arXiv subjects

Atul Narang

Publications and source records attributed to Atul Narang.

8 recordsLinked to original sources

arXiv2008

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 7 times 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. Here, we formulate a model accounting for both fluxes. We show that: (a) The thresholds of bistability are profoundly affected by both fluxes. The diffusive influx reduces the on threshold by enhancing inducer accumulation in non-induced cells. The carrier efflux increases the off threshold by decreasing inducer accumulation in induced cells. (b) Simulations of the model with experimentally measured parameter values are in good agreement with the data for IPTG. However, there are discrepancies with respect to the data for TMG. They are most likely due to two features missing from the model, namely, the variation of the inducer exclusion effect and the specific growth rate with the lactose enzyme levels. (c) The steady states and thresholds obtained in the presence of both fluxes are well approximated by simple analytical expressions, which may be useful for the preliminary design of the lac genetic switch in synthetic biology.

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arXiv2008

Gene regulation in continuous cultures: A unified theory for bacteria and yeasts

During batch growth on mixtures of two growth-limiting substrates, microbes consume the substrates either sequentially or simultaneously. These growth patterns are manifested in all types of bacteria and yeasts. The ubiquity of these growth patterns suggests that they are driven by a universal mechanism common to all microbial species. In previous work, we showed that a minimal model accounting only for enzyme induction and dilution explains the phenotypes observed in batch cultures of various wild-type and mutant/recombinant cells. Here, we examine the extension of the minimal model to continuous cultures. We show that: (1) Several enzymatic trends, usually attributed to specific regulatory mechanisms such as catabolite repression, are completely accounted for by dilution. (2) The bifurcation diagram of the minimal model for continuous cultures, which classifies the substrate consumption pattern at any given dilution rate and feed concentrations, provides a a precise explanation for the empirically observed correlation between the growth patterns in batch and continuous cultures. (3) Numerical simulations of the model are in excellent agreement with the data. The model captures the variation of the steady state substrate concentrations, cell densities, and enzyme levels during the single- and mixed-substrate growth of bacteria and yeasts at various dilution rates and feed concentrations. (4) This variation is well-approximated by simple analytical expressions that furnish physical insights into the steady states of continuous cultures. The minimal model provides a framework for quantitating the effect of regulatory mechanisms. We illustrate this by analyzing several data sets from the literature.

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arXiv2007

Effect of DNA looping on the induction kinetics of the lac operon

The induction of the lac operon follows cooperative kinetics.The first mechanistic model of these kinetics is the de facto standard in the modeling literature (Yagil & Yagil, Biophys J, 11, 11-27, 1971). Yet, subsequent studies have shown that the model is based on incorrect assumptions. Specifically, the repressor is a tetramerwith four (not two) inducer-binding sites, and the operon contains two auxiliary operators (in addition to the main operator). Furthermore, these structural features are crucial for the formation of DNA loops, the key determinants of lac repression and induction. Indeed, the repression is determined almost entirely (>95%) by the looped complexes (Oehler et al, EMBO J, 13, 3348, 1990), and the pronounced cooperativity of the induction curve hinges upon the existence of the looped complexes (Oehler et al, Nucleic Acids Res, 34, 606, 2006). Here, we formulate a model of lac induction taking due account of the tetrameric structure of the repressor and the existence of looped complexes. We show that: (1) The kinetics are significantly more cooperative than those predicted by the Yagil & Yagil model. (2) The model provides good fits to the repression data for cells containing tetrameric (or mutant dimeric) repressor, as well as the induction curves for 6 different strains of E. coli. It also implies that the ratios of certain looped and non-looped complexes are independent of inducer and repressor levels, a conclusion that can be rigorously tested by gel electrophoresis. (3) Repressor overexpression dramatically increases the cooperativity of the induction curve. This suggests that repressor overexpression can induce bistability in systems, such as growth of E. coli on lactose, that are otherwise monostable.

