Mathematical modeling of bacterial virulence and host-pathogen interactions in the Dictyostelium/Pseudomonas system

We present some studies on the mechanisms of pathogenesis based on experimental work and on its interpretation through a mathematical model. Using a collection of clinical strains of the opportunistic human pathogen Pseudomonas aeruginosa, we performed co-culture experiments with Dictyostelium amoebae, to investigate the two organisms’ interaction, characterized by a cross action between amoeba, feeding on bacteria, and bacteria exerting their pathogenic action against amoeba. In order to classify bacteria virulence, independently of this cross interaction, we have also performed killing experiments of bacteria against the nematode Caenorhabditis elegans.A mathematical model was developed to infer how the populations of the amoeba-bacteria system evolve according to a number of parameters, taking into account the specific features underlying the interaction. The model does not fall within the class of traditional prey-predator models because not only does an amoeba feed on bacteria, but also it is in turn attacked by them; thus the model must include a feedback term modeling this further interaction aspect. The model shows the existence of multiple steady states and the resulting behavior of the solutions, showing bi-stability of the system, gives a qualitative explanation of the co-culture experiments.     

Overview of Mathematical Approaches Used to Model Bacterial Chemotaxis I: The Single Cell

Mathematical modeling of bacterial chemotaxis systems has been influential and insightful in helping to understand experimental observations. We provide here a comprehensive overview of the range of mathematical approaches used for modeling, within a single bacterium, chemotactic processes caused by changes to external gradients in its environment. Specific areas of the bacterial system which have been studied and modeled are discussed in detail, including the modeling of adaptation in response to attractant gradients, the intracellular phosphorylation cascade, membrane receptor clustering, and spatial modeling of intracellular protein signal transduction. The importance of producing robust models that address adaptation, gain, and sensitivity are also discussed. This review highlights that while mathematical modeling has aided in understanding bacterial chemotaxis on the individual cell scale and guiding experimental design, no single model succeeds in robustly describing all of the basic elements of the cell. We conclude by discussing the importance of this and the future of modeling in this area.     

Frontiers in population ecology of microtine rodents: A pluralistic approach to the study of population ecology

Current challenges for the study of population ecology of microtine rodents are reviewed. Comparisons with other taxonomic groups (other mammals, birds and insects) are given throughout. A major challenge is to link patterns and processes (i.e. mechanisms) better than is the case today. Other major challenges include the furthering of our understanding of the interaction between deterministic and stochastic processes, and as part thereof, the interaction between density-dependent and density-independent processes. The applicability of comparative studies on populations exhibiting different temporal dynamical patterns is, in this connection, emphasized. Understanding spatiotemporal dynamical patterns is another major challenge, not the least from a methodological point of view. Long-term and large-scale ecological data on population dynamics (in space and time) are critical for this purpose. Looking for consistency between hypothesized mechanisms and observed patterns is emphasized as a good platform for further empirical and theoretical work. The intellectual feedback process between different approaches to the study of microtine population ecology (observational studies, experimental manipulative studies, statistical modeling and mathematical modeling) are discussed. We recommend a pluralistic approach (involving both observational and experimental as well as theoretical studies) to the study of small rodent ecology.     

Kinetic models in industrial biotechnology – Improving cell factory performance

An increasing number of industrial bioprocesses capitalize on living cells by using them as cell factories that convert sugars into chemicals. These processes range from the production of bulk chemicals in yeasts and bacteria to the synthesis of therapeutic proteins in mammalian cell lines. One of the tools in the continuous search for improved performance of such production systems is the development and application of mathematical models. To be of value for industrial biotechnology, mathematical models should be able to assist in the rational design of cell factory properties or in the production processes in which they are utilized. Kinetic models are particularly suitable towards this end because they are capable of representing the complex biochemistry of cells in a more complete way compared to most other types of models. They can, at least in principle, be used to in detail understand, predict, and evaluate the effects of adding, removing, or modifying molecular components of a cell factory and for supporting the design of the bioreactor or fermentation process. However, several challenges still remain before kinetic modeling will reach the degree of maturity required for routine application in industry. Here we review the current status of kinetic cell factory modeling. Emphasis is on modeling methodology concepts, including model network structure, kinetic rate expressions, parameter estimation, optimization methods, identifiability analysis, model reduction, and model validation, but several applications of kinetic models for the improvement of cell factories are also discussed.     

