Encounters in predator-prey systems: a simple discrete model

Predator-prey systems are often described by exploitation models. These models can mimic experimental data very accurately, but it is sometimes difficult to realize the relationships between the models and the behavior of individual predator and prey animals. A simple discrete model is proposed here that tries to elucidate the connections between: the animals' movements, the predator/prey encounters; and the dynamics in the system as globally represented by the exploitation models. In these models, the term "area of discovery" plays an essential role. This term is shown to be a predictable coefficient that is composed of measurable physical properties of the analyzed predator-prey system. The model takes into account that predators and prey in experimental systems often do not search randomly but prefer some parts of the test area. The model is applied to the mite system Phytoseiulus persimilis/Tetranychus urticae under simple artificial conditions.     

A simple model to describe transient differences between cell number and biomass growth rates of Escherichia coli

Information on the response of a microbial culture to dynamic environmental conditions is necessary for the design of transient operation processes. However, most attempts at modelling culture response have been directed at describing the steady-state behavior. Thus, there is a need for adequate dynamic models for process design. Simulations of nutrient shifts were completed using a "single-cell" model for Escherichia coli. It was discovered that the specific mass growth rate and the specific number of cells growth rate were different under transient conditions, whereas at steady state (balanced growth) these rates are equivalent. Using these observations, a simple delay model to describe the transient behavior of the two growth rates is formulated and tested. The model contains as state variables only the readily measurable macroscopic quantities (biomass, cell number, and limiting nutrient). This model agreed well with the predictions of the single-cell model.     

Kinetic and fluorometric behavior of a phenol fermentation

Summary The kinetic and fluorometric behavior ofPseudomonas putida (ATCC 17484) growing on phenol as the carbon limiting substrate was investigated. A model was developed to describe the behavior under dynamic conditions of flow or substrate concentration shift-up. Parameters contained in the model were estimated. It was observed that the model described the kinetic behavior reasonably well. Factors which affected the fluorescence output of the whole broth culture were also studied.     

Direct observation of steady-state microtubule dynamics

Different types of unusual dynamic behavior have been reported for steady-state microtubules. While almost all earlier reports relied on kinetic measurements of bulk polymerization, we have directly visualized the steady-state addition of subunits to individual microtubules through the use of tubulin derivitized with biotin. Biotinylated tubulin was used both as an internal "seed" for polymerization and as a marker for assembly onto the ends of microtubules composed of purified tubulin. Biotinylated segments were distinguished from unmodified tubulin by double-label immunofluorescence. Microtubule lengths, number concentrations, and segment lengths have been monitored with time at steady state under two buffer conditions. The results indicate that the microtubule steady state under these conditions is a balance between a majority of slowly growing microtubules and a minority of rapidly depolymerizing ones as described by the "dynamic instability" model (Mitchison T., and M. Kirschner, 1984, Nature (Lond.)., 312:232-242). Microtubules show no evidence of treadmilling; instead most show progressive growth off both ends at steady state. Although solvent conditions markedly influence the growth rates, qualitatively the behavior is unchanged.     

One- and two-locus models of the origin of worker behavior in hymenoptera

Hamilton, 1964, Hamilton, 1972 suggested that, if females are singly inseminated, the asymmetries in intra-familial relationships inherent in haplo-diploidy should predispose the Hymenoptera to evolve female sex-limited worker behavior, if either a worker raises sibs as reproductives but raises a bias of sisters (pathway 1), or she raises a combination of sibs and sons as reproductives but substitutes sons for brothers preferentially (pathway 2). To investigate these hypotheses when mating is random, we present mathematical and numerical analyses of the one-locus two-allele model of Charnov (1978a) which we generalize. Furthermore, we extend the Charnov model to a more realistic two-locus situation where we postulate that the ability of a worker to raise a bias of sisters or to substitute sons for brothers preferentially is controlled by a locus separate from the locus controlling worker behavior, rather than being a pleiotropic effect of that locus. Considerations of the relative stringencies of the conditions for substitution of the allele for worker behavior and the constraints on linkage suggest that pathway 2 is more likely than pathway 1 for the origin of worker behavior. For pathway 1, we compare the Charnov model with its diplo-diploid analogue. This comparison reveals that, depending on the penetrance of the allele for worker behavior in the heterozygous state, both models permit the evolution of worker behavior even when workers raise the ratio of sisters to brothers laid by the queens, and that an advantage to haplo-diploidy becomes apparent only when workers raise a bias of sisters. For pathway 1, we also consider a generalization of the Craig model (Craig, 1979) which is quite similar to the Charnov model.     