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arXiv2006

Bacterial gene regulation in diauxic and nondiauxic growth

When bacteria are grown on 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. Here, we construct the bifurcation diagram of the minimal model. The bifurcation diagram explains several general properties of mixed-substrate growth. (1) In almost all 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 optimality of regulatory mechanisms. Here, we show that the minimal model, which contains only induction, 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.(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, 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 size regulation in development, since it suggests that protein dilution is one mechanism for coupling patterning and growth.

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arXiv2005

Comparative analysis of some models of mixed-substrate microbial growth

Mixed-substrate microbial growth is among the most intensely studied systems in molecular microbiology. 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, Biotech. Bioeng., 59, 116, 1998; Thattai & Shraiman, Biophys. J, 85, 744, 2003; Brandt et al, Water Research, 38, 1004, 2004). We show that these models are dynamically similar - the initial motion of the inducible enzymes in all the models is described by Lotka-Volterra equations for competing species. The dynamic similarity occurs because in all the models, the inducible enzymes possess properties characteristic of competing species: Their synthesis is autocatalytic, 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 captures only the diauxic growth pattern, whereas the remaining two models capture 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, the mutual inhibition occurs because the enzymes for each substrate enhance the dilution of the enzymes for the other substrate. In the Thattai & Shraiman model, the mutual inhibition is entirely due to competition for the phosphoryl groups.

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arXiv2005

Pure competition of multiple species during mixed-substrate microbial growth: Extending the resource-based theory

The simultaneous growth of multiple microbial species is a problem of fundamental ecological interest. In media containing more than one growth-limiting substrate, multiple species can coexist. The question then arises: Can single-species data predict the existence and stability of mixed-culture steady states in mixed-substrate environments? This question has been extensively studied with the help of resource-based models. These studies have shown that the single-species data required to predict mixed-culture behavior consists of the growth isoclines and consumption vectors, which in turn are determined from single-substrate data by making specific assumptions about the kinetics of mixed-substrate growth. Here, we show that these assumptions are not valid for microbial growth on mixtures of substitutable substrates. However, the theory can be developed by determining the growth isoclines and consumption vectors directly from the mixed-substrate data, thus obviating the need for specific assumptions about the kinetics of mixed-substrate growth. We show furthermore that in addition to the growth isoclines and consumption vectors, the single-species, mixed-substrate data yields a new family of curves, which we call the consumption curves. Consideration of the growth isoclines and the consumption curves yields deeper insights into the behavior of the mixed cultures. It yields a priori bounds on the substrate concentrations achieved during coexistence, permits the extension of the theory to systems in which the growth isoclines are non-monotonic, and clarifies earlier results obtained by considering only the growth isoclines.

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arXiv2005

Identification of the growth-limiting step in continuous cultures from initial rates measured in response to substrate-excess conditions

When steady state chemostat cultures are abruptly exposed to substrate-excess conditions, they exhibit long lags before adjusting to the new environment. The identity of the rate-limiting step for this slow response can be inferred from the initial yields and specific growth rates measured by exposing steady state cultures at various dilution rates to substrate-excess conditions. We measured these parameters for glucose-limited cultures of E. coli ML308 growing at various dilution rates between 0.03 and 0.6 1/hr. In all the cases, the initial yields were 20-30% less than the steady state yields. The decline of the yield implies that overflow metabolism is triggered in response to excess glucose. It is therefore unlikely that the initial response of the cells is limited by substrate uptake. The initial specific growth rates of cultures growing at low dilution rates (D = 0.03, 0.05, 0.075, 0.1, 0.3 1/hr) were significantly higher than the steady state specific growth rates. However, the increment in the specific growth rate decreased with the dilution rate, and at D=0.6 1/hr, there was no improvement in the specific growth rate. The initial specific growth rates varied hyperbolically with the dilution, decreasing sharply at dilution rates below 0.1 1/hr and saturating at D=0.6 1/hr. This is consistent with a picture in which the initial response is limited by the activity of glutamate dehydrogenase.

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arXiv2005

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, Cell, 114, 201--214, 2003). We show that mutual inhibition alone, without the help of any positive feedback, can trigger spontaneous polarization of the frontness and backness pathways. The spatial distribution of the frontness and backness molecules in response to inhbition 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).

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