Novel mathematical modeling on pilot-scale of plug-flow aerated submerged biofilm reactor for dissolved organic matter and nitrogen removal

The investigation aimed to present mathematical models for describing the dynamic behavior of the dissolved organic matter removal and nitrification in the Aerated Submerged Bio-Film (ASBF) for a plug-flow reactor. Based on the experimental data from the batch system of the ASBF pilot plant, mathematical models for the plug-flow reactor were developed to predict dissolved organic matter and ammonia nitrogen removal rates as a function of heterotrophic and autotrophic bacteria populations, dissolved organic matter concentrations, ammonia nitrogen concentrations, dissolved oxygen concentrations, and temperature. The mathematical models for dissolved organic matter and ammonia nitrogen removal in ASBF include two differential equations reflecting heterotrophic and autotrophic bacteria populations, and a number of kinetic parameters. Consequently, the results present a better insight into the dynamics behavior of heterotrophic and autotrophic biofilm growth and their practical application to wastewater for dissolved organic matter and ammonia nitrogen removal process. The mathematical model for ammonia nitrogen and dissolved organic matter removals present good results for the plug-flow reactor.     

Computational approaches for modeling regulatory cellular networks

Cellular components interact with each other to form networks that process information and evoke biological responses. A deep understanding of the behavior of these networks requires the development and analysis of mathematical models. In this article, different types of mathematical representations for modeling signaling networks are described, and the advantages and disadvantages of each type are discussed. Two experimentally well-studied signaling networks are then used as examples to illustrate the insight that could be gained through modeling. Finally, the modeling approach is expanded to describe how signaling networks might regulate cellular machines and evoke phenotypic behaviors.     

Sediment Transport Modeling: Calibration,Verification, and Evaluation

Numerical modeling of sediment transport in fluvial and estuarine systems can be a reliable way of predicting sediment mobility. If approached naïvely, however, such modeling can produce results that do not have sufficient accuracy or reliability to be useful in decision making or design regarding a range of remediation or stabilization alternatives. It is important to recognize the numerical modeling process as merely one step toward a more complete and balanced understanding of the fluvial or estuarine system in question. Other steps include qualitative and quantitative geomorphic and engineering analyses used to evaluate the accuracy and reliability of numerical modeling as part of a three-level approach to analyze sediment mobility and overall channel behavior and trends. It must first be recognized that attempting to quantitatively analyze sediment mobility involves developing and applying simplified mathematical algorithms to the complexities of continually varying hydrodynamic and sediment transport processes through natural or modified bodies of water. Accuracy in sediment modeling can only be assessed by comparing measured data to model results with accuracy being defined as the model results matching the data within some acceptable band of uncertainty. Reliability of a sediment model is the concept of dependability in reproducing the processes one is attempting to model and implies that a model includes appropriate mathematical expressions that cover the pertinent physical processes of hydrodynamics and sediment mobility. The concept of reasonableness in sediment modeling is the evaluation of results, when compared with other independent analyses in the application of the three-level process, provide an acceptable level of consistency and consensus of conclusions. The importance of modeling software selection, data quality, model calibration, verification, validation, and reasonableness of results are discussed along with two case studies.     

Estrous behavior in dairy cows: identification of underlying mechanisms and gene functions

