On the effects of diabetes mellitus on the mechanical properties of DRG sensory neurons and their possible relation with diabetic neuropathy.

Diabetic neuropathy (DN) is one of the principal complications of diabetes mellitus (DM). Dorsal root ganglion (DRG) neurons are the primary sensory neurons that transduce mechanical, chemical, thermal, and pain stimuli. Diabetes-caused sensitivity alterations and presence of pain are due to cellular damage originated by persistent hyperglycemia, microvascular insufficiency, and oxidative and nitrosative stress. However, the underlying mechanisms have not been fully clarified. The present work addresses this problem by hypothesizing that sensitivity changes in DN result from mechanotransduction-system alterations in sensory neurons; especially, plasma membrane affectations. This hypothesis is tackled by means of elastic-deformation experiments performed on DGR neurons from a murine model for type-1 DM, as well a mathematical model of the cell mechanical structure. The obtained results suggest that the plasma-membrane fluidity of DRG sensory neurons is modified by the induction of DM, and that this alteration may correlate with changes in the cell calcium transient that results from mechanical stimuli.

Hybrid reaction-diffusion and clock-and-wavefront model for the arrest of oscillations in the somitogenesis segmentation clock.

The clock and wavefront paradigm is arguably the most widely accepted model for explaining the embryonic process of somitogenesis. According to this model, somitogenesis is based upon the interaction between a genetic oscillator, known as segmentation clock, and a differentiation wavefront, which provides the positional information indicating where each pair of somites is formed. Shortly after the clock and wavefront paradigm was introduced, Meinhardt presented a conceptually different mathematical model for morphogenesis in general, and somitogenesis in particular. Recently, Cotterell et al. [A local, self-organizing reaction-diffusion model can explain somite patterning in embryos, Cell Syst. 1, 257-269 (2015)] rediscovered an equivalent model by systematically enumerating and studying small networks performing segmentation. Cotterell et al. called it a progressive oscillatory reaction-diffusion (PORD) model. In the Meinhardt-PORD model, somitogenesis is driven by short-range interactions and the posterior movement of the front is a local, emergent phenomenon, which is not controlled by global positional information. With this model, it is possible to explain some experimental observations that are incompatible with the clock and wavefront model. However, the Meinhardt-PORD model has some important disadvantages of its own. Namely, it is quite sensitive to fluctuations and depends on very specific initial conditions (which are not biologically realistic). In this work, we propose an equivalent Meinhardt-PORD model and then amend it to couple it with a wavefront consisting of a receding morphogen gradient. By doing so, we get a hybrid model between the Meinhardt-PORD and the clock-and-wavefront ones, which overcomes most of the deficiencies of the two originating models.

Crosstalk dynamics between the circadian clock and the mTORC1 pathway.

Crosstalk between the circadian clock clockwork and cellular metabolic regulatory networks is crucial to ensure an adequate response of an organism to the day/night cycle. mTOR (mammalian/mechanistic target of rapamycin) is a master growth regulator and sensor of nutrient status, which is part of the mTOR complex 1 (mTORC1). While the circadian clock confers rhythmicity to the mTOR protein by regulating its degradation rate, mTORC1 activity diminishes period and augments amplitude of circadian oscillations at the cellular level by a currently unknown mechanism. Here, we develop a mathematical deterministic DAE (differential-algebraic equation) model, to explore the possible interactions that allow mTORC1 to display such regulation of the core circadian clock. Our results suggest that mTORC1 is capable of regulating amplitude by exerting translational control on core the clock protein BMAL1, and that period-tuning is achieved by controlling post-translational localization of BMAL1. Since, in our model, mTORC1 control of BMAL1 localization greatly diminishes the ability of the clock to oscillate, and regulation of BMAL1 translation reduces this effect, our results also suggest that both levels of regulation must be present to ensure the robustness of oscillations. Together, the above results emphasize the importance of the influence of mTORC1 on the circadian rhythms.

