Quantitative Biology

In this paper I have given a mathematical model of Cell reprogramming from a different contexts. Here I considered there is a delay in differential regulator rate equations due to intermediate regulator's regulations. At first I gave some basic mathematical models by Ferell Jr.[2] of reprogramming and after that I gave mathematical model of cell reprogramming by Mithun Mitra[4]. In the last section I contributed a mathematical model of cell reprogramming from intermediate steps regulations and tried to find the critical point of pluripotent cell.

We present the first mathematical model of flow-mediated primary hemostasis in an extravascular injury, which can track the process from initial deposition to occlusion. The model consists of a system of ordinary differential equations (ODE) that describe platelet aggregation (adhesion and cohesion), soluble-agonist-dependent platelet activation, and the flow of blood through the injury. The formation of platelet aggregates increases resistance to flow through the injury, which is modeled using the Stokes-Brinkman equations. Data from analogous experimental (microfluidic flow) and partial differential equation models informed parameter values used in the ODE model description of platelet adhesion, cohesion, and activation. This model predicts injury occlusion under a range of flow and platelet activation conditions. Simulations testing the effects of shear and activation rates resulted in delayed occlusion and aggregate heterogeneity. These results validate our hypothesis that flow-mediated dilution of activating chemical ADP hinders aggregate development. This novel modeling framework can be extended to include more mechanisms of platelet activation as well as the addition of the biochemical reactions of coagulation, resulting in a computationally efficient high throughput screening tool.

In cell extrusion, a cell embedded in an epithelial monolayer loses its apical or basal surface and is subsequently squeezed out of the monolayer by neighboring cells. Cell extrusions occur during apoptosis, epithelial-mesenchymal transition, or pre-cancerous cell invasion. They play important roles in embryogenesis, homeostasis, carcinogenesis, and many other biological processes. Although many of the molecular factors involved in cell extrusion are known, little is known about the mechanical basis of cell extrusion. We used a three-dimensional (3D) vertex model to investigate the mechanical stability of cells arranged in a monolayer with 3D foam geometry. We found that when the cells composing the monolayer have homogeneous mechanical properties, cells are extruded from the monolayer when the symmetry of the 3D geometry is broken due to an increase in cell density or a decrease in the number of topological neighbors around single cells. Those results suggest that mechanical instability inherent in the 3D foam geometry of epithelial monolayers is sufficient to drive epithelial cell extrusion. In the situation where cells in the monolayer actively generate contractile or adhesive forces under the control of intrinsic genetic programs, the forces act to break the symmetry of the monolayer, leading to cell extrusion that is directed to the apical or basal side of the monolayer by the balance of contractile and adhesive forces on the apical and basal sides. Although our analyses are based on a simple mechanical model, our results are in accordance with observations of epithelial monolayers {\it in vivo} and consistently explain cell extrusions under a wide range of physiological and pathophysiological conditions. Our results illustrate the importance of a mechanical understanding of cell extrusion and provide a basis by which to link molecular regulation to physical processes.

Many eukaryotic cells, including Dictyostelium discoideum (Dicty), neutrophils and other cells of the immune system, can detect and reliably orient themselves in chemoattractant gradients. In Dicty, signal detection and transduction involves a G-protein-coupled receptor (GPCR) through which extracellular cAMP signals are transduced into Ras activation via an intermediate heterotrimeric G-protein (G2). Ras activation is the first polarized response to cAMP gradients in Dicty. Recent work has revealed mutiple new characteristics of Ras activation in Dicty, thereby providing new insights into direction sensing mechanisms and pointing to the need for new models of chemotaxis. Here we propose a novel reaction-diffusion model of Ras activation based on three major components: one involving the GPCR, one centered on G2, and one involving the monomeric G protein Ras. In contrast to existing local excitation, global inhibition (LEGI) models of direction sensing, in which a fast-responding but slowly-diffusing activator and a slow-acting rapidly diffusing inhibitor set up an internal gradient of activity, our model is based on equal diffusion coefficients for all cytosolic species, and the unbalanced local sequestration of some species leads to gradient sensing and amplification. We show that Ric8-modulated G2 cycling between the cytosol and membrane can account for many of the observed responses in Dicty. including imperfect adaptation, multiple phases of Ras activity in a cAMP gradient, rectified directional sensing, and cellular memory.

Using a Multi-agent systems paradigm, the present project develops, validates and exploits a computational testbed that simulates micro-biological complex systems, namely the aggregation patterns of the social amoeba Dyctiostelium discoideum . We propose a new design and implementation for managing discrete simulations with autonomous agents on a microscopic scale, thus focusing on their social behavior and mutual interactions. Then, the dependence on the main physical variables is tested, namely density and number of amoebas; in addition, we analyze the robustness of the dynamics against various noise sources. Along with these results, we suggest a methodology for further studies that make use of our validated model.