Selection in dairy cattle for a higher milk yield has coincided with declined fertility. One of the factors is reduced expression of estrous behavior. Changes in systems that regulate the estrous behavior could be manifested by altered gene expression. This literature review describes the current knowledge on mechanisms and genes involved in the regulation of estrous behavior. The endocrinological regulation of the estrous cycle in dairy cows is well described. Estradiol (E2) is assumed to be the key regulator that synchronizes endocrine and behavioral events. Other pivotal hormones are, for example, progesterone, gonadotropin releasing hormone and insulin-like growth factor-1. Interactions between the latter and E2 may play a role in the unfavorable effects of milk yield-related metabolic stress on fertility in high milk-producing dairy cows. However, a clear understanding of how endocrine mechanisms are tied to estrous behavior in cows is only starting to emerge. Recent studies on gene expression and signaling pathways in rodents and other animals contribute to our understanding of genes and mechanisms involved in estrous behavior. Studies in rodents, for example, show that estrogen-induced gene expression in specific brain areas such as the hypothalamus play an important role. Through these estrogen-induced gene expressions, E2 alters the functioning of neuronal networks that underlie estrous behavior, by affecting dendritic connections between cells, receptor populations and neurotransmitter releases. To improve the understanding of complex biological networks, like estrus regulation, and to deal with the increasing amount of genomic information that becomes available, mathematical models can be helpful. Systems biology combines physiological and genomic data with mathematical modeling. Possible applications of systems biology approaches in the field of female fertility and estrous behavior are discussed.     

Population Dynamics of a Salmonella Lytic Phage and Its Host: Implications of the Host Bacterial Growth Rate in Modelling

The prevalence and impact of bacteriophages in the ecology of bacterial communities coupled with their ability to control pathogens turn essential to understand and predict the dynamics between phage and bacteria populations. To achieve this knowledge it is essential to develop mathematical models able to explain and simulate the population dynamics of phage and bacteria. We have developed an unstructured mathematical model using delay-differential equations to predict the interactions between a broad-host-range Salmonella phage and its pathogenic host. The model takes into consideration the main biological parameters that rule phage-bacteria interactions likewise the adsorption rate, latent period, burst size, bacterial growth rate, and substrate uptake rate, among others. The experimental validation of the model was performed with data from phage-interaction studies in a 5 L bioreactor. The key and innovative aspect of the model was the introduction of variations in the latent period and adsorption rate values that are considered as constants in previous developed models. By modelling the latent period as a normal distribution of values and the adsorption rate as a function of the bacterial growth rate it was possible to accurately predict the behaviour of the phage-bacteria population. The model was shown to predict simulated data with a good agreement with the experimental observations and explains how a lytic phage and its host bacteria are able to coexist.     

Ecosystem engineering in the Quaternary of the West Coast of South Africa

Despite advances in our understanding of the geographic and temporal scope of the Paleolithic record, we know remarkably little about the evolutionary and ecological consequences of changes in human behavior. Recent inquiries suggest that human evolution reflects a long history of interconnections between the behavior of humans and their surrounding ecosystems (e.g., niche construction). Developing expectations to identify such phenomena is remarkably difficult because it requires understanding the multi‐generational impacts of changes in behavior. These long‐term dynamics require insights into the emergent phenomena that alter selective pressures over longer time periods which are not possible to observe, and are also not intuitive based on observations derived from ethnographic time scales. Generative models show promise for probing these potentially unexpected consequences of human‐environment interaction. Changes in the uses of landscapes may have long term implications for the environments that hominins occupied. We explore other potential proxies of behavior and examine how modeling may provide expectations for a variety of phenomena.     

A Model for Bacterial Colonization of Sinking Aggregates

Sinking aggregates provide important nutrient-rich environments for marine bacteria. Quantifying the rate at which motile bacteria colonize such aggregations is important in understanding the microbial loop in the pelagic food web. In this paper, a simple analytical model is presented to predict the rate at which bacteria undergoing a random walk encounter a sinking aggregate. The model incorporates the flow field generated by the sinking aggregate, the swimming behavior of the bacteria, and the interaction of the flow with the swimming behavior. An expression for the encounter rate is computed in the limit of large Péclet number when the random walk can be approximated by a diffusion process. Comparison with an individual-based numerical simulation is also given.     

A community model of ciliateTetrahymena and bacteriaE. coli: Part II. Interactions in a batch system

Premised on relatively simple assumptions, mathematical models like those of Monod, Pirt or Droop inadequately explain the complex transient behavior of microbial populations. In particular, these models fail to explain many aspects of the dynamics of aTetrahymena pyriformis-Escherichia coli community. In this study an alternative approach, an individual-based model, is employed to investigate the growth and interactions ofTetrahymena pyriformis andE. coli in a batch culture. Due to improved representation of physiological processes, the model provides a better agreement with experimental data of bacterial density and ciliate biomass than previous modeling studies. It predicts a much larger coexistence domain than rudimentary models, dependence of biomass dynamics on initial conditions (bacteria to ciliate biomasses ratio) and appropriate timing of minimal bacteria density. Moreover, it is found that accumulation ofE. coli sized particles andE. coli toxic metabolites has a stabilizing effect on the system.     

