Considerations of varied thermoregulatory expressions in migration theory

Optimal migration theory has been used for three decades to generate predictions of stopover behavior and understand migration ecology. Yet, to date, there have been no attempts to understand the impacts of thermoregulation on migration theory predictions of stopover behavior. Though most migrants are homeothermic, a diverse group of migrants from bats to hummingbirds and warblers make use of some degree of heterothermy. We consider how thermoregulation influences stopover fuel deposition rates, and thus alters optimal migration theory predictions of stopover behavior using a hypothetical migratory bat as a model organism. We update the analytical models of optimal migration theory by considering scenarios of fixed metabolic rate (the current assumption of optimal migration theory) and three different mass-specific metabolic rates including homeothermy, shallow torpor heterothermy and deep torpor heterothermy. Our results predict that heterotherms will make shorter stopovers, have a decreased departure fuel load, and reduce the overall time and energy costs associated with stopovers relative to homeotherms, highlighting that thermoregulation can drastically influence stopover behavior and ultimately play a critical role in population level patterns of migration.     

Steps in the Bacterial Flagellar Motor

The bacterial flagellar motor is a highly efficient rotary machine used by many bacteria to propel themselves. It has recently been shown that at low speeds its rotation proceeds in steps. Here we propose a simple physical model, based on the storage of energy in protein springs, that accounts for this stepping behavior as a random walk in a tilted corrugated potential that combines torque and contact forces. We argue that the absolute angular position of the rotor is crucial for understanding step properties and show this hypothesis to be consistent with the available data, in particular the observation that backward steps are smaller on average than forward steps. We also predict a sublinear speed versus torque relationship for fixed load at low torque, and a peak in rotor diffusion as a function of torque. Our model provides a comprehensive framework for understanding and analyzing stepping behavior in the bacterial flagellar motor and proposes novel, testable predictions. More broadly, the storage of energy in protein springs by the flagellar motor may provide useful general insights into the design of highly efficient molecular machines.     

Dynamics of bacterial population waves as dependent on the type of the chemotactic response function

A study was made of the time of formation and the rate of propagation of bacterial population waves as dependent on substrate concentration. Experimentally and theoretically it is shown that the time of bacterial wave formation grows with increasing concentration of the nutritive component. At the same time, the wave propagation rate drops at relatively high concentrations of the nutritive component. In numerical experiments with a mathematical model, comparative analysis has been made of the dynamics of the behavior of bacterial waves at different chemotactic responses.     

Software Sensors to Monitor the Dynamics of Microbial Communities: Application to Anaerobic Digestion

A mass balance based model has been derived to represent the dynamical behavior of the ecosystem contained in an anaerobic digester. The model considers two bacterial populations: acidogenic and methanogenic bacteria. It forms the basis for the design of a software sensor considering both a model of the biological system and on-line gaseous measurements. The software sensor computes the concentration of inorganic carbon and volatile fatty acids (VFA) in the digester. Another software sensor is dedicated to the estimation of the bacterial biomasses. The predictions of the software sensors for a real experiment are very close to the actual off-line measurements. The software sensors monitor the accumulation of VFA and thus very early detect a destabilization of the digester due to overloading. The presented methodology demonstrates the usefulness of advanced monitoring techniques for an improved understanding of the internal working of a biological system.     

Modeling and analysis of biooxidation of gold bearing pyrite-arsenopyrite concentrates by Thiobacillus ferrooxidans

The results of modeling the biooxidation of a mixed sulfidic concentrate by Thiobacillus ferrooxidans is reported here. A kinetic model, which accounts for the dissolution of sulfide matrix due to both bacterial attachment onto the mineral surface and indirect leaching, has been proposed. A comprehensive system approach is employed for modeling the complex biooxidation process by (a) the decomposition of the complete system into several subsystems, (b) modeling individual systems, and (c) integrating the subsystems model in a final system model. The model for subsystems was developed by writing mass balance equations for the different species involved. The bacterial balance accounts for its growth, both on solid substrate and in solution, and for the attachment to and detachment from the surface. The kinetic parameters of the model were determined by designing the experiments in such a manner that only one subsystem was operational. This model was tested in both laboratory scale batch and continuous biooxidation processes. The model predictions agreed with the experimental data reasonably well. A further analysis of the model was carried out to predict the conditions for efficient biooxidation. Studies on the effect of residence time and pulp density on steady-state behavior showed that there is a critical residence time and pulp density below which washout conditions occur. Operation at pulp densities lower than 5% and residence times lower than 72 h was found unfavorable for efficient leaching.     