Identification of alterations in the Jacobian of biochemical reaction networks from steady state covariance data at two conditions

Model building of biochemical reaction networks typically involves experiments in which changes in the behavior due to natural or experimental perturbations are observed. Computational models of reaction networks are also used in a systems biology approach to study how transitions from a healthy to a diseased state result from changes in genetic or environmental conditions. In this paper we consider the nonlinear inverse problem of inferring information about the Jacobian of a Langevin type network model from covariance data of steady state concentrations associated to two different experimental conditions. Under idealized assumptions on the Langevin fluctuation matrices we prove that relative alterations in the network Jacobian can be uniquely identified when comparing the two data sets. Based on this result and the premise that alteration is locally confined to separable parts due to network modularity we suggest a computational approach using hybrid stochastic-deterministic optimization for the detection of perturbations in the network Jacobian using the sparsity promoting effect of $\ell _p$ -penalization. Our approach is illustrated by means of published metabolomic and signaling reaction networks.     

Experimental investigation and modeling of oscillatory behavior in the continuous culture of Zymomonas mobilis

The mechanism causing oscillation in continuous ethanol fermentation by Zymomonas mobilis under certain operating conditions has been examined. A new term, "dynamic specific growth rate," which considers inhibitory culture conditions in the recent past affecting subsequent cell behavior, is proposed in this article. Based on this concept, a model was formulated to simulate the oscillatory behavior in continuous fermentation of Zymomonas mobilis. Forced oscillation fermentation experiments, in which exogenous ethanol was added at a controlled rate to generate oscillatory behavior, were performed in order to obtain estimates for the model parameters and to validate the proposed model. In addition, data from a literature example of a sustained oscillation were analyzed by means of the model, and excellent agreement between the model simulation and experimental results was obtained. The lag in the cells' response to a changing environment, i.e., ethanol concentration change rate experienced by the cells, was shown to be the major factor contributing to the oscillatory behavior in continuous fermentation of Zymomonas mobilis under certain operating conditions. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 56: 99-105, 1997.     

Higher mental functions and the systems analysis of behavior under conditions of uncertainty

Superior psychical functions (skills) are usually formed in great subjective uncertainty conditions. Because of that exact knowledge of information mechanisms of behavior activity under uncertainty conditions is very importent. Some difficulties of traditional notions (classic behavior act model developed by P. K. Anokhin, systems quantization of behavior) are discussed. The model of probabilitive training allows to describe various training uncertainty conditions, and it operates as the Anokhin model in a specific case. The system-shaping factor in this model is an adaptive result. Afferent synthesis, aim for action, acceptor of the action result and the programme of actions have the traditional senses. Besides those it is proposed to use a concept of probability decision to alter the program of action, as well as an idea of memory buffer (results of search reactions). The organizational features of the functional system of behavior under great uncertainty conditions should be taken into account while specifying the informational mechanism responsible for systems quantization of behavior. The above mechanism can be used for explain the discreteness of an action in the program alteration process when the same quantum of behavior is implemented. These ideas are profitable for systems analysis of superior psychical functions, based on the reflex formation under environmental uncertainty conditions.     

