Elucidating the Implications of Diverse Dynamical Responses in p53 Protein.

p53 is a well-known tumor suppressor gene that acts as a transcription factor to exhibit a variety of dynamical responses by sensing different types and extent of stress conditions causing DNA damage in Mammalian cells. Mathematical modeling has played a crucial role to correlate cell fate decision-making with some of these dynamic p53 regulations. However, it is extremely challenging to explain the various cell-type and stimulus-specific p53 protein dynamics under different stress conditions by using a single mathematical model. In this article, we propose a simple mathematical model of p53 regulation based on a generic p53 regulatory network that elucidates a range of p53 dynamical responses. By employing bifurcation analysis along with deterministic and stochastic simulations, we explain an array of p53 dynamics by correlating it with the corresponding cell fate regulations in a cell type-specific and stimulus-dependent manner. Moreover, our model makes experimentally testable predictions to fine-tune p53 dynamics under various DNA damage conditions and can be systematically used and improved to analyze complex p53 dynamics in the future.

Modulation of signaling cross-talk between pJNK and pAKT generates optimal apoptotic response.

Tumor necrosis factor alpha (TNFα) is a well-known modulator of apoptosis by maintaining a balance between proliferation and cell-death in normal cells. Cancer cells often evade apoptotic response following TNFα stimulation by altering signaling cross-talks. Thus, varying the extent of signaling cross-talk could enable optimal TNFα mediated apoptotic dynamics. Herein, we use an experimental data-driven mathematical modeling to quantitate the extent of synergistic signaling cross-talk between the intracellular entities phosphorylated JNK (pJNK) and phosphorylated AKT (pAKT) that orchestrate the phenotypic apoptosis level by modulating the activated Caspase3 dynamics. Our study reveals that this modulation is orchestrated by the distinct dynamic nature of the synergism at early and late phases. We show that this synergism in signal flow is governed by branches originating from either TNFα receptor and NFκB, which facilitates signaling through survival pathways. We demonstrate that the experimentally quantified apoptosis levels semi-quantitatively correlates with the model simulated Caspase3 transients. Interestingly, perturbing pJNK and pAKT transient dynamics fine-tunes this accumulated Caspase3 guided apoptotic response. Thus, our study offers useful insights for identifying potential targeted therapies for optimal apoptotic response.

Incoherent modulation of bi-stable dynamics orchestrates the Mushroom and Isola bifurcations.

In biological networks, steady state dynamics of cell-fate regulatory genes often exhibit Mushroom and Isola kind of bifurcations. How these complex bifurcations emerge for these complex networks, and what are the minimal network structures that can generate these bifurcations, remain elusive. Herein, by employing Waddington's landscape theory and bifurcation analysis, we demonstrate that Mushroom and Isola bifurcations can be realized with four minimal network motifs that are constituted by combining a positive feedback motif with various incoherent feed-forward loops. Our study reveals that the intrinsic bi-stable dynamics originating from the positive feedback motif can be fine-tuned by altering the extent of the incoherence of these minimal networks to produce these complex bifurcations. These modeling insights will be useful in identifying the possible network motifs that may give rise to either Mushroom or Isola bifurcation in other biological systems.

Unraveling the origin of glucose mediated disparate proliferation dynamics of cancer stem cells.

Cancer stem cells (CSCs) often switch on their self-renewal programming aggressively to cause a relapse of cancer. Intriguingly, glucose triggers the proliferation propensities in CSCs by controlling the expression of the key transcription factor-like Nanog. However, the factors that critically govern this glucose-stimulated proliferation dynamics of CSCs remain elusive. Herein, by proposing a mathematical model of glucose-mediated Nanog regulation, we showed that the differential proliferation behavior of CSCs and cell-type similar to CSCs can be explained by considering the experimentally observed varied expression levels of key positive (STAT3) and negative (p53) regulators of Nanog. Our model reconciles various experimental observations and predicts ways to fine-tune the proliferation dynamics of these cell types in a context-dependent manner. In future, these modeling insights will be useful in developing improved therapeutic strategies to get rid of harmful CSCs.

Alteration in Cross Diffusivities Governs the Nature and Dynamics of Spatiotemporal Pattern Formation.