Mixed culture model of anaerobic digestion: application to the evaluation of startup procedures

The successful operation of anaerobic digestion depends on the balanced growth of many bacterial species. The functions of the main groups of microorganisms present in a digester have been analyzed and a mathematical model constructed that describes the interactions among the microbial populations and their effect on the digester performance. The model was validated by comparing its predictions with actual digester operation. Several startup procedures were evaluated in the light of the model predictions and improvements on current operational practices suggested in order to minimize startup time.     

Rheological characteristics of microbial suspensions of Pseudomonas aeruginosa and Bacillus cereus

The rheological properties of the bacteria Pseudomonas aeruginosa and Bacillus cereus have been investigated. The apparent viscosity of the bacterial suspensions has been measured at different conditions. The results showed that the bacterial suspensions' apparent viscosity increased with increasing biomass concentration of each of these strains. The P. aeruginosa suspension followed shear thinning behavior while B. cereus suspension followed shear thickening behavior. The shear stress versus shear rate experimental data were best represented by the Herschel-Bulkley model. The apparent viscosity of the P. aeruginosa and B. cereus suspensions decreased with increasing temperature. The relationship between the apparent viscosity and the shearing time highlighted the rheopectic behavior of the suspensions used in this work.     

Precision and Variability in Bacterial Temperature Sensing

In Escherichia coli, the ratio of the two most abundant chemoreceptors, Tar/Tsr, has become the focus of much attention in bacterial taxis studies. This ratio has been shown to change under various growth conditions and to determine the response of the bacteria to the environment. Here, we present a study that makes a quantitative link between the ratio Tar/Tsr and the favored temperature of the cell in a temperature gradient and in various chemical environments. From the steady-state density-profile of bacteria with one dominant thermo-sensor, Tar or Tsr, we deduce the response function of each receptor to temperature changes. Using the response functions of both receptors, we determine the relationship between the favored temperature of wild-type bacteria with mixed clusters of receptors and the receptor ratio. Our model is based on the assumption that the behavior of a wild-type bacterium in a temperature gradient is determined by a linear combination of the independent responses of the two receptors, factored by the receptor’s relative abundance in the bacterium. This is confirmed by comparing our model predictions with measurements of the steady-state density-profile of several bacterial populations in a temperature gradient. Our results reveal that the density-profile of wild-type bacteria can be accurately described by measuring the distribution of the ratio Tar/Tsr in the population, which is then used to divide the population into groups with distinct Tar/Tsr values, whose behavior can be described in terms of independent Gaussian distributions. Each of these Gaussians is centered about the favored temperature of the subpopulation, which is determined by the receptor ratio, and has a width defined by the temperature-dependent speed and persistence time.     

Advances in modeling microbial growth

Summary A mathematical model for bacterial growth, survival and death has been developed. This equation has been applied to a large set of data obtained withYersinia enterocolitica to produce a predictive model. Favorable comparisons were obtained between predictions from the model, primarily as estimates of the population size as affected by local conditions, and data from an experiment with an inoculated food.     

Analysis of a lumped model for tissue inflammation dynamics

The inflammatory response to bacterial invasion of tissue is a complex combination of chemical and physical events, and the outcome of a particular challenge is dependent upon the interaction of these. Thus a wide variety of behavior can be observed for the operation of this response. In this paper we develop and analyze a mathematical model for a generalized inflammatory response to bacterial invasion of a tissue region assumed to be homogeneous on a macroscopic scale, in order to study the dynamical behavior of the system. Our analysis allows interpretation of the outcome of a challenge in terms of key parameters representing the rate processes involved. It demonstrates how abnormalities in these processes can lead to pathological behavior. Numerical values for the parameters are estimated from experimental literature sources, and used in example computations to illustrate the predictions of the model under physiological conditions.     