Parametric study of a 6-column countercurrent solvent gradient purification (MCSGP) unit

The novel "multicolumn countercurrent solvent gradient purification" (MCSGP) process has been modeled for the purification of a polypeptide mixture characterized by a strong non-linear competitive adsorption isotherm. As a model system, the purification of an industrial polypeptide mixture containing 46% of the hormone calcitonin has been selected. The many impurities contained in the mixture have been lumped into three key impurities, which are selected as the ones eluting closer to the main component. The simulation model allows for a better understanding of the complex operating behavior of the multicolumn system, which has been experimentally investigated in a previous work. Through a systematic parametric analyses of the model behavior, the main operating parameters controlling the process performance in terms of purity and yield are investigated. The study of internal liquid and adsorbed phase concentration profiles along the unit for the different operating conditions allow elucidating the working principle of the new separation process. It is found that the MCSGP unit achieves much higher yields for a given product purity than the corresponding single-column batch units.     

Kinetics of organic removal in fixed-bed aerobic biological reactor

The process kinetics of a lab-scale upflow aerobic immobilized biomass (UAIB) reactor using simulated sugar-manufacturing wastewater as feed was investigated. The experimental unit consisted of a 22l reactor filled with high porosity pumice stone. The UAIB reactor was tested under different organic loads and different hydraulic retention times (HRT) and the substrate loading removal rate was compared with prediction of Stover-Kincannon model, second-order model and the first order substrate removal model. After obtaining steady-state conditions, organic loading rate was increased from 750 to 4500 g COD/m(3) day to resemble wastewater from sugar production lines, and hydraulic retention time was decreased from 1 to 0.5 days, stepwise. Nine different operational conditions were applied changing these two parameters in a certain program. As a result of the calculations, Stover-Kincannon model and second-order model known as "Grau" model were found to be the most appropriate models for this reactor. Stover-Kincannon model and Grau second-order model gave high correlation coefficients, which were 99.7% and 99.4%, respectively. Therefore, these models could be used in predicting the behavior or design of the UAIB reactors.     

Regulation of hSos1 activity is a system-level property generated by its multi-domain structure

The multi-domain protein hSos1 plays a major role in cell growth and differentiation through its Ras-specific guanine nucleotide exchange domain whose complex regulation involves intra-molecular, inter-domain rearrangements. We present a stochastic mathematical model describing intra-molecular regulation of hSos1 activity. The population macroscopic effect is reproduced through a Monte-Carlo approach. Key model parameters have been experimentally determined by BIAcore analysis. Complementation experiments of a Saccharomyces cerevisiae cdc25(ts) strain with Sos deletion mutants provided a comprehensive data set for estimation of unknown parameters and model validation. The model is robust against parameter alteration and describes both the behavior of Sos deletion mutants and modulation of activity of the full length molecule under physiological conditions. By incorporating the calculated effect of amino acid changes at an inter-domain interface, the behavior of a mutant correlating with a developmental syndrome could be simulated, further validating the model. The activation state of Ras-specific guanine nucleotide exchange domain of hSos1 arises as an "emergent property" of its multi-domain structure that allows multi-level integration of a complex network of intra- and inter-molecular signals.     

STABILITY IN THE PROPORTION OF HARBOR SEALS HAULED OUT UNDER LOCALLY IDEAL CONDITIONS

We monitored the haul-out behavior of 68 radio-tagged harbor seals ( Phoca vitulina ) during the molt season at two Alaskan haul-out sites (Grand Island, August-September 1994; Nanvak Bay, August-September 2000). For each site, we created a statistical model of the proportion of seals hauled out as a function of date, time of day, tide, and weather covariates. Using these models, we identified the conditions that would result in the greatest proportion of seals hauled out. Although those "ideal conditions" differed between sites, the proportion of seals predicted to be hauled out under those conditions was very similar (81.3% for Grand Island and 85.7% for Nanvak Bay). The similar estimates for both sites suggest that haul-out proportions under locally ideal conditions may be constant between years and geographic regions, at least during the molt season.     

