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Polyhedral models of metabolic networks are computationally tractable and can predict some cellular functions. A longstanding challenge is incorporating metabolites without losing tractability. In this paper, we do so using a new second-order cone representation of the Michaelis–Menten kinetics. The resulting model consists of linear stoichiometric constraints alongside second-order cone constraints that couple the reaction fluxes to metabolite concentrations. We formulate several new problems around this model: conic flux balance analysis, which augments flux balance analysis with metabolite concentrations; dynamic conic flux balance analysis; and finding minimal cut sets of networks with both reactions and metabolites. Solving these problems yields information about both fluxes and metabolite concentrations. They are second-order cone or mixed-integer second-order cone programs, which, while not as tractable as their linear counterparts, can nonetheless be solved at practical scales using existing software. [ABSTRACT FROM AUTHOR]

We study the dynamics of a model of membrane vesicle transport into dendritic spines, which are bulbous intracellular compartments in neurons driven by molecular motors. We reduce the lubrication model proposed in Fai et al. (Phys Rev Fluids 2:113601, 2017) to a fast–slow system, yielding an analytically and numerically tractable equation equivalent to the original model in the overdamped limit. The model’s key parameters include: (1) the ratio of motors that prefer to push toward the head of the dendritic spine to the motors that prefer to push in the opposite direction, and (2) the viscous drag exerted on the vesicle by the spine constriction. We perform a numerical bifurcation analysis in these parameters and find that steady-state vesicle velocities appear and disappear through several saddle-node bifurcations. This process allows us to identify the region of parameter space in which multiple stable velocities exist. We show by direct calculations that there can only be unidirectional motion for sufficiently close vesicle-to-spine diameter ratios. Our analysis predicts the critical vesicle-to-spine diameter ratio, at which there is a transition from unidirectional to bidirectional motion, consistent with experimental observations of vesicle trajectories in the literature. [ABSTRACT FROM AUTHOR]

We develop a mathematical model to study the immediate effect of low-dose radiation on the G2 checkpoint and the G2/M transition of the cell cycle via a radiation pathway (the ATM–Chk2 pathway) of an individual mammalian cell. The model consists of a system of nonlinear differential equations describing the dynamics of a network of regulatory proteins that play key roles in the G2/M transition, cell cycle oscillations, and the radiation pathway. We simulate the application of a single pulse of low-dose radiation at different intensities (∼ 0–0.4 Gy) and times during the latter part of the G2-phase. We use bifurcation analysis to characterize the effect of radiation on the G2/M transition via the ATM–Chk2 pathway. We show that radiation between 0.1 and 0.3 Gy can delay the G2/M transition, and radiation higher than 0.3 Gy can fully activate the G2 checkpoint. Also, our results show that radiation can be low enough to neither delay the G2/M transition nor activate the G2 checkpoint (∼ 0.1 Gy). Our model supports the idea that the cell response to radiation during G2-phase explains hyper-radiosensitivity and increased radioresistance (HRS/IRR) observed at low dose. [ABSTRACT FROM AUTHOR]

Cell polarization, in which intracellular substances are asymmetrically distributed, enables cells to carry out specialized functions. While cell polarity is often induced by intracellular or extracellular spatial cues, spontaneous polarization (the so-called symmetry breaking) may also occur in the absence of spatial cues. Many computational models have been used to investigate the mechanisms of symmetry breaking, and it was proved that spontaneous polarization occurs when the lateral diffusion of inactive signaling molecules is much faster than that of active signaling molecules. This conclusion leaves an important question of how, as observed in many biological systems, cell polarity emerges when active and inactive membrane-bound molecules diffuse at similar rates while cycling between cytoplasm and membrane takes place. The recent studies of Rätz and Röger showed that, when the cytosolic and membrane diffusion are very different, spontaneous polarization is possible even if the membrane-bound species diffuse at the same rate. In this paper, we formulate a two-equation non-local reaction-diffusion model with general forms of positive feedback. We apply Turing stability analysis to identify parameter conditions for achieving cell polarization. Our results show that spontaneous polarization can be achieved within some parameter ranges even when active and inactive signaling molecules diffuse at similar rates. In addition, different forms of positive feedback are explored to show that a non-local molecule-mediated feedback is important for sharping the localization as well as giving rise to fast dynamics to achieve robust polarization. [ABSTRACT FROM AUTHOR]

