Biomedical subjects

Atul Narang

Publications and source records attributed to Atul Narang.

10 recordsLinked to original sources

PubMed2006

Bacterial gene regulation in diauxic and non-diauxic growth.

When bacteria are grown in a batch culture containing a mixture of two growth-limiting substrates, they exhibit a rich spectrum of substrate consumption patterns including diauxic growth, simultaneous consumption, and bistable growth. In previous work, we showed that a minimal model accounting only for enzyme induction and dilution captures all the substrate consumption patterns [Narang, A., 1998a. The dynamical analogy between microbial growth on mixtures of substrates and population growth of competing species. Biotechnol. Bioeng. 59, 116-121, Narang, A., 2006. Comparitive analysis of some models of gene regulation in mixed-substrate microbial growth, J. Theor. Biol. 242, 489-501]. In this work, we construct the bifurcation diagram of the minimal model, which shows the substrate consumption pattern at any given set of parameter values. The bifurcation diagram explains several general properties of mixed-substrate growth. (1) In almost all the cases of diauxic growth, the "preferred" substrate is the one that, by itself, supports a higher specific growth rate. In the literature, this property is often attributed to the optimality of regulatory mechanisms. Here, we show that the minimal model, which accounts for induction and growth only, displays the property under fairly general conditions. This suggests that the higher growth rate of the preferred substrate is an intrinsic property of the induction and dilution kinetics. It can be explained mechanistically without appealing to optimality principles. (2) The model explains the phenotypes of various mutants containing lesions in the regions encoding for the operator, repressor, and peripheral enzymes. A particularly striking phenotype is the "reversal of the diauxie" in which the wild-type and mutant strains consume the very same two substrates in opposite order. This phenotype is difficult to explain in terms of molecular mechanisms, such as inducer exclusion or CAP activation, but it turns out to be a natural consequence of the model. We show furthermore that the model is robust. The key property of the model, namely, the competitive dynamics of the enzymes, is preserved even if the model is modified to account for various regulatory mechanisms. Finally, the model has important implications for the problem of size regulation in development. It suggests that protein dilution may be the mechanism coupling patterning and growth.

Bacteria↗

PubMed2006

Comparative analysis of some models of gene regulation in mixed-substrate microbial growth.

Mixed-substrate microbial growth is of fundamental interest in microbiology and bioengineering. Several mathematical models have been developed to account for the genetic regulation of such systems, especially those resulting in diauxic growth. In this work, we compare the dynamics of three such models (Narang, 1998a. The dynamical analogy between microbial growth on mixtures of substrates and population growth of competing species. Biotechnol. Bioeng. 59, 116-121; Thattai and Shraiman, 2003. Metabolic switching in the sugar phosphotransferase system of Escherichia coli. Biophys. J. 85(2), 744-754; Brandt et al., 2004. Modelling microbial adaptation to changing availability of substrates. Water Res. 38, 1004-1013). We show that these models are dynamically similar--the initial motion of the inducible enzymes in all the models is described by the Lotka-Volterra equations for competing species. In particular, the prediction of diauxic growth corresponds to "extinction" of one of the enzymes during the first few hours of growth. The dynamic similarity occurs because in all the models, the inducible enzymes possess properties characteristic of competing species: they are required for their own synthesis, and they inhibit each other. Despite this dynamic similarity, the models vary with respect to the range of dynamics captured. The Brandt et al. model always predicts the diauxic growth pattern, whereas the remaining two models exhibit both diauxic and non-diauxic growth patterns. The models also differ with respect to the mechanisms that generate the mutual inhibition between the enzymes. In the Narang model, mutual inhibition occurs because the enzymes for each substrate enhance the dilution of the enzymes for the other substrate. The Brandt et al. model superimposes upon this dilution effect an additional mechanism of mutual inhibition. In the Thattai and Shraiman model, the mutual inhibition is entirely due to competition for the phosphoryl groups. For quantitative agreement with the data, all models must be modified to account for specific mechanisms of mutual inhibition, such as inducer exclusion.

Bacteria↗

PubMed2005

Spontaneous polarization in eukaryotic gradient sensing: a mathematical model based on mutual inhibition of frontness and backness pathways.