Realizing spatiotemporal patterns out of a chemical reaction diffusion system remains an experimental challenge owing to the difficulty in overcoming the stringent condition of diffusion driven instability. Herein, by considering the spatially extended Gray-Scott model system, we have investigated how the cross diffusivities of the reactants involved influence the nature and dynamics of spatiotemporal patterns. Our study unravels that in absence of diffusion driven instability, spatially inhomogeneous patterns can be obtained for the Gray-Scott model system, and unstable time dependent patterns can be stabilized just by adjusting cross diffusivities of the reactants. Interestingly, the effect of cross diffusion in presence of the diffusion driven instability can differentially alter the speed of pattern formation, and potentially modify the nature of the spatiotemporal patterns obtained under different parametric conditions. Experimental verification of our findings may allow us to observe spatiotemporal patterns beyond the regime of classical Turing instability.

Unraveling the diverse nature of electric field induced spatial pattern formation in Gray-Scott model.

We have considered a Gray-Scott kind of model chemical reaction-diffusion system that comprises ionic reactants and auto-catalysts to investigate the possibilities of mobility induced spatial pattern formation under the influence of an external electric field. Our study reveals that applying a uni-directional electric field can deform the already existing Turing patterns obtained due to diffusion driven instability, but cannot produce mobility driven instability and consequent spatial patterns in the absence of diffusion driven instability for a Gray-Scott like system. However, application of the electric field along two mutually perpendicular directions produces a mobility induced pattern in the absence of any differences in the diffusivities of the corresponding chemical reactants. Additionally, we have shown a systematic way to predict the range of absolute values of the pair of electric field intensities along two directions that will lead to spatially heterogeneous patterns in the absence of diffusion driven instability. Our study further demonstrates that the stability of the patterns formed and the nature of the patterns evolved varies with the increasing level of electric field intensities. The insights gained from this study will allow us to develop future experimental strategies to produce diverse range of stable and unique spatial patterns.

Deciphering the Dynamical Origin of Mixed Population during Neural Stem Cell Development.

Neural stem cells (NSCs) often give rise to a mixed population of cells during differentiation. However, the dynamical origin of these mixed states is poorly understood. In this article, our mathematical modeling study demonstrates that the bone morphogenetic protein 2 (BMP2) mediated disparate differentiation dynamics of NSCs in central and peripheral nervous systems essentially function through two distinct bistable switches that are mutually interconnected via a mushroom-like bifurcation. Stochastic simulations of the model reveal that the mixed population originates due to the existence of these bistable switching regulations and that the maintenance of such mixed states depends on the level of stochastic fluctuations of the system. It further demonstrates that due to extrinsic variability, cells in an NSC population can dynamically transit from mushroom to a unique isola kind of bifurcation state, which essentially extends the range of the BMP2-driven mixed population state during differentiation. Importantly, the model predicts that by individually altering the expression level of key regulatory proteins, the NSCs can be converted entirely to a preferred phenotype for BMP2 doses that previously resulted in a mixed population. Our findings show that efficient neuronal regeneration can be achieved by systematically maneuvering the differentiation dynamics.

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.

Interlinked bi-stable switches govern the cell fate commitment of embryonic stem cells.

The development of embryonic stem (ES) cells to extraembryonic trophectoderm and primitive endoderm lineages manifests distinct steady-state expression patterns of two key transcription factors-Oct4 and Nanog. How dynamically such kind of steady-state expressions are maintained remains elusive. Herein, we demonstrate that steady-state dynamics involving two bistable switches which are interlinked via a stepwise (Oct4) and a mushroom-like (Nanog) manner orchestrate the fate specification of ES cells. Our hypothesis qualitatively reconciles various experimental observations and elucidates how different feedback and feedforward motifs orchestrate the extraembryonic development and stemness maintenance of ES cells. Importantly, the model predicts strategies to optimize the dynamics of self-renewal and differentiation of embryonic stem cells that may have therapeutic relevance in the future.

Efficient Quantification of Extrinsic Fluctuations via Stochastic Simulations.

At the molecular level, all the biological processes are exposed to fluctuations emanating from various sources in and around the cellular system. Often these fluctuations dictate the outcome of a cell-fate decision-making event. Thus, having an accurate estimate of these fluctuations for any biological network is extremely important. There are well-established theoretical and numerical methods to quantify the intrinsic fluctuation present within a biological network arising due to the low copy numbers of cellular components. Unfortunately, the extrinsic fluctuations arising due to cell division events, epigenetic regulation, etc. have received very little attention. However, recent studies demonstrate that these extrinsic fluctuations significantly affect the transcriptional heterogeneity of certain important genes. Herein, we propose a new stochastic simulation algorithm to efficiently estimate these extrinsic fluctuations for experimentally constructed bidirectional transcriptional reporter systems along with the intrinsic variability. We use the Nanog transcriptional regulatory network and its variants to illustrate our numerical method. Our method reconciled experimental observations related to Nanog transcription, made exciting predictions, and can be applied to quantify intrinsic and extrinsic fluctuations for any similar transcriptional regulatory network.

