Atul Narang

A Mathematical Model for Chemoattractant Gradient Sensing Based on Receptor-Regulated Membrane Phospholipid Signaling Dynamics

AbstractThe crawling movement of cells in response to a chemoattractant gradient is a complex process requiring the coordination of various subcellular activities. Although a complete description of the mechanisms underlying cell movement remains elusive, the very first step of directional sensing, enabling the cell to perceive the imposed gradient, is becoming more transparent. A fundamental problem of directional sensing is its exquisite sensitivity. Even in the presence of relatively shallow chemoattractant gradients, cell projections are extended precisely in the region exposed to the highest chemoattractant concentration. This reflects the existence of a mechanism for amplifying the external signal. Recent experiments have identified a potential candidate for the seat of this amplification—membrane phosphoinositides such as PI4,5P2 and PI3,4,5P3 appear to be the first components of the signal transduction pathway to be amplified. Perturbing the cell with various chemoattractant gradients reveals a rich spectrum of phosphoinositide dynamics (Parent, C. A., and P. N. Devreotes. Science 284:765, 1999). The goal of this work is to develop a mathematical model of these phosphoinositide dynamics. Specifically, we address the following questions: (a) Which signaling pathway could lead to the localized accumulation of membrane phosphoinositides? (b) Why is this accumulation independent of the slope and mean value of the chemoattractant gradient? The model is based on the phosphoinositide cycle that transfers phosphoinositides between the plasma membrane and endoplasmic reticulum. We show that a mathematical model taking due account of receptor desensitization and the reaction-diffusion processes of the phosphoinositide cycle captures many of the experimentally observed dynamics. Having shown the plausibility of the model with respect to directional sensing, we discuss its implications for lamellipod extension, the process that follows directional sensing.

Immunostaining evidence for PI(4,5)P2 localization at the leading edge of chemoattractant-stimulated HL-60 cells

It is well known that in fMLP‐stimulated neutrophils, phosphatidyl inositol 3,4,5‐trisphosphate [PI(3,4,5)P3] localizes at the leading edge of the cells. However, no effort has been made to study the PI 4,5‐bisphosphate [PI(4,5)P2] distribution in these cells. In fact, it has been suggested that PI(4,5)P2 is unlikely to localize, as its basal level is orders of magnitude higher than that of PI(3,4,5)P3. We developed an optimized immunostaining protocol for studying the endogenous distribution of PI(4,5)P2 in neutrophil‐like HL‐60 cells. We show that PI(4,5)P2 localizes sharply at the leading edge with an intensity gradient similar to that for PI(3,4,5)P3. The enzymes for the production of PI(4,5)P2, namely, PI5KIα and PI5KIγ, were also found to localize at the leading edge, further supporting our finding that PI(4,5)P2 localizes at the leading edge. These results imply that complementary regulation of PI3K and phosphate and tensin homolog (PTEN) is not the sole or dominant mechanism of PI(3,4,5)P3 polarization in HL‐60 cells.

Molecular modeling of key elastic properties for inhomogeneous lipid bilayers

Fusion and fission of biological membranes play a crucial role in intracellular transport. Until recently, it was believed that membrane shape transformations involved in these processes are driven by proteins. However, recent evidence shows that lipids, by themselves, can drive membrane deformations. It has been hypothesized that the localized formation of certain lipids changes elastic properties of a membrane in such a way that the membrane deforms spontaneously. This study represents a step towards a systematic investigation of the role of various lipids in local changes of membrane elastic properties. We use coarse-grained molecular dynamics (CGMD) simulations to determine possible effects of addition of phosphatidylinositol-4-phosphate (PI4P) lipids on elastic properties of dipalmitoyl phosphatidyl choline (DPPC) lipid bilayers. We investigate the splay (bending) and the molecular tilt moduli of mixed DPPC/PI4P bilayers, as well as the line tension between domains of pure DPPC and mixed DPPC/PI4P bilayers. Although our results indicate negligible effects of PI4P on elastic properties of DPPC bilayers, the developed methodology can be applied to a wide range of lipid systems.

The diffusive influx and carrier efflux have a strong effect on the bistability of the lac operon in Escherichia coli

In the presence of gratuitous inducers, the lac operon of Escherichia coli exhibits bistability. Most models in the literature assume that the inducer enters the cell via the carrier (permease), and exits by a diffusion-like process. The diffusive influx and carrier efflux are neglected. However, analysis of the data shows that in non-induced cells, the diffusive influx is comparable to the carrier influx, and in induced cells, the carrier efflux is comparable to the diffusive efflux. Since bistability entails the coexistence of steady states corresponding to both non-induced and induced cells, neither one of these fluxes can be ignored. We present a model accounting for both fluxes, and show that: (1) The thresholds (i.e., the extracellular inducer levels at which transcription turns on or off) are profoundly affected by both fluxes. The diffusive influx reduces the on threshold, and eliminates irreversible bistability, a phenomenon that is inconsistent with data. The carrier efflux increases the off threshold, and abolishes bistability at large permease activities, a conclusion that can be tested experimentally. (2) The thresholds are well approximated by simple analytical expressions obtained by considering two limiting cases (no carrier efflux and no diffusive influx). (3) The simulations are in good agreement with the data for isopropyl thiogalactoside (IPTG), but somewhat discrepant with respect to the data for thiomethyl galactoside (TMG). We discuss the potential sources of the discrepancy.