A key problem of eukaryotic cell motility is the signaling mechanism of chemoattractant gradient sensing. Recent experiments have revealed the molecular correlate of gradient sensing: Frontness molecules, such as PI3P and Rac, localize at the front end of the cell, and backness molecules, such as Rho and myosin II, accumulate at the back of the cell. Importantly, this frontness-backness polarization occurs spontaneously even if the cells are exposed to uniform chemoattractant profiles. The spontaneous polarization suggests that the gradient sensing machinery undergoes a Turing bifurcation. This has led to several classical activator-inhibitor and activator-substrate models which identify the frontness molecules with the activator. Conspicuously absent from these models is any accounting of the backness molecules. This stands in sharp contrast to experiments which show that the backness pathways inhibit the frontness pathways. Here, we formulate a model based on the mutually inhibitory interaction between the frontness and backness pathways. The model builds upon the mutual inhibition model proposed by Bourne and coworkers [Xu et al., 2003. Divergent signals and cytoskeletal assemblies regulate self-organizing polarity in neutrophils. Cell 114, 201-214.]. We show that mutual inhibition alone, without the help of any positive feedback (autocatalysis), can trigger spontaneous polarization of the frontness and backness pathways. The spatial distribution of the frontness and backness molecules in response to inhibition and activation of the frontness and backness pathways are consistent with those observed in experiments. Furthermore, depending on the parameter values, the model yields spatial distributions corresponding to chemoattraction (frontness pathways in-phase with the external gradient) and chemorepulsion (frontness pathways out-of-phase with the external gradient). Analysis of the model suggests a mechanism for the chemorepulsion-to-chemoattraction transition observed in neurons.

Animals↗

PubMed2005

Structured model for denitrifier diauxic growth.

We present a model for diauxic growth of denitrifying bacteria in which nitrate reductase synthesis kinetics dominate the overall growth kinetics. The model is based on the assumption of the existence of a nitrate respiration operon, thereby linking the rate of nitrate uptake to the activity of nitrate reductase. We show that this approach can model diauxic growth of Pseudomonas denitrificans by conducting experiments in which nitrate reductase activity was measured during both lag and ensuing exponential growth phases. We consistently observed the pattern of low nitrate reductase enzyme activity during the lag phase, increasing before the onset of growth. By fitting model parameters we were able to successfully match experimental data for growth, nitrate uptake, and enzyme activity level.

Models, Biological↗

PubMed2005

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

When a chemostat is perturbed from its steady state, it displays complex dynamics. For instance, if the identity of the growth-limiting substrate is switched abruptly, the substrate concentration and cell density undergo a pronounced excursion from the steady state that can last several days. These dynamics occur because certain physiological variables respond slowly. In the literature, several physiological variables have been postulated as potential sources of the slow response. These include transport enzymes, biosynthetic enzymes, and ribosomes. We have been addressing this problem by systematically exploring the role of these variables. In previous work Shoemaker et al. (J. Theor. Biol., 222 (2003) 307-322), we studied the role of transport enzymes, and we showed that transients starting from low transport enzyme levels could be quantitatively captured by a model taking due account of transport enzyme synthesis. However, there is some experimental data indicating that slow responses occur even if the initial enzyme levels are high. Here, we analyse this data to show that in these cases, the sluggish response is most probably due to slow adjustment of the ribosome levels. To test this hypothesis, we extend our previous model by accounting for the evolution of both the transport enzyme and the ribosomes. Based on a kinetic analysis of the data in the literature, we assume that the specific protein synthesis rate is proportional to the ribosome level, and the specific ribosome synthesis rate is autocatalytic. Simulations of the model show remarkable agreement with experimentally observed steady states and the transients. Specifically, the model predictions are in good agreement with (1) the steady-state profiles of the cell density, substrate concentration, RNA, proteins, and transport enzymes, (2) the instantaneous specific substrate uptake, growth, and respiration rates in response to a continuous-to-batch shift, and (3) the transient profiles of the cell density, substrate concentration, and RNA in response to feed switches and dilution rate shifts. Time-scale analysis of the model reveals that every transient response is a combination of two fundamental (and simpler) dynamics, namely, substrate-sufficient batch dynamics and cell-sufficient fed-batch dynamics. We obtain further insight into the transient response by analysing the equations describing these fundamental dynamics. The analysis reveals that in feed switches or dilution rate shift-ups, the transport enzyme reaches a maximum before RNA achieves its maximum, and in dilution rate shift-downs the cell density reaches a maximum before RNA achieves a minimum.

