Sandip Kar

Exploring the roles of noise in the eukaryotic cell cycle

The DNA replication–division cycle of eukaryotic cells is controlled by a complex network of regulatory proteins, called cyclin-dependent kinases, and their activators and inhibitors. Although comprehensive and accurate deterministic models of the control system are available for yeast cells, reliable stochastic simulations have not been carried out because the full reaction network has yet to be expressed in terms of elementary reaction steps. As a first step in this direction, we present a simplified version of the control system that is suitable for exact stochastic simulation of intrinsic noise caused by molecular fluctuations and extrinsic noise because of unequal division. The model is consistent with many characteristic features of noisy cell cycle progression in yeast populations, including the observation that mRNAs are present in very low abundance (≈1 mRNA molecule per cell for each expressed gene). For the control system to operate reliably at such low mRNA levels, some specific mRNAs in our model must have very short half-lives (<1 min). If these mRNA molecules are longer-lived (perhaps 2 min), then the intrinsic noise in our simulations is too large, and there must be some additional noise suppression mechanisms at work in cells.

Heterogeneous kinetics of AKT signaling in individual cells are accounted for by variable protein concentration

In most solid cancers, cells harboring oncogenic mutations represent only a sub-fraction of the entire population. Within this sub-fraction the expression level of mutated proteins can vary significantly due to cellular variability limiting the efficiency of targeted therapy. To address the causes of the heterogeneity, we performed a systematic analysis of one of the most frequently mutated pathways in cancer cells, the phosphatidylinositol 3 kinase (PI3K) signaling pathway. Among others PI3K signaling is activated by the hepatocyte growth factor (HGF) that regulates proliferation of hepatocytes during liver regeneration but also fosters tumor cell proliferation. HGF-mediated responses of PI3K signaling were monitored both at the single cell and cell population level in primary mouse hepatocytes and in the hepatoma cell line Hepa1_6. Interestingly, we observed that the HGF-mediated AKT responses at the level of individual cells is rather heterogeneous. However, the overall average behavior of the single cells strongly resembled the dynamics of AKT activation determined at the cell population level. To gain insights into the molecular cause for the observed heterogeneous behavior of individual cells, we employed dynamic mathematical modeling in a stochastic framework. Our analysis demonstrated that intrinsic noise was not sufficient to explain the observed kinetic behavior, but rather the importance of extrinsic noise has to be considered. Thus, distinct from gene expression in the examined signaling pathway fluctuations of the reaction rates has only a minor impact whereas variability in the concentration of the various signaling components even in a clonal cell population is a key determinant for the kinetic behavior.

Exact solutions of Fisher and Burgers equations with finite transport memory

The Fisher and Burgers equations with finite memory transport, describing reaction–diffusion and convection–diffusion processes, respectively have recently attracted a lot of attention in the context of chemical kinetics, mathematical biology and turbulence. We show here that they admit exact solutions. While the speed of the travelling wavefront is dependent on the relaxation time in the Fisher equation, memory effects significantly smoothen out the shock wave nature of the Burgers solution, without any influence on the corresponding wave speed. We numerically analyse the ansatz for the exact solution and show that for the reaction–diffusion system the strength of the reaction term must be moderate enough not to exceed a critical limit to allow a travelling wave solution to exist for appreciable finite memory effect.

Mobility-induced instability and pattern formation in a reaction-diffusion system

Ions undergoing a reaction-diffusion process are susceptible to electric field. We show that a constant external field may induce a kind of instability on the state stabilized by diffusion in a reaction-diffusion system giving rise to formation of pattern even when the diffusion coefficients of the reactants are equal. The origin of the pattern is due to the difference in mobilities of the two species and is thus markedly different from that of deformed Turing pattern in presence of the field. While this differential flow instability had been shown earlier to result in traveling waves, we realize in the context of stationary pattern formation in a typical reaction-diffusion-advective system. Our analysis is based on a numerical simulation of a generic model on a two-dimensional domain.

Class of self-limiting growth models in the presence of nonlinear diffusion.

