Modeling the interactions of bacteria and Toll-like receptor-mediated inflammation in necrotizing enterocolitis.

Necrotizing enterocolitis (NEC) is a severe disease of the gastrointestinal tract in premature infants, characterized by a disrupted intestinal epithelium and an exaggerated pro-inflammatory response. Since the activation of Toll-like receptor-4 (TLR4) blocks cell migration and proliferation and contributes to an uncontrolled inflammatory response within the intestine, this receptor has been identified as a key contributor to the development of NEC. Toll-like receptor-9 (TLR9) has been shown to sense bacterial genome components (CpG DNA) and to play an anti-inflammatory role in NEC. We present in vitro results demonstrating direct inhibition of TLR4 activation by CpG DNA, and we develop a mathematical model of bacteria-immune interactions within the intestine to investigate how such inhibition of TLR4 signaling might alter inflammation, associated bacterial invasion of tissue, and resulting outcomes. The model predicts that TLR9 can inhibit both the beneficial and detrimental effects of TLR4, and thus a proper balance of action by these two receptors is needed to promote intestinal health. The model results are also used to explore three interventions that could potentially prevent the development of NEC: reducing bacteria in the mucus layer, administering probiotic treatment, and blocking TLR4 activation. While the model shows that these interventions would be successful in most cases, the model is also used to identify situations in which the proposed treatments might be harmful.

Dopamine and gamma band synchrony in schizophrenia--insights from computational and empirical studies.

Dopamine modulates cortical circuit activity in part through its actions on GABAergic interneurons, including increasing the excitability of fast-spiking interneurons. Though such effects have been demonstrated in single cells, there are no studies that examine how such mechanisms may lead to the effects of dopamine at a neural network level. With this motivation, we investigated the effects of dopamine on synchronization in a simulated neural network composed of excitatory and fast-spiking inhibitory Wang-Buzsaki neurons. The effects of dopamine were implemented through varying leak K+ conductance of the fast-spiking interneurons and the network synchronization within the gamma band (∼40 Hz) was analyzed. Parametrically varying the leak K+ conductance revealed an inverted-U shaped relationship, with low gamma band power at both low and high conductance levels and optimal synchronization at intermediate conductance levels. We also examined the effects of modulating excitability of the inhibitory neurons more generically using an idealized model with theta neurons, with similar findings. Moreover, such a relationship holds when the external input is both tonic and periodic. Our computational results mirror our empirical study of dopamine modulation in schizophrenia and healthy controls, which showed that amphetamine administration increased gamma power in patients but decreased it in controls. Together, our computational and empirical investigations indicate that dopamine can modulate cortical gamma band synchrony in an inverted-U fashion and that the physiologic effects of dopamine on single fast-spiking interneurons can give rise to such non-monotonic effects at the network level.

Rotational model for actin filament alignment by myosin.

Dynamics of the actomyosin cytoskeleton regulate cellular processes such as secretion, cell division, cell motility, and shape change. Actomyosin dynamics are themselves regulated by proteins that control actin filament polymerization and depolymerization, and myosin motor contractility. Previous theoretical work has focused on translational movement of actin filaments but has not considered the role of filament rotation. Since filament rotational movements are likely sources of forces that direct cell shape change and movement we explicitly model the dynamics of actin filament rotation as myosin II motors traverse filament pairs, drawing them into alignment. Using Monte Carlo simulations we find an optimal motor velocity for alignment of actin filaments. In addition, when we introduce polymerization and depolymerization of actin filaments, we find that alignment is reduced and the filament arrays exist in a stable, asynchronous state. Further analysis with continuum models allows us to investigate factors contributing to the stability of filament arrays and their ability to generate force. Interestingly, we find that two different morphologies of F-actin arrays generate the same amount of force. We also identify a phase transition to alignment which occurs when either polymerization rates are reduced or motor velocities are optimized. We have extended our analysis to include a maximum allowed stretch of the myosin motors, and a non-uniform length for filaments leading to little change in the qualitative results. Through the integration of simulations and continuum analysis, we are able to approach the problem of understanding rotational alignment of actin filaments by myosin II motors.