A link between neuroscience and informatics: large-scale modeling of memory processes

Utilizing advances in functional neuroimaging and computational neural modeling, neuroscientists have increasingly sought to investigate how distributed networks, composed of functionally defined subregions, combine to produce cognition. Large-scale, biologically realistic neural models, which integrate data from cellular, regional, whole brain, and behavioral sources, delineate specific hypotheses about how these interacting neural populations might carry out high-level cognitive tasks. In this review, we discuss neuroimaging, neural modeling, and the utility of large-scale biologically realistic models using modeling of short-term memory as an example. We present a sketch of the data regarding the neural basis of short-term memory from non-human electrophysiological, computational and neuroimaging perspectives, highlighting the multiple interacting brain regions believed to be involved. Through a review of several efforts, including our own, to combine neural modeling and neuroimaging data, we argue that large scale neural models provide specific advantages in understanding the distributed networks underlying cognition and behavior.     

The Effects of Vaccination and Immunity on Bacterial Infection Dynamics In Vivo

Salmonella enterica infections are a significant global health issue, and development of vaccines against these bacteria requires an improved understanding of how vaccination affects the growth and spread of the bacteria within the host. We have combined in vivo tracking of molecularly tagged bacterial subpopulations with mathematical modelling to gain a novel insight into how different classes of vaccines and branches of the immune response protect against secondary Salmonella enterica infections of the mouse. We have found that a live Salmonella vaccine significantly reduced bacteraemia during a secondary challenge and restrained inter-organ spread of the bacteria in the systemic organs. Further, fitting mechanistic models to the data indicated that live vaccine immunisation enhanced both the bacterial killing in the very early stages of the infection and bacteriostatic control over the first day post-challenge. T-cell immunity induced by this vaccine is not necessary for the enhanced bacteriostasis but is required for subsequent bactericidal clearance of Salmonella in the blood and tissues. Conversely, a non-living vaccine while able to enhance initial blood clearance and killing of virulent secondary challenge bacteria, was unable to alter the subsequent bacterial growth rate in the systemic organs, did not prevent the resurgence of extensive bacteraemia and failed to control the spread of the bacteria in the body.     

Needle insertions modeling: Identifiability and limitations

Soft tissues modeling is a very present preoccupation in different scientific fields, from computer simulation to biomechanics or medical robotics. In this article, we consider the interaction of a needle with living tissues, which is a particularly complex modeling problem since it is characterized by inhomogeneity and nonlinearity properties. We propose a robust method to online estimate forces involved in typical percutaneous interventions. The ability to obtain physically consistent models during in vivo insertions is also discussed.     

Monitoring Bacterial Transport by Stable Isotope Enrichment of Cells

Understanding the transport and behavior of bacteria in the environment has broad implications in diverse areas, ranging from agriculture to groundwater quality, risk assessment, and bioremediation. The ability to reliably track and enumerate specific bacterial populations in the context of native communities and environments is key to developing this understanding. We report a novel bacterial tracking approach, based on altering the stable carbon isotope value (δ¹³C) of bacterial cells, which provides specific and sensitive detection and quantification of those cells in environmental samples. This approach was applied to the study of bacterial transport in saturated porous media. The transport of introduced organisms was indicated by mass spectrometric analysis of groundwater samples, where the presence of ¹³C-enriched bacteria resulted in increased δ¹³C values of the samples, allowing specific and sensitive detection and enumeration of the bacteria of interest. We demonstrate the ability to produce highly ¹³C-enriched bacteria, present data indicating that results obtained with this approach accurately represent intact introduced bacteria, and include field data on the use of this stable isotope approach to monitor in situ bacterial transport. This detection strategy allows sensitive detection of an introduced, unmodified bacterial strain in the presence of the indigenous bacterial community, including itself in its unenriched form.