Polymerization of sarcoplasmic-reticulum calcium-binding proteins might explain observed reticulum kinetics-on-demand behavior.

Reported experimental results, in which transient elevations of sarcoplasmic calcium levels are induced by caffeine in smooth muscle cells, apparently contradict the principle of mass conservation. The commonly accepted model assumes that the total number of Ca2+ binding sites is fixed. A former work dealing with this problem proved that assuming the presence within the reticulum of calcium sequestering proteins whose total number of calcium binding sites increases as the existent sites get occupied, is enough to explain the above referred counter-intuitive experimental results. However, no chemical explanation was given to account for this binding-site count increase. In the present work, we propose a chemical-kinetics scheme for the binding of calcium to calsequestrin (a protein found within the reticulum) and the polymerization of this protein. On the one hand, this scheme is in agreement with reported results on calsequestrin binding kinetics, but it is also fully capable of explaining the observed intriguing performance of the sarcoplasmic reticulum. We further explore the behavior of the resulting nonlinear dynamic system and discuss possible physiological implications of the proposed scheme.

Optimization and Stability of Heat Engines: The Role of Entropy Evolution.

Local stability of maximum power and maximum compromise (Omega) operation regimes dynamic evolution for a low-dissipation heat engine is analyzed. The thermodynamic behavior of trajectories to the stationary state, after perturbing the operation regime, display a trade-off between stability, entropy production, efficiency and power output. This allows considering stability and optimization as connected pieces of a single phenomenon. Trajectories inside the basin of attraction display the smallest entropy drops. Additionally, it was found that time constraints, related with irreversible and endoreversible behaviors, influence the thermodynamic evolution of relaxation trajectories. The behavior of the evolution in terms of the symmetries of the model and the applied thermal gradients was analyzed.

The utility of simple mathematical models in understanding gene regulatory dynamics.

In this review, we survey work that has been carried out in the attempts of biomathematicians to understand the dynamic behaviour of simple bacterial operons starting with the initial work of the 1960's. We concentrate on the simplest of situations, discussing both repressible and inducible systems and then turning to concrete examples related to the biology of the lactose and tryptophan operons. We conclude with a brief discussion of the role of both extrinsic noise and so-called intrinsic noise in the form of translational and/or transcriptional bursting.

Optimal performance of the tryptophan operon of E. coli: a stochastic, dynamical, mathematical-modeling approach.

In this work, we develop a detailed, stochastic, dynamical model for the tryptophan operon of E. coli, and estimate all of the model parameters from reported experimental data. We further employ the model to study the system performance, considering the amount of biochemical noise in the trp level, the system rise time after a nutritional shift, and the amount of repressor molecules necessary to maintain an adequate level of repression, as indicators of the system performance regime. We demonstrate that the level of cooperativity between repressor molecules bound to the first two operators in the trp promoter affects all of the above enlisted performance characteristics. Moreover, the cooperativity level found in the wild-type bacterial strain optimizes a cost-benefit function involving low biochemical noise in the tryptophan level, short rise time after a nutritional shift, and low number of regulatory molecules.

In vitro characterization of Trypanosoma cruzi infection dynamics in skeletal and cardiac myotubes models suggests a potential cell-to-cell transmission in mediating cardiac pathology.

Chagas disease predominantly affects the heart, esophagus, and colon in its chronic phase. However, the precise infection mechanisms of the causal agent Trypanosoma cruzi in these tissue types remain incompletely understood. This study investigated T. cruzi infection dynamics in skeletal (SM) and cardiac myotubes (CM) differentiated from H9c2(2-1) myoblasts (control). SM and CM were generated using 1% fetal bovine serum (FBS) without or with retinoic acid, respectively. Initial invasion efficiencies and numbers of released parasites were equivalent between undifferentiated and differentiated cells (~0.3-0.6%). Concomitantly, parasite motility patterns were similar across cell lines. However, CM demonstrated significantly higher infection kinetics over time, reaching 13.26% infected cells versus 3.12% for SM and 3.70% for myoblasts at later stages. Cellular automata modeling suggested an enhanced role for cell-to-cell transmission in driving the heightened parasitism observed in CM. The increased late-stage susceptibility of CM, potentially mediated by cell-to-cell transfer mechanisms of the parasite, aligns with reported clinical tropism patterns. The myotube infection models provide novel insights into Chagas disease pathogenesis that are not fully attainable through in vivo examination alone. Expanding knowledge in this area could aid therapeutic development for this neglected illness.