The source term in a reaction-diffusion system, in general, does not involve explicit time dependence. A class of self-limiting growth models dealing with animal and tumor growth and bacterial population in a culture, on the other hand, are described by kinetics with explicit functions of time. We analyze a reaction-diffusion system to study the propagation of spatial front for these models.

Protein abundance of AKT and ERK pathway components governs cell type-specific regulation of proliferation

Signaling through the AKT and ERK pathways controls cell proliferation. However, the integrated regulation of this multistep process, involving signal processing, cell growth and cell cycle progression, is poorly understood. Here, we study different hematopoietic cell types, in which AKT and ERK signaling is triggered by erythropoietin (Epo). Although these cell types share the molecular network topology for pro‐proliferative Epo signaling, they exhibit distinct proliferative responses. Iterating quantitative experiments and mathematical modeling, we identify two molecular sources for cell type‐specific proliferation. First, cell type‐specific protein abundance patterns cause differential signal flow along the AKT and ERK pathways. Second, downstream regulators of both pathways have differential effects on proliferation, suggesting that protein synthesis is rate‐limiting for faster cycling cells while slower cell cycles are controlled at the G1‐S progression. The integrated mathematical model of Epo‐driven proliferation explains cell type‐specific effects of targeted AKT and ERK inhibitors and faithfully predicts, based on the protein abundance, anti‐proliferative effects of inhibitors in primary human erythroid progenitor cells. Our findings suggest that the effectiveness of targeted cancer therapy might become predictable from protein abundance.

Alteration in microRNA‐17‐92 dynamics accounts for differential nature of cellular proliferation

MicroRNAs associated with the mir‐17‐92 cluster are crucial regulators of the mammalian cell cycle, as they inhibit transcription factors related to the E2F family that tightly control decision‐making events for a cell to commit for active cellular proliferation. Intriguingly, in many solid cancers, these mir‐17‐92 cluster members are overexpressed, whereas in some hematopoietic cancers they are down‐regulated. Our proposed model of the Myc/E2F/mir‐17‐92 network demonstrates that the differential expression pattern of mir‐17‐92 in different cell types can be conceived due to having a contrasting E2F dynamics induced by mir‐17‐92. The model predicts that by explicitly altering the mir‐17‐92‐related part of the network, experimentally it is possible to control cellular proliferation in a cell type‐dependent manner for therapeutic intervention.

Unraveling the differential dynamics of developmental fate in central and peripheral nervous systems

Bone morphogenetic protein 2 (BMP2), differentially regulates the developmental lineage commitment of neural stem cells (NSC’s) in central and peripheral nervous systems. However, the precise mechanism beneath such observations still remains illusive. To decipher the intricacies of this mechanism, we propose a generic mathematical model of BMP2 driven differentiation regulation of NSC’s. The model efficiently captures the dynamics of the wild-type as well as various mutant and over-expression phenotypes for NSC’s in central nervous system. Our model predicts that the differential developmental dynamics of the NSC’s in peripheral nervous system can be reconciled by altering the relative positions of the two mutually interconnected bi-unstable switches inherently present in the steady state dynamics of the crucial developmental fate regulatory proteins as a function of BMP2 dose. This model thus provides a novel mechanistic insight and has the potential to deliver exciting therapeutic strategies for neuronal regeneration from NSC’s of different origin.

Unraveling Cell-Cycle Dynamics in Cancer.

Single-cell imaging data are used to disentangle the dynamics of a critical cell-cycle checkpoint dysregulated in a human cancer cell line.

NONLINEAR DYNAMICS OF GLYCOLYSIS

Glycolysis is the most important cellular process yielding ATP, the universal energy carrier molecule in all living organisms. The characteristic oscillations of the intermediates of glycolysis have been the subject of extensive experimental and theoretical research over the last four decades. A conspicuous property of the glycolytic oscillations is their critical control by the substrate injection rate. In this brief review, we trace its experimental background and explore the essential underlying theoretical models to elucidate a number of nonlinear dynamical phenomena observed in the weak noise limit of the substrate injection rate. Simultaneous oscillations of glycolytic intermediates and insulin have also been discussed within the framework of a phenomenological model in the context of basic experimental issues.