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 (approximately 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.

Transcriptional Fluctuations Govern the Serum-Dependent Cell Cycle Duration Heterogeneities in Mammalian Cells.

Mammalian cells exhibit a high degree of intercellular variability in cell cycle period and phase durations. However, the factors orchestrating the cell cycle duration heterogeneities remain unclear. Herein, by combining cell cycle network-based mathematical models with live single-cell imaging studies under varied serum conditions, we demonstrate that fluctuating transcription rates of cell cycle regulatory genes across cell lineages and during cell cycle progression in mammalian cells majorly govern the robust correlation patterns of cell cycle period and phase durations among sister, cousin, and mother-daughter lineage pairs. However, for the overall cellular population, alteration in the serum level modulates the fluctuation and correlation patterns of cell cycle period and phase durations in a correlated manner. These heterogeneities at the population level can be fine-tuned under limited serum conditions by perturbing the cell cycle network using a p38-signaling inhibitor without affecting the robust lineage-level correlations. Overall, our approach identifies transcriptional fluctuations as the key controlling factor for the cell cycle duration heterogeneities and predicts ways to reduce cell-to-cell variabilities by perturbing the cell cycle network regulations.

Deciphering the Role of Fluctuation Dependent Intercellular Communication in Neural Stem Cell Development.

Neural stem cells (NPCs) efficiently communicate in an intercellular manner to govern specific cell fate decisions during the developmental process despite withstanding the fluctuating cellular environment. How these fluctuations from diverse origins functionally affect the precise cell fate decision making remains elusive. By taking a stochastic mathematical modeling approach, we unravel that the transcriptional variability arising within an NPC population due to intermittent cell cycle events significantly influences the neuron to NPC ratio during development. Our model proficiently quantifies the impact of different sources of heterogeneities in maintaining an exact neuron to NPC ratio and predicts plausible experimental ways to fine-tune the development of NPCs. In the future, these modeling insights may lead to better therapeutic avenues to regenerate neurons from NPCs.

A generic approach to decipher the mechanistic pathway of heterogeneous protein aggregation kinetics.

Amyloid formation is a generic property of many protein/polypeptide chains. A broad spectrum of proteins, despite having diversity in the inherent precursor sequence and heterogeneity present in the mechanism of aggregation produces a common cross ß-spine structure that is often associated with several human diseases. However, a general modeling framework to interpret amyloid formation remains elusive. Herein, we propose a data-driven mathematical modeling approach that elucidates the most probable interaction network for the aggregation of a group of proteins (α-synuclein, Aß42, Myb, and TTR proteins) by considering an ensemble set of network models, which include most of the mechanistic complexities and heterogeneities related to amyloidogenesis. The best-fitting model efficiently quantifies various timescales involved in the process of amyloidogenesis and explains the mechanistic basis of the monomer concentration dependency of amyloid-forming kinetics. Moreover, the present model reconciles several mutant studies and inhibitor experiments for the respective proteins, making experimentally feasible non-intuitive predictions, and provides further insights about how to fine-tune the various microscopic events related to amyloid formation kinetics. This might have an application to formulate better therapeutic measures in the future to counter unwanted amyloidogenesis. Importantly, the theoretical method used here is quite general and can be extended for any amyloid-forming protein.

Fine-tuning Nanog expression heterogeneity in embryonic stem cells by regulating a Nanog transcript-specific microRNA.

In embryonic stem cells (ESCs), the transcription factor Nanog maintains the stemness of ESCs despite exhibiting heterogeneous expression patterns under varied culture conditions. Efficient fine-tuning of Nanog expression heterogeneity could enable ESC proliferation and differentiation along specific lineages to be regulated. Herein, by employing a stochastic modeling approach, we show that Nanog expression heterogeneity can be controlled by modulating the regulatory features of a Nanog transcript-specific microRNA, mir-296. We demonstrate how and why the extent of origin-dependent fluctuations in Nanog expression level can be altered by varying either the binding efficiency of the microRNA-mRNA complex or the expression level of mir-296. Moreover, our model makes experimentally feasible and insightful predictions to maneuver Nanog expression heterogeneity explicitly to achieve cell-type-specific differentiation of ESCs.

