Limited by sensing - A minimal stochastic model of the lag-phase during diauxic growth

Programming Molecular Systems To Emulate a Learning Spiking Neuron

Hebbian theory seeks to explain how the neurons in the brain adapt to stimuli to enable learning. An interesting feature of Hebbian learning is that it is an unsupervised method and, as such, does not require feedback, making it suitable in contexts where systems have to learn autonomously. This paper explores how molecular systems can be designed to show such protointelligent behaviors and proposes the first chemical reaction network (CRN) that can exhibit autonomous Hebbian learning across arbitrarily many input channels. The system emulates a spiking neuron, and we demonstrate that it can learn statistical biases of incoming inputs. The basic CRN is a minimal, thermodynamically plausible set of microreversible chemical equations that can be analyzed with respect to their energy requirements. However, to explore how such chemical systems might be engineered de novo, we also propose an extended version based on enzyme-driven compartmentalized reactions. Finally, we show how a purely DNA system, built upon the paradigm of DNA strand displacement, can realize neuronal dynamics. Our analysis provides a compelling blueprint for exploring autonomous learning in biological settings, bringing us closer to realizing real synthetic biological intelligence.

Pseudomonad reverse carbon catabolite repression, interspecies metabolite exchange, and consortial division of labor

Microorganisms acquire energy and nutrients from dynamic environments, where substrates vary in both type and abundance. The regulatory system responsible for prioritizing preferred substrates is known as carbon catabolite repression (CCR). Two broad classes of CCR have been documented in the literature. The best described CCR strategy, referred to here as classic CCR (cCCR), has been experimentally and theoretically studied using model organisms such as Escherichia coli. cCCR phenotypes are often used to generalize universal strategies for fitness, sometimes incorrectly. For instance, extremely competitive microorganisms, such as Pseudomonads, which arguably have broader global distributions than E. coli, have achieved their success using metabolic strategies that are nearly opposite of cCCR. These organisms utilize a CCR strategy termed 'reverse CCR' (rCCR), because the order of preferred substrates is nearly reverse that of cCCR. rCCR phenotypes prefer organic acids over glucose, may or may not select preferred substrates to optimize growth rates, and do not allocate intracellular resources in a manner that produces an overflow metabolism. cCCR and rCCR have traditionally been interpreted from the perspective of monocultures, even though most microorganisms live in consortia. Here, we review the basic tenets of the two CCR strategies and consider these phenotypes from the perspective of resource acquisition in consortia, a scenario that surely influenced the evolution of cCCR and rCCR. For instance, cCCR and rCCR metabolism are near mirror images of each other; when considered from a consortium basis, the complementary properties of the two strategies can mitigate direct competition for energy and nutrients and instead establish cooperative division of labor.

Emergent Subpopulation Behavior Uncovered with a Community Dynamic Metabolic Model of Escherichia coli Diauxic Growth

Microbes have adapted to greatly variable environments in order to survive both short-term perturbations and permanent changes. A classical and yet still actively studied example of adaptation to dynamic environments is the diauxic shift of Escherichia coli, in which cells grow on glucose until its exhaustion and then transition to using previously secreted acetate. Here we tested different hypotheses concerning the nature of this transition by using dynamic metabolic modeling. To reach this goal, we developed an open source modeling framework integrating dynamic models (ordinary differential equation systems) with structural models (metabolic networks) which can take into account the behavior of multiple subpopulations and smooth flux transitions between time points. We used this framework to model the diauxic shift, first with a single E. coli model whose metabolic state represents the overall population average and then with a community of two subpopulations, each growing exclusively on one carbon source (glucose or acetate). After introduction of an environment-dependent transition function that determined the balance between subpopulations, our model generated predictions that are in strong agreement with published data. Our results thus support recent experimental evidence that diauxie, rather than a coordinated metabolic shift, would be the emergent pattern of individual cells differentiating for optimal growth on different substrates. This work offers a new perspective on the use of dynamic metabolic modeling to investigate population heterogeneity dynamics. The proposed approach can easily be applied to other biological systems composed of metabolically distinct, interconverting subpopulations and could be extended to include single-cell-level stochasticity. IMPORTANCE Escherichia coli diauxie is a fundamental example of metabolic adaptation, a phenomenon that is not yet completely understood. Further insight into this process can be achieved by integrating experimental and computational modeling methods. We present a dynamic metabolic modeling approach that captures diauxie as an emergent property of subpopulation dynamics in E. coli monocultures. Without fine-tuning the parameters of the E. coli core metabolic model, we achieved good agreement with published data. Our results suggest that single-organism metabolic models can only approximate the average metabolic state of a population, therefore offering a new perspective on the use of such modeling approaches. The open source modeling framework that we provide can be applied to model general subpopulation systems in more-complex environments and can be extended to include single-cell-level stochasticity.