Model of bacterial band formation in aerotaxis

Aerotaxis is a particular form of "energy taxis". It is based on a largely elusive signal transduction machinery. In aerotaxis, oxygen dissolved in water plays the role of both attractant (at moderate concentrations) and repellent (at high and low concentrations). Cells swimming from favorable oxygen concentrations into regions with unfavorable concentrations increase the frequency of reversals, turn back into the favorable domain, and become effectively trapped there. At the same time, bacteria consume oxygen, creating an oxygen gradient. This behavior leads to a pattern formation phenomenon: bacteria self-organize into a dense band at a certain distance from the air-water interface. We incorporate experimental observations of the aerotactic bacterium, Azospirillum brasilense, into a mathematical model. The model consists of a system of differential equations describing swimming bacterial cells and diffusing oxygen. The cells' frequency of reversals depends on the concentration of oxygen and its time derivative while oxygen is depleted by the bacteria. We suggest a hypothetical model of energy sensing mediated by aerotactic receptors Aer and Tsr. Computer simulations and analysis of the model equations allow comparisons of theoretical and experimental results and provide insight into the mechanisms of bacterial pattern formation and underlying signal transduction machinery. We make testable predictions about position and density of the bacterial band.     

Bacterial chemotaxis in a two-dimensional attractant gradient

The motion of a population of chemotactic bacteria in a radial exponential gradient of attractant in a cylindrical container has been calculated using a mathematical model suggested by Keller and Segel. Numerical solutions for the equations of bacterial migration have been found which give for all times the cell density at distances from the center of the cylinder. The ultimate distribution of bacteria is a simple stationary exponential function of the distance. Experiments to verify the theoretical predictions are suggested.     

Toward a Quantitative Modeling of the Synthesis of the Pectate Lyases,Essential Virulence Factors in Dickeya dadantii

A dynamic mathematical model has been developed and validated to describe the synthesis of pectate lyases (Pels), the major virulence factors in Dickeya dadantii. This work focuses on the simultaneous modeling of the metabolic degradation of pectin by Pel enzymes and the genetic regulation of pel genes by 2-keto-3-deoxygluconate (KDG), a catabolite product of pectin that inactivates KdgR, one of the main repressors of pel genes. This modeling scheme takes into account the fact that the system is composed of two time-varying compartments: the extracellular medium, where Pel enzymes cleave pectin into oligomers, and the bacterial cytoplasm where, after internalization, oligomers are converted to KDG. Using the quasi-stationary state approximations, the model consists of some nonlinear differential equations for which most of the parameters could be estimated from the literature or from independent experiments. The few remaining unknown parameters were obtained by fitting the model equations against a set of Pel activity data. Model predictions were verified by measuring the time courses of bacterial growth, Pel production, pel mRNA accumulation, and pectin consumption under various growth conditions. This work reveals that pectin is almost totally consumed before the burst of Pel production. This paradoxical behavior can be interpreted as an evolutionary strategy to control the diffusion process so that as soon as a small amount of pectin is detected by the bacteria in its surroundings, it anticipates more pectin to come. The model also predicts the possibility of bistable steady states in the presence of constant pectin compounds.     

Does the resource dispersion hypothesis explain group living?

The resource dispersion hypothesis (RDH) asserts that, if resources are heterogeneous in space or time, group living might be less costly than was previously thought, regardless of whether individuals gain direct benefits from group membership. The RDH was first proposed more than 20 years ago and has since accumulated considerable support. However, it is sometimes discredited because a priori tests of specific predictions are few, relevant variables have proved difficult to define and measure, and because its assumptions and predictions remain unclear. This is unfortunate because the RDH provides a potentially powerful model of grouping behavior in a diversity of conditions. Moreover, it can be generalized to predict other phenomena, including spacing behavior in nonsocial animals and utilization of resources other than food. Here, we review the empirical support, clarify the predictions of the RDH and argue that they can be used to provide better tests.     