Thermodynamic performance of coupled enzymatic reactions: A chemical kinetics model for analyzing cotransporters, ion pumps, and ATP synthases.

Previous research has suggested that molecular energy converters such as ATP synthases, ion pumps, and cotransporters operate via spatially separate pathways for free energy donor and acceptor reactions linked by a protein molecule. We present a chemical kinetics model based on these works, with the basic assumption that all molecular energy converters can be thought of as linked enzymatic reactions, one running downhill the chemical potential gradient and driving the other uphill. To develop the model we first look at how an enzyme process can be forced to go backwards using a basic kinetic model. We then use these findings to suggest a thermodynamically consistent method of linking two enzymatic reactions. Finally, in the context of the aforementioned energy converters, the thermodynamic performance of the resulting model is thoroughly investigated and the obtained results are contrasted with experimental data.

Exploring the mechanisms underlying stroke volume variability reduction in a murine model of heart failure with reduced ejection fraction.

Heart failure with reduced ejection fraction (HFrEF) is accompanied by disregulation of cardiovascular function. Heart rate variability (HRV) is commonly used to assess autonomic dysfunction in HFrEF. However, analysis of stroke volume variability (SVV) may provide additional insights. We examined HRV and SVV in a mouse model of HFrEF. HFrEF mice exhibited reduced stroke volume and ejection fraction versus controls, confirming cardiac contractile dysfunction. HRV was preserved in HFrEF mice. However, SVV was markedly diminished, indicating dissociation between HRV and SVV regulation. Using a mathematical model, we propose that Frank-Starling mechanism abnormalities in HFrEF disrupt SVV independent of HRV. Assessing SVV could thus provide unique insights beyond HRV into cardiovascular control deficits in HFrEF.

What is the core oscillator in the speract-activated pathway of the Strongylocentrotus purpuratus sperm flagellum?

Sperm chemotaxis has an important role in fertilization. Most of our knowledge regarding this phenomenon comes from studies in organisms whose fertilization occurs externally, like sea urchins. Sea urchin spermatozoa respond to sperm-activating peptides, which diffuse from the egg jelly coat and interact with their receptor in the flagellum, triggering several physiological responses: changes in membrane potential, intracellular pH, cyclic nucleotide levels, and intracellular Ca2+ concentration ([Ca2+]). In particular, flagellar [Ca2+] has been shown to oscillate. These [Ca2+] oscillations are correlated with changes in the flagellar shape and so with the regulation of the sperm swimming paths. In this study, we demonstrate, from a mathematical modeling perspective, that the reported speract-activated signaling pathway in Strongylocentrotus purpuratus (speract being a sperm-activating peptide specific to this species) has the necessary elements to replicate the reported [Ca2+] oscillations. We further investigate which elements of this signaling pathway constitute the core oscillator.

Influence of the feedback loops in the trp operon of B. subtilis on the system dynamic response and noise amplitude.

In this paper we introduce a mathematical model for the tryptophan operon regulatory pathway in Bacillus subtilis. This model considers the transcription-attenuation, and the enzyme-inhibition regulatory mechanisms. Special attention is paid to the estimation of all the model parameters from reported experimental data. With the aid of this model we investigate, from a mathematical-modeling point of view, whether the existing multiplicity of regulatory feedback loops is advantageous in some sense, regarding the dynamic response and the biochemical noise in the system. The tryptophan operon dynamic behavior is studied by means of deterministic numeric simulations, while the biochemical noise is analyzed with the aid of stochastic simulations. The model feasibility is tested comparing its stochastic and deterministic results with experimental reports. Our results for the wildtype and for a couple of mutant bacterial strains suggest that the enzyme-inhibition feedback loop, dynamically accelerates the operon response, and plays a major role in the reduction of biochemical noise. Also, the transcription-attenuation feedback loop makes the trp operon sensitive to changes in the endogenous tryptophan level, and increases the amplitude of the biochemical noise.