A bet-hedging strategy for denitrifying bacteria curtails their release of N2O

When oxygen becomes limiting, denitrifying bacteria must prepare for anaerobic respiration by synthesizing the reductases NAR (NO3- → NO2-), NIR (NO2- → NO), NOR (2NO → N2O), and NOS (N2O → N2), either en bloc or sequentially, to avoid entrapment in anoxia without energy. Minimizing the metabolic burden of this precaution is a plausible fitness trait, and we show that the model denitrifier Paracoccus denitrificans achieves this by synthesizing NOS in all cells, while only a minority synthesize NIR. Phenotypic diversification with regards to NIR is ascribed to stochastic initiation of gene transcription, which becomes autocatalytic via NO production. Observed gas kinetics suggest that such bet hedging is widespread among denitrifying bacteria. Moreover, in response to oxygenation, P. denitrificans preserves NIR in the poles of nongrowing persister cells, ready to switch to anaerobic respiration in response to sudden anoxia. Our findings add dimensions to the regulatory biology of denitrification and identify regulatory traits that decrease N2O emissions.

An ensemble of mathematical models showing diauxic growth behaviour

Background

Carbon catabolite repression (CCR) controls the order in which different carbon sources are metabolised. Although this system is one of the paradigms of regulation in bacteria, the underlying mechanisms remain controversial. CCR involves the coordination of different subsystems of the cell - responsible for the uptake of carbon sources, their breakdown for the production of energy and precursors, and the conversion of the latter to biomass. The complexity of this integrated system, with regulatory mechanisms cutting across metabolism, gene expression, and signalling, has motivated important modelling efforts over the past four decades, especially in the enterobacterium Escherichia coli.

Results

Starting from a simple core model with only four intracellular metabolites, we develop an ensemble of model variants, all showing diauxic growth behaviour during a batch process. The model variants fall into one of the four categories: flux balance models, kinetic models with growth dilution, kinetic models with regulation, and resource allocation models. The model variants differ from one another in only a single aspect, each breaking the symmetry between the two substrate assimilation pathways in a different manner, and can be quantitatively compared using a so-called diauxic growth index. For each of the model variants, we predict the behaviour in two new experimental conditions, namely a glucose pulse for a culture growing in minimal medium with lactose and a batch culture with different initial concentrations of the components of the transport systems. When qualitatively comparing these predictions with experimental data for these two conditions, a number of models can be excluded while other model variants are still not discriminable. The best-performing model variants are based on inducer inclusion and activation of enzymatic genes by a global transcription factor, but the other proposed factors may complement these well-known regulatory mechanisms.

Conclusions

The model ensemble presented here offers a better understanding of the variety of mechanisms that have been proposed to play a role in CCR. In addition, it provides an educational resource for systems biology, as it gives an introduction to a broad range of modeling approaches in the context of a simple but biologically relevant example.

Electronic supplementary material

The online version of this article (10.1186/s12918-018-0604-8) contains supplementary material, which is available to authorized users.

Thermodynamics of quasideterministic digital computers

A central result of stochastic thermodynamics is that irreversible state transitions of Markovian systems entail a cost in terms of an infinite entropy production. A corollary of this is that strictly deterministic computation is not possible. Using a thermodynamically consistent model, we show that quasideterministic computation can be achieved at finite, and indeed modest cost with accuracies that are indistinguishable from deterministic behavior for all practical purposes. Concretely, we consider the entropy production of stochastic (Markovian) systems that behave like and and a not gates. Combinations of these gates can implement any logical function. We require that these gates return the correct result with a probability that is very close to 1, and additionally, that they do so within finite time. The central component of the model is a machine that can read and write binary tapes. We find that the error probability of the computation of these gates falls with the power of the system size, whereas the cost only increases linearly with the system size.