It is widely accepted that the primary immune system contains a subpopulation of cells, known as regulatory T cells whose function is to regulate the immune response. There is conflicting biological evidence regarding the ability of regulatory cells to lose their regulatory capabilities and turn into immune promoting cells. In this paper, we develop mathematical models to investigate the effects of regulatory T cell switching on the immune response. Depending on environmental conditions, regulatory T cells may transition, becoming effector T cells that are immunostimulatory rather than immunoregulatory. We consider this mechanism both in the context of a simple, ordinary differential equation (ODE) model and in the context of a more biologically detailed, delay differential equation (DDE) model of the primary immune response. It is shown that models that incorporate such a mechanism express the usual characteristics of an immune response (expansion, contraction, and memory phases), while being more robust with respect to T cell precursor frequencies. We characterize the affects of regulatory T cell switching on the peak magnitude of the immune response and identify a biologically testable range for the switching parameter. We conclude that regulatory T cell switching may play a key role in controlling immune contraction. [ABSTRACT FROM AUTHOR]

Critical to epithelial cell viability is prompt and direct recovery, following a perturbation of cellular conditions. Although a number of transporters are known to be activated by changes in cell volume, cell pH, or cell membrane potential, their importance to cellular homeostasis has been difficult to establish. Moreover, the coordination among such regulated transporters to enhance recovery has received no attention in mathematical models of cellular function. In this paper, a previously developed model of proximal tubule (Weinstein, 1992, Am. J. Physiol. 263, F784–F798), has been approximated by its linearization about a reference condition. This yields a system of differential equations and auxiliary linear equations, which estimate cell volume and composition and transcellular fluxes in response to changes in bath conditions or membrane transport coefficients. Using the singular value decomposition, this system is reduced to a linear dynamical system, which is stable and reproduces the full model behavior in a useful neighborhood of the reference. Cost functions on trajectories formulated in the model variables (e.g., time for cell volume recovery) are translated into cost functions for the dynamical system. When the model is extended by the inclusion of linear dependence of membrane transport coefficients on model variables, the impact of each such controller on the recovery cost can be estimated with the solution of a Lyapunov matrix equation. Alternatively, solution of an algebraic Riccati equation provides the ensemble of controllers that constitute optimal state feedback for the dynamical system. When translated back into the physiological variables, the optimal controller contains some expected components, as well as unanticipated controllers of uncertain significance. This approach provides a means of relating cellular homeostasis to optimization of a dynamical system. [Copyright &y& Elsevier]

Abstract: Cellular metabolites frequently have more than a single function in the cell. For example they may be sources of energy as well as building blocks for several macromolecules. The relative cellular needs for these different functions depend on environmental and intracellular factors. The intermediary products of phosphorylation of pyruvate by mitochondria, for example, are used for growth, while the released ATP is used for both growth and maintenance. Since maintenance has priority over growth, and maintenance is proportional to a cell’s mass, a cell’s need for ATP vs. building blocks depends on the growth rate, and hence on substrate availability. We show how the concept of Synthesising Units (SUs) in linear and cyclic pathways takes care of the correct variation of the ATP/building block ratio in the context of the Dynamic Energy Budget (DEB) theory. This can only be achieved by an interaction between subsequent SUs in transferring metabolites. Apart from this interaction we also needed an essential feature of the performance of the pathway in the DEB context: the relative amount of enzymes varies with the growth rate in a special way. We solved an important consistency problem between the DEB model at the whole-cell level and a model for pathway dynamics. We observe that alternative whole-cell models, such as the Marr–Pirt model, that keep the relative amount of enzymes constant, and hence independent of the growth rate, will have problems in explaining how pathways can meet cells’ growth-dependent needs for building blocks vs. ATP. [Copyright &y& Elsevier]