Distributions for negative-feedback-regulated stochastic gene expression: dimension reduction and numerical solution of the chemical master equation.

In this work we introduce a novel approach to study biochemical noise. It comprises a simplification of the master equation of complex reaction schemes (via an adiabatic approximation) and the numerical solution of the reduced master equation. The accuracy of this procedure is tested by comparing its results with analytic solutions (when available) and with Gillespie stochastic simulations. We further employ our approach to study the stochastic expression of a simple gene network, which is subject to negative feedback regulation at the transcriptional level. Special attention is paid to the influence of negative feedback on the amplitude of intrinsic noise, as well as on the relaxation rate of the system probability distribution function to the steady solution. Our results suggest the existence of an optimal feedback strength that maximizes this relaxation rate.

Cycling expression and cooperative operator interaction in the trp operon of Escherichia coli.

Oscillatory behaviour in the tryptophan operon of an Escherichia coli mutant strain lacking the enzyme-inhibition regulatory mechanism has been observed by Bliss et al. but not confirmed by others. This behaviour could be important from the standpoint of synthetic biology, whose goals include the engineering of intracellular genetic oscillators. This work is devoted to investigating, from a mathematical modelling point of view, the possibility that the trp operon of the E. coli inhibition-free strain expresses cyclically. For that we extend a previously introduced model for the regulatory pathway of the tryptophan operon in Escherichia coli to account for the observed multiplicity and cooperativity of repressor binding sites. Thereafter we investigate the model dynamics using deterministic numeric solutions, stochastic simulations, and analytic studies. Our results suggest that a quasi-periodic behaviour could be observed in the trp operon expression level of single bacteria.

Dynamics of Mammalian Cell Infection by Trypanosoma cruzi trypomastigotes.

In a recent work we demonstrated that Trypanosoma cruzi trypomastigotes change their motility patterns in the presence of mammalian cells, that the extent of the changes depends on the cell line, and that this extent is positively correlated with the efficiency with which parasites invade the different cell lines. These results open the question of what cellular characteristics are relevant for parasite identification and invasion. In the present work, we tackled such question. We performed infection-kinetics experiments on various cell lines, and developed a mathematical model to simulate the experimental outcomes. An analysis of the cell-parasite mechanisms included in the model, together with the parameter values that allowed it to replicate the experimental results, suggests that a process related to the cell replication rate may strongly influence the parasite invasion efficiency, and the infection dynamics in general.

Motility patterns of Trypanosoma cruzi trypomastigotes correlate with the efficiency of parasite invasion in vitro.

Numerous works have demonstrated that trypanosomatid motility is relevant for parasite replication and sensitivity. Nonetheless, although some findings indirectly suggest that motility also plays an important role during infection, this has not been extensively investigated. This work is aimed at partially filling this void for the case of Trypanosoma cruzi. After recording swimming T. cruzi trypomastigotes (CL Brener strain) and recovering their individual trajectories, we statistically analyzed parasite motility patterns. We did this with parasites that swim alone or above monolayer cultures of different cell lines. Our results indicate that T. cruzi trypomastigotes change their motility patterns when they are in the presence of mammalian cells, in a cell-line dependent manner. We further performed infection experiments in which each of the mammalian cell cultures were incubated for 2 h together with trypomastigotes, and measured the corresponding invasion efficiency. Not only this parameter varied from cell line to cell line, but it resulted to be positively correlated with the corresponding intensity of the motility pattern changes. Together, these results suggest that T. cruzi trypomastigotes are capable of sensing the presence of mammalian cells and of changing their motility patterns accordingly, and that this might increase their invasion efficiency.