A genomically/chemically complete module for synthesis of lipid membrane in a minimal cell

A minimal cell is a hypothetical cell defined by the essential functions required for life. We have developed a module for the synthesis of membrane precursors for a mathematical minimal cell model. This module describes, with chemical and genomic detail the production of the constituents required to build a cell membrane and identifies the corresponding essential genes. Membranes allow selective nutrient passage, harmful substance exclusion, and energy generation. Bacterial membrane components range from lipids to fatty acids with embedded proteins and are structurally similar to eukaryotic cell membranes. Membranes are dynamic structures and experimental analyses show great variations in bacterial membrane composition. The flexibility of the model is such that different membrane compositions could be obtained in response to simulated changes in culture conditions. The model's predictions are in close agreement with the observed biological trends. The model's predictions correspond well with the experimental values of total lipid content in cells grown in chemostat culture, but less well with data from batch growth. Cell shape and size results agree especially well for data for growth rate relative to maximum growth rate larger than 0.5; and DNA, RNA, and protein predictions are consistent with experimental observations. A better understanding of the simplest bacterial membrane should lead to insights on the more complex behavior of membranes of higher species as well as identification of potential targets for antimicrobials.     

Rates of molecular evolution in bacteria are relatively constant despite spore dormancy

Rates of molecular evolution are known to vary considerably among lineages, partially due to differences in life-history traits such as generation time. The generation-time effect has been well documented in some eukaryotes, but its prevalence in prokaryotes is unknown. "Because many species of Firmicute bacteria spend long periods of time as metabolically dormant spores, which could result in fewer DNA substitutions per unit time, they present an excellent system for testing predictions of the molecular clock hypothesis." To test whether spore-forming bacteria evolve more slowly than their non-spore-forming relatives, I used phylogenetic methods to determine if there were differences in rates of amino acid substitution between spore-forming and non-spore-forming lineages of Firmicute bacteria. Although rates of evolution do vary among lineages, I find no evidence for an effect of spore-formation on evolutionary rate and, furthermore, evolutionary rates are similar to those calculated for enteric bacteria. These results support the notion that variation in generation time does not affect evolutionary rates in bacterial lineages.     

Radio-frequency bioeffects at the membrane level: Separation of thermal and athermal contributions in the characeae

Summary Single cells ofChara braunii andNitella flexilis were placed in a microstrip exposure apparatus and subjected to isolated bursts of radiofrequency irradiation. Their electrical responses were observed both extra- and intracellularly and found to be in accordance with theoretical predictions. In particular, the cell membrane displays rectifier-like behavior up to a cutoff near 10 MHz; this cutoff implies for the principal current carriers a transit time through the membrane of roughly 50 nsec and a mobility within the membrane approximately onefifth that of potassium in free solution. An electrical response of purely thermal origin was also detected; it was separated from the athermal rectifier response on the basis of rise time and frequency dependence. This is believed to be the first instance in which (i) a biological effect of radio-frequency radiation has had its thermal and athermal components clearly separated and (ii) a primary effect of ion transit time through the membrane has been directly detected.     

GeneMark.hmm: new solutions for gene finding.

The number of completely sequenced bacterial genomes has been growing fast. There are computer methods available for finding genes but yet there is a need for more accurate algorithms. The GeneMark. hmm algorithm presented here was designed to improve the gene prediction quality in terms of finding exact gene boundaries. The idea was to embed the GeneMark models into naturally derived hidden Markov model framework with gene boundaries modeled as transitions between hidden states. We also used the specially derived ribosome binding site pattern to refine predictions of translation initiation codons. The algorithm was evaluated on several test sets including 10 complete bacterial genomes. It was shown that the new algorithm is significantly more accurate than GeneMark in exact gene prediction. Interestingly, the high gene finding accuracy was observed even in the case when Markov models of order zero, one and two were used. We present the analysis of false positive and false negative predictions with the caution that these categories are not precisely defined if the public database annotation is used as a control.