Bacterial Physiological Phenomena↗

PubMed2004

Predicting stability of mixed microbial cultures from single species experiments: 2. Physiological model.

In this paper, we study the equilibria of a physiological model describing the continuous culture in which two microbial populations compete for two substitutable resources. This work is an extension of the stability analysis of the phenomenological model of mixed microbial growth [M.M. Ballyk, G.S.K. Wolkowicz, Exploitative competition in the chemostat for two perfectly substitutable resources, Math. Biosci. 118 (1993) 127-180; S.S. Pilyugin, G.T. Reeves, A. Narang, Predicting stability of mixed microbial cultures from single species experiments: 2. Phenomenological model]. Here, we investigate the influence of the peripheral enzymes that catabolize the substrate uptake on the stability of the mixed culture. We show that, under steady state conditions, an increase in the concentration of one substrate inhibits the uptake of the other substrate(s). We present the criteria for existence, uniqueness, and stability of various types of equilibria. We formulate these criteria in terms of growth isoclines and consumption curves for each of the competing species. Since both types of curves can be obtained from a single species experiment, our approach provides a direct connection between theory and experiment and allows one to infer the dynamics of mixed cultures from the dynamics of single species cultures. By expressing the stability criteria in terms of intracellular properties, the model establishes a link between ecology and molecular biology.

Culture Media↗

PubMed2004

Predicting stability of mixed microbial cultures from single species experiments: 1. Phenomenological model.

The growth of mixed microbial cultures on mixtures of substrates is a fundamental problem of both theoretical and practical interest. On the one hand, the literature is abundant with experimental studies of mixed-substrate phenomena [T. Egli, The ecological and physiological significance of the growth of heterotrophic microorganisms with mixtures of substrates, Adv. Microbiol. Ecol. 14 (1995) 305-386]. On the other hand, a number of mathematical models of mixed-substrate growth have been analyzed in the last three decades. These models typically assume specific kinetic expressions for substrate uptake and biomass growth rates and their predictions are formulated in terms of parameters of the model. In this work, we formulate and analyze a general mathematical model of mixed microbial growth on mixtures of substitutable substrates. Using this model, we study the effect of mutual inhibition of substrate uptake rates on the stability of the equilibria of the model. Specifically, we address the following question: How much of the dynamics exhibited by two competing species can be inferred from single species data? We provide geometric criteria for stability of various types of equilibria corresponding to non-competitive exclusion, competitive exclusion, and coexistence of two competing species in terms of growth isoclines and consumption curves. A growth isocline is a curve in the plane of substrate concentrations corresponding to the zero net growth of a given species. In [G.T. Reeves, A. Narang, S.S. Pilyugin, Growth of mixed cultures on mixtures of substitutable substrates: The operating diagram for a structured model, J. Theor. Biol. 226 (2004) 143-157], we introduced consumption curves as sets of all possible combinations of substrate concentrations corresponding to balanced growth of a single microbial species. Both types of curves can be obtained in single species experiments.

Culture Media↗

PubMed2004

A mechanistic model for eukaryotic gradient sensing: spontaneous and induced phosphoinositide polarization.

The crawling movement of cells in response to a chemoattractant gradient is a complex process requiring coordination of various 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 s of applying a weak chemoattractant gradient, membrane phosphoinositides such as PIP(3) localize at the front end of the cell. It is currently believed that the gradient sensing mechanism is precisely the mechanism leading to this localization. We have formulated a reaction-diffusion model based on the phosphoinositide cycle which predicts various responses of motile cells in addition to the phosphoinositide polarization induced by chemoattractant gradients. The responses include: (a) Polarized sensitivity wherein a polarized cell responds to a change in the direction of the gradient by turning its existing front. (b) Spontaneous polarization wherein cells polarize in a random direction even if the surrounding chemoattractant concentration is uniform. (c) Unique localization which refers to the formation of a unique polarity even in the face of multiple chemoattractant sources. The above responses preclude the hypothesis that the cell merely amplifies the external signal. Our model indicates that the cell must be viewed as a system that nonlinearly processes chemoattractant inputs. We show in particular that these seemingly complex dynamics can be explained very simply in terms of the instabilities and wavefront dynamics that are characteristic of the activator-inhibitor class of models.

Animals↗

PubMed2004

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.

Bacteria↗

PubMed2003

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.

Bacteria↗