Three-Way Interactions in an Artificial Community of Bacterial Strains Directly Isolated From the Environment and Their Effect on the System Population Dynamics.

This work is motivated by previous studies that have analyzed the population ecology of a collection of culturable thermoresistant bacteria, isolated from the Churince lagoon in Cuatro Cienegas, Mexico. In particular, it is aimed at testing a hypothesis from a modeling study, which states that antagonistic and sensitive bacteria co-exist thanks to resistant bacteria that protect sensitive ones by forming physical barriers. We selected three different bacterial strains from the referred collection: one antagonistic, one sensitive, and one resistant, and studied the population dynamics of mixed colonies. Our results show that, although the proposed protective mechanism does not work in this case, the resistant strain confers some kind of protection to sensitive bacteria. Further modeling and experimental results suggest that the presence of resistant bacteria indirectly improves the probability that patches of sensitive bacteria grow in a mixed colony. More precisely, our results suggest that by making antagonistic bacteria produce and secrete an antagonistic substance (with the concomitant metabolic cost and growth rate reduction), resistant bacteria increase the likelihood that sensitive bacteria locally outcompete antagonistic ones.

Bistable behaviour and medium-dependent post-translational regulation of the tryptophanase operon regulatory pathway in Echerichia coli.

The present work is aimed at studying the dynamic behaviour of the tryptopnanase (tna) operon, which encodes the proteins necessary to uptake and metabolise tryptophan to use it as a carbon source in the absence of glucose. To this end, we designed a micro-bioreactor capable of driving a bacterial culture to a stationary state. This allowed us to explore (at the single cell level) the tna operon steady-state dynamics under multiple culture conditions. Our experimental results suggest that the tna operon is bistable for a specific range of environmental tryptophan and glucose concentrations, and evidence that both reagents play a role on the activation of the enzyme in charge of metabolising tryptophan: tryptophanase (TnaA). Based on our experimental data and the already known regulatory mechanisms, we developed a mathematical model for the tna operon regulatory pathway. Our modelling results reinforce the claim that the tna operon is bistable, and further suggest that the activity of enzyme TnaA is regulated by the environmental levels of glucose and tryptophan via a common signalling pathway. Possible biological implications of our findings are further discussed.

Quantitative approaches to the study of bistability in the lac operon of Escherichia coli.

In this paper, the history and importance of the lac operon in the development of molecular and systems biology are briefly reviewed. We start by presenting a description of the regulatory mechanisms in this operon, taking into account the most recent discoveries. Then we offer a survey of the history of the lac operon, including the discovery of its main elements and the subsequent influence on the development of molecular and systems biology. Next the bistable behaviour of the operon is discussed, both with respect to its discovery and its molecular origin. A review of the literature in which this bistable phenomenon has been studied from a mathematical modelling viewpoint is then given. We conclude with some brief remarks.

Dynamic stability versus thermodynamic performance in a simple model for a Brownian motor.

Homeostasis allows living organisms to perform in optimal conditions despite ever-changing surroundings. Dynamically, it corresponds to a stable steady state, and so its quality can be judged by the volume of the corresponding basin of attraction and/or the length of the relaxation time. Motivated by the fact that the vast majority of intracellular processes involve enzymatic reactions and, as some people have suggested, models similar to those of Brownian motors can be used to study them, here we introduce a simple Brownian motor model and use it to gain insight into the relation between efficiency and stability properties previously observed in macroscopic systems. For this, we analyze the existence, uniqueness, and stability of the motor's steady state; study its thermodynamic process variables, their relation, and their dependence on the model parameters; and compare the Brownian motor relaxation time and thermodynamic properties. Finally, since the steady state is unique and globally stable, we discuss our results from the standpoint of the energetic costs of maintaining a homeostatic state with short relaxation times.