Hallucinogen persisting perception disorder in neuronal networks with adaptation.

We study the spatiotemporal dynamics of neuronal networks with spike frequency adaptation. In particular, we compare the effects of adaptation being either a linear or nonlinear function of neural activity. We find that altering parameters controlling the strength of synaptic connections in the network can lead to spatially structured activity suggestive of symptoms of hallucinogen persisting perception disorder (HPPD). First, we study how both networks track spatially homogeneous flickering stimuli, and find input is encoded as continuous at lower flicker frequencies when the network's synapses exhibit more net excitation. Mainly, we study instabilities of stimulus-driven traveling pulse solutions, representative of visual trailing phenomena common to HPPD patients. Visual trails are reported as discrete afterimages in the wake of a moving input. Thus, we analyze several solutions arising in response to moving inputs in both networks: an ON state, stimulus-locked pulses, and traveling breathers. We find traveling breathers can arise in both networks when an input moves beyond a critical speed. These possible neural substrates of visual trails occur at slower speeds when the modulation of synaptic connectivity is increased.

A mathematical model of pulmonary gas exchange under inflammatory stress.

During a severe local or systemic inflammatory response, immune mediators target lung tissue. This process may lead to acute lung injury and impaired diffusion of gas molecules. Although several mathematical models of gas exchange have been described, none simulate acute lung injury following inflammatory stress. In view of recent laboratory and clinical progress in the understanding of the pathophysiology of acute lung injury, such a mathematical model would be useful. We first derived a partial differential equations model of gas exchange on a small physiological unit of the lung ( approximately 25 alveoli), which we refer to as a respiratory unit (RU). We next developed a simple model of the acute inflammatory response and implemented its effects within a RU, creating a single RU model. Linking multiple RUs with various ventilation/perfusion ratios and taking into account pulmonary venous blood remixing yielded our lung-scale model. Using the lung-scale model, we explored the predicted effects of inflammation on ventilation/perfusion distribution and the resulting pulmonary venous partial pressure oxygen level during systemic inflammatory stresses. This model represents a first step towards the development of anatomically faithful models of gas exchange and ventilation under a broad range of local and systemic inflammatory stimuli resulting in acute lung injury, such as infection and mechanical strain of lung tissue.

Actin filament branching and protrusion velocity in a simple 1D model of a motile cell.

We formulate and analyse a 1D model for the spatial distribution of actin density at the leading edge of a motile cell. The model incorporates nucleation, capping, growth and decay of actin filaments, as well as retrograde flow of the actin meshwork and known parameter values based on the literature. Using a simplified geometry, and reasonable assumptions about the biochemical processes, we derive PDEs for the density of actin filaments and their tips. Analytic travelling wave solutions are used to predict how the speed of the cell depends on rates of nucleation, capping, polymerization and membrane resistance. Analysis and simulations agree with experimental profiles for measured actin distributions. Extended versions of the model are studied numerically. We find that our model produces stable travelling wave solutions with reasonable cell speeds. Increasing the rate of nucleation of filaments (by the actin related protein Arp2/3) or the rate of actin polymerization leads to faster cell speed, whereas increasing the rate of capping or the membrane resistance reduces cell speed. We consider several variants of nucleation (spontaneous, tip, and side branching) and find best agreement with experimentally measured spatial profiles of filament and tip density in the side branching case.

A reduced mathematical model of the acute inflammatory response: I. Derivation of model and analysis of anti-inflammation.

The acute inflammatory response, triggered by a variety of biological or physical stresses on an organism, is a delicate system of checks and balances that, although aimed at promoting healing and restoring homeostasis, can result in undesired and occasionally lethal physiological responses. In this work, we derive a reduced conceptual model for the acute inflammatory response to infection, built up from consideration of direct interactions of fundamental effectors. We harness this model to explore the importance of dynamic anti-inflammation in promoting resolution of infection and homeostasis. Further, we offer a clinical correlation between model predictions and potential therapeutic interventions based on modulation of immunity by anti-inflammatory agents.