Atherosclerosis is characterised by the growth of fatty plaques in the inner (intimal) layer of the artery wall. In mature plaques, vascular smooth muscle cells (SMCs) are recruited from the adjacent medial layer to deposit a cap of fibrous collagen over the fatty plaque core. The fibrous cap isolates the thrombogenic content of the plaque from the bloodstream and prevents the formation of blood clots that cause myocardial infarction or stroke. Despite the important protective role of the cap, the mechanisms that regulate cap formation and maintenance are not well understood. It remains unclear why certain caps become stable, while others become vulnerable to rupture. We develop a multiphase PDE model with non-standard boundary conditions to investigate collagen cap formation by SMCs in response to growth factor signals from the endothelium. Diffusible platelet-derived growth factor (PDGF) stimulates SMC migration, proliferation and collagen degradation, while diffusible transforming growth factor (TGF)- β stimulates SMC collagen synthesis and inhibits collagen degradation. The model SMCs respond haptotactically to gradients in the collagen phase and have reduced rates of migration and proliferation in dense collagenous tissue. The model, which is parameterised using a range of in vivo and in vitro experimental data, reproduces several observations from studies of plaque growth in atherosclerosis-prone mice. Numerical simulations and model analysis demonstrate that a stable cap can be formed by a relatively small SMC population and emphasise the critical role of TGF- β in effective cap formation and maintenance. These findings provide unique insight into the cellular and biochemical mechanisms that may lead to plaque destabilisation and rupture. This work represents an important step towards the development of a comprehensive in silico plaque.

Biofilms are communities of bacteria that exhibit a multitude of multiscale biomechanical behaviors. Recent experimental advances have lead to characterizations of these behaviors in terms of measurements of the viscoelastic moduli of biofilms grown in bioreactors and the fracture and fragmentation properties of biofilms. These properties are macroscale features of biofilms; however, a previous work by our group has shown that heterogeneous microscale features are critical in predicting biofilm rheology. In this paper we use tools from statistical physics to develop a generative statistical model of the positions of bacteria in biofilms. We show through simulation that the macroscopic mechanical properties of biofilms depend on the choice of microscale spatial model. Our key finding is that a biologically inspired model of the locations of bacteria in a biofilm is critical to the simulation of biofilms with realistic in silico mechanical properties and statistical characteristics.

The purpose of this paper is to show that it is possible to replace Monod's type model of a chemostat by a constraint based model of bacteria at the genome scale. This new model is an extension of the RBA model of bacteria developed in a batch mode to the chemostat. This new model, and the associated framework, leads to a dramatic improvement in the prediction capacities of the chemostat behaviour. Indeed, for example, the internal states of the bacteria are now part of the prediction outputs and the chemostat behaviour can now be predicted for any limiting source. Finally, the first interests of this new predictive method are illustrated on a set of classic situations where predictions are already close of the well-known biological observations about chemostat. This paper is an extended version of [8] that includes a discussion on the modeling assumptions.

The organization of the axonal cytoskeleton is a key determinant of the normal function of an axon, which is a long thin projection away from a neuron. Under normal conditions two axonal cytoskeletal polymers microtubules and neurofilaments align longitudinally in axons and are interspersed in axonal cross-sections. However, in many neurotoxic and neurodegenerative disorders, microtubules and neurofilaments segregate apart from each other, with microtubules and membranous organelles clustered centrally and neurofilaments displaced to the periphery. This striking segregation precedes abnormal and excessive neurofilament accumulation in these diseases, which in turn leads to focal axonal swellings. While neurofilament accumulation suggests the impairment of neurofilament transport along axons, the underlying mechanism of their segregation from microtubules remains poorly understood for over 30 years. To address this question, we developed a stochastic multiscale model for the cross-sectional distribution of microtubules and neurofilaments in axons. The model describes microtubules, neurofilaments and organelles as interacting particles in a 2D cross-section, and incorporates the stochastic interactions these particles through molecular motors. Simulations of the model demonstrate that organelles can pull nearby microtubules together, and in the absence of neurofilament transport, this mechanism gradually segregates microtubules from neurofilaments on a time scale of hours, similar to that observed in toxic neuropathies. This suggests that the microtubule-neurofilament segregation is simply a consequence of the selective impairment of neurofilament transport. The model generates the experimentally testable prediction that the rate and extent of segregation will be dependent on the sizes of the moving organelles as well as the density of their traffic.

In this paper, we introduce a three-dimensional mathematical model of collagen contraction with microbuckling based on the two-dimensional model previously developed by the authors. The model both qualitatively and quantitatively replicates experimental data including lattice contraction over a time course of 40 hours for lattices with various cell densities, cell density profiles within contracted lattices, radial cut angles in lattices, and cell force propagation within a lattice. The importance of the model lattice formation and the crucial nature of its connectivity are discussed including differences with models which do not include microbuckling. The model suggests that most cells within contracting lattices are engaged in directed motion.