Dynamical Reorganization of Transcriptional Events Governs Robust Nanog Heterogeneity.

Nanog maintains the pluripotency of embryonic stem cells (ESCs), while demonstrating high expression heterogeneity. Intriguingly, the overall heterogeneity at the Nanog mRNA level under various culture conditions gets precisely partitioned into intrinsic and extrinsic fluctuations. However, the dynamical origin of such a robust transcriptional noise regulation still remains illusive. Herein, we propose a new stochastic simulation strategy that efficiently reconciles the strict apportioning of fluctuations observed in Nanog transcription, while predicting possible experimental scenarios to avoid such an exact noise segregation. Importantly, our model analyses reveal that different culture conditions essentially preserve the robust Nanog expression heterogeneity by altering the dynamics of transcriptional events. In the future, these insights will be useful to systematically maneuver cell-fate decision-making events of ESCs.

Alteration in MicroRNA Expression Governs the Nature and Timing of Cellular Fate Commitment.

In the central nervous system, the expression level of transcriptional repressor Hes1 (hairy and enhancer of split-1) tightly controls the alternative cell fate commitment during differentiation as well as the time required for such cellular transitions. A microRNA, miR-9, that interacts with Hes1 in a mutually antagonistic manner, influences both the process of lineage specification and timing of differentiation significantly, but the impact of the miR-9 in guiding these events still remains poorly understood. Here, we proposed a stochastic mathematical model of the miR-9/Hes1 double-negative feedback interaction network that at the outset shows how alternative cell fate such as quiescence, progenitor, and neuronal states can be accomplished through fine-tuning the Hes1 dynamics by altering the expression level of miR-9. The model simulations further foretell a correlated variation of the period of oscillation of Hes1, and the time delay observed between Hes1 mRNA and protein as the transcription rate of miR-9 increases during the neural progenitor state attainment. Importantly, the model simulations aided by the systematic sensitivity analysis predict that the timing of differentiation to the neuronal state crucially depends on the negative regulators (miR-9 and Hes6) of the Hes1. Our results indicate that miR-9/Hes1 interaction network can be effectively exploited for an efficient and well-timed neuronal transformation.

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.

Disproportionate feedback interactions govern cell-type specific proliferation in mammalian cells.

In mammalian cells, the decision to maintain quiescence over proliferation commitment during G1 -S transition depends on more than one intertwined feedback interaction and is highly cell-type dependent. However, the precise role played by these individual feedback regulations in organizing such diverse proliferation dynamics is still poorly understood. Herein, we propose a predictive mathematical model of G1 -S transition in mammalian cells that reconciles distinct single-cell experimental observations in a cell-type specific manner. The model analysis reveals that the feedback motifs responsible for the G1 -S transition act in a disparate fashion to organize the cell-type specific proliferation response. Importantly, the proposed model can be effectively tuned to gain insights into the proliferation commitment of diverse mammalian cell types and can find wide applicability.

Decoding the regulatory mechanism of glucose and insulin induced phosphatidylinositol 3,4,5-trisphosphate dynamics in ß-cells.

In MIN6 pancreatic ß-cells, glucose and insulin act in a synergistic manner to regulate the dynamics of Phosphatidylinositol (3,4,5)-trisphosphate (PIP3). However, the precise regulatory mechanism behind such an experimentally observed synergy is poorly understood. In this article, we propose a phenomenological mathematical model for studying the glucose and insulin driven PIP3 activation dynamics under various stimulatory conditions to unfold the mechanism responsible for the observed synergy. The modeling study reveals that the experimentally observed oscillation in PIP3 dynamics with disparate time scales for different external glucose doses is mainly orchestrated by the complex dynamic regulation of cytosolic Ca2+ in ß-cells. The model accounts for the dose-dependent activation of PIP3 as a function of externally added insulin, and further shows that even in the absence of Ca2+ signaling, externally added glucose can still maintain a basal level of endogenous insulin secretion via the fatty acid metabolism pathway. Importantly, the model analysis suggests that the glucose mediated ROS (reactive oxygen species) activation often contributes considerably to the synergistic activation of PIP3 by glucose and insulin in a context dependent manner. Under the physiological conditions that keep ß-cells in an insulin responsive state, the effect of glucose induced ROS signaling plays a moderate role in PIP3 activation. As ß-cells approach an insulin resistant state, the glucose induced ROS signaling significantly affects the PIP3 dynamics. Our findings provide a plausible mechanistic insight into the experimentally observed synergy, and can lead to novel therapeutic strategies.