cell kill rate. 2) They don’t work as well when there are multiple biological processes operating under different time and length scales such as receptor-based signaling (4-6 hours) and cell cycle (24-48 hours). 3) The parameter space of such models often exhibits sloppy/stiff character which affects the accuracy of predictions and the robustness of these models. Apart from single-cell systems models of signaling, pharmacokinetic and cell population-based pharmacodynamic models are also extensively used to predict the efficacy of a particular therapy in a clinical setting. However, there are no direct or consistent ways of incorporating patient-specific gene/protein expression data in these models. This thesis describes the development and applications of a multiscale and multiparadigm framework for signaling and pharmacodynamic models that helps us address some of the above short- comings. First two single scale systems models are described which introduces methods of exploration of parameter space and their effect on model predictions. Then the multiscale framework is described and it is applied to two different cancers - Prostate Adenocarcinoma and Nephroblastoma (Wilm’s Tumor). Special mathematical techniques were used to de- velop algorithms that can integrate models of disparate time scales and time resolutions (continuous vs. discrete-time). Such multiscale modeling frameworks have great potential in the field of personalized medicine and in understanding the physics of cancer taking into account the biology of the cells

Mathematical modeling of intracellular signaling pathways

Dynamic modeling and simulation of signal transduction pathways is an important topic in systems biology and is obtaining growing attention from researchers with experimental or theoretical background. Here we review attempts to analyze and model specific signaling systems. We review the structure of recurrent building blocks of signaling pathways and their integration into more comprehensive models, which enables the understanding of complex cellular processes. The variety of mechanisms found and modeling techniques used are illustrated with models of different signaling pathways. Focusing on the close interplay between experimental investigation of pathways and the mathematical representations of cellular dynamics, we discuss challenges and perspectives that emerge in studies of signaling systems

Unraveling the intricacies of spatial organization of the ErbB receptors and downstream signaling pathways

Faced with the complexity of diseases such as cancer which has 1012 mutations, altering gene expression, and disrupting regulatory networks, there has been a paradigm shift in the biological sciences and what has emerged is a much more quantitative field of biology. Mathematical modeling can aid in biological discovery with the development of predictive models that provide future direction for experimentalist. In this work, I have contributed to the development of novel computational approaches which explore mechanisms of receptor aggregation and predict the effects of downstream signaling. The coupled spatial non-spatial simulation algorithm, CSNSA is a tool that I took part in developing, which implements a spatial kinetic Monte Carlo for capturing receptor interactions on the cell membrane with Gillespies stochastic simulation algorithm, SSA, for temporal cytosolic interactions. Using this framework we determine that receptor clustering significantly enhances downstream signaling. In the next study the goal was to understand mechanisms of clustering. Cytoskeletal interactions with mobile proteins are known to hinder diffusion. Using a Monte Carlo approach we simulate these interactions, determining at what cytoskeletal distribution and receptor concentration optimal clustering occurs and when it is inhibited. We investigate oligomerization induced trapping to determine mechanisms of clustering, and our results show that the cytoskeletal interactions lead to receptor clustering. After exploring the mechanisms of clustering we determine how receptor aggregation effects downstream signaling. We further proceed by implementing the adaptively coarse grained Monte Carlo, ACGMC to determine if \u27receptor-sharing\u27 occurs when receptors are clustered. In our proposed \u27receptor-sharing\u27 mechanism a cytosolic species binds with a receptor then disassociates and rebinds a neighboring receptor. We tested our hypothesis using a novel computational approach, the ACGMC, an algorithm which enables the spatial temporal evolution of the system in three dimensions by using a coarse graining approach. In this framework we are modeling EGFR reaction-diffusion events on the plasma membrane while capturing the spatial-temporal dynamics of proteins in the cytosol. From this framework we observe \u27receptor-sharing\u27 which may be an important mechanism in the regulation and overall efficiency of signal transduction. In summary, I have helped to develop predictive computational tools that take systems biology in a new direction.\u2

Quantification of signaling networks

Studies in living system in the past several decades have generated qualitative understanding of the molecular interactions resulting in large networks. These networks were essentially deciphered by breaking the components of a cell through a reductionist approach. Biological networks comprising of interactions between genes, proteins and metabolites co-ordinate in the regulation of cellular processes. However, understanding the cellular function also requires quantitative information including network dynamics, which results due to an inherent design principle embedded in the network. Interactions within the network are well organized to form a definite regulatory structure, which in turn exhibits different emergent properties. The property of the network helps the cell to achieve the desired phenotypic state in a controlled manner. The dynamics of the network or the relationship between network structure and cellular behavior cannot be understood intuitively from the interaction map of the network. Computational methods can now be employed to study these networks at system level. The field of systems biology looks at integrating the interaction maps obtained through molecular biological approach. Various studies at the system level have been reported for pathways namely chemotactic response in bacteria, cell cycle and osmotic signaling in yeast, growth factor stimulated signaling pathways in mammals. This review focuses on understanding signaling networks with the help of mathematical models