Growth of mixed cultures on mixtures of substitutable substrates: the operating diagram for a structured model

The growth of mixed microbial cultures on mixtures of substrates is a problem of fundamental biological interest. In the last two decades, several unstructured models of mixed-substrate growth have been studied. It is well known, however, that the growth patterns in mixed-substrate environments are dictated by the enzymes that catalyse the transport of substrates into the cell. We have shown previously that a model taking due account of transport enzymes captures and explains all the observed patterns of growth of a single species on two substitutable substrates (J. Theor. Biol. 190 (1998) 241). Here, we extend the model to study the steady states of growth of two species on two substitutable substrates. The model is analysed to determine the conditions for existence and stability of the various steady states. Simulations are performed to determine the flow rates and feed concentrations at which both species coexist. We show that if the interaction between the two species is purely competitive, then at any given flow rate, coexistence is possible only if the ratio of the two feed concentrations lies within a certain interval; excessive supply of either one of the two substrates leads to annihilation of one of the species. This result simplifies the construction of the operating diagram for purely competing species. This is because the two-dimensional surface that bounds the flow rates and feed concentrations at which both species coexist has a particularly simple geometry: It is completely determined by only two coordinates, the flow rate and the ratio of the two feed concentrations. We also study commensalistic interactions between the two species by assuming that one of the species excretes a product that can support the growth of the other species. We show that such interactions enhance the coexistence region.

The dynamics of single-substrate continuous cultures: the role of transport enzymes.

A chemostat limited by a single growth-limiting substrate displays a rich spectrum of dynamics. Depending on the flow rate and feed concentration, the chemostat settles into a steady state or executes sustained oscillations. The transients in response to abrupt increases in the flow rate or the feed concentration are also quite complex. For example, if the increase in the flow rate is small, there is no perceptible change in the substrate concentration. If the increase in the flow rate is large, there is a large increase in the substrate concentration lasting several hours or days before the culture adjusts to a new steady state. In the latter case, the substrate concentration and cell density frequently undergo damped oscillations during their approach to the steady state. In this work, we formulate a simple structured model containing the inducible transport enzyme as the key intracellular variable. The model displays the foregoing dynamics under conditions similar to those employed in the experiments. The model suggests that long recovery times (on the order of several hours to several days) can occur because the initial transport enzyme level is too small to cope with the increased substrate supply. The substrate concentration, therefore, increases until the enzyme level is built up to a sufficiently high level by the slow process of enzyme induction. Damped and sustained oscillations can occur because transport enzyme synthesis is autocatalytic, and hence, destabilizing. At low dilution rates, the response of stabilizing processes, such as enzyme dilution and substrate consumption, becomes very slow, leading to damped and sustained oscillations.

cAMP does not have an important role in carbon catabolite repression of the Escherichia coli lac operon

cAMP does not have an important role in carbon catabolite repression of the Escherichia coli lac operon

Spatiotemporal Dynamics of Eukaryotic Gradient Sensing

The crawling movement of eukaryotic cells in response to a chemical gradient is a complex process involving the orchestration of several subcellular activities. Although a complete description of the mechanisms underlying cell movement remains elusive, the very first step of gradient sensing, enabling the cell to perceive the imposed gradient, is becoming more transparent. The increased understanding of this step has been driven by the discovery that within 5–10 seconds of applying a weak chemoattractant gradient, membrane phosphoinositides, such as PIP3, localize at the front end of the cell, where they activate a process of intense actin polymerization and trigger the extension of a protrusion. This train of events implies that the key to gradient sensing is a mechanistic understanding of the phosphoinositide localization. Since the phosphoinositide distribution is highly localized compared to the shallow chemoattractant gradient, it has been suggested that the cell merely amplifies the chemoattractant gradient. However, this cannot be true since the phosphoinositide localization can display a bewildering array of spatial distributions that bear no resemblance to the external chemoattractant profile. For instance, a single phosphoinositide localization is produced in the face of multiple chemoattractant sources. More surprisingly, the localization forms at a random location even if the chemoattractant concentration is uniform. Here we show that all these seemingly complex dynamics are consistent with the so-called activator-inhibitor class of models. To this end, we formulate and simulate an activator-inhibitor model of gradient sensing based on the phosphoinositide signaling pathways.