Subthalamic lesions eliminate sexual behavior in the male rat

Electrical stimulation of parts of the subthalamus and mesencephalon produces coordinated stepping movements, and for this reason these areas are sometimes referred to as the subthalamic and mesencephalic "locomotor" regions. In this study we contrast the sexual behavioral effect of electrolytic destruction of these two regions in the male rat. Lesions of the mesencephalic locomotor region had no significant effect on male sexual behavior. In contrast, subthalamic lesions centered on the caudal zona incerta just dorsal to the subthalamic nucleus eliminated sexual behavior in 6 of 15 males. The sexual behavior of the remaining males was affected to a lesser degree, for the most part in accord with the extent of destruction to this "critical zone." Subthalamic lesions produced no obvious impairment in locomotion, posture, limb use, muscle tone or sensorimotor orientation. Even so, the fact that electrical stimulation of the subthalamus elicits coordinated stepping suggests that the region is linked with systems directly concerned with movement and locomotion. These links could be particularly important in the process by which sexual motivation is translated into sexual behavior.     

Unique arm-flapping behavior of the pharaoh cuttlefish, <Emphasis Type="Italic">Sepia pharaonis</Emphasis>: putative mimicry of a hermit crab

Cephalopods are able to control their arms sophisticatedly and use them for various behaviors, such as camouflage, startling predators and hunting prey. Here, we report a previously undescribed arm-flapping behavior of the pharaoh cuttlefish, Sepia pharaonis, observed in captivity. S. pharaonis raised the first pair of arms and wrinkled the parts near the distal end, where the skin color was darkened. Additionally, S. pharaonis spread the second and third pairs of arms and bent them as if they were jointed, and flapped the distal ends. S. pharaonis showed this behavior in two different situations: after being introduced into a large space, and during hunting. We discuss the putative functions of this behavior, including possible mimicry of a hermit crab, considering the situations in which the behavior was observed.     

Kinetic studies of the lactic acid fermentation in batch and continuous cultures

The fermentation kinetics of the homofermentative organism Lactobacillus delbrueckii in a glucose-yeast extract medium is studied in both batch and continuous culture under conditions of controlled pH. From a graphical analysis of the batch data, a mathematical model of the process is derived which relates bacterial growth, glucose utilization, and lactic acid formation. The parameters in the model represent the activity of the organism and are a function of pH, having a maximum value at about 5.90. In a continuous stirred tank fermentor (CSTF), the effect of pH, feed concentration, and residence time is observed. The feed medium is a constant ratio of two parts glucose to one part yeast extract plus added mineral salts. An approximate prediction of the steady-state behavior of the CSTF can be made using a method based on the kinetic model derived for the batch case. In making step changes from one steady state to another, the transient response is observed. Using the kinetic model to simulate the transient period, the calculated behavior qualitatively predicts the observed response.     

Biotherapeutic protein formulation variables influence protein integrity and can promote post-translational modifications as shown using chicken egg white lysozyme as a model system

Objectives

The effect of different formulations variables on protein integrity were investigated using lysozyme as a model protein for the development of biotherapeutic protein formulations for use in the clinic.

Results

Buffer composition/concentration was the key variable of formulation reagents investigated in determining lysozyme stability and authenticity independent of protein concentration whilst the storage temperature and time, not surprisingly, were also key variables. Tryptic peptide mapping of the protein showed that the modifications occurred when formulated under specific conditions but not others. A model peptide system was developed that reflected the same behavior under formulation conditions as intact lysozyme.

Conclusions

Peptide models may mirror the stability of proteins, or regions of proteins, in the same formulations and be used to help develop a rapid screen of formulations for stabilisation of biotherapeutic proteins.

     

A finite element model of the lower limb during stance phase of gait cycle including the muscle forces

Background

Results of finite element (FE) analyses can give insight into musculoskeletal diseases if physiological boundary conditions, which include the muscle forces during specific activities of daily life, are considered in the FE modelling. So far, many simplifications of the boundary conditions are currently made. This study presents an approach for FE modelling of the lower limb for which muscle forces were included.

Methods

The stance phase of normal gait was simulated. Muscle forces were calculated using a musculoskeletal rigid body (RB) model of the human body, and were subsequently applied to a FE model of the lower limb. It was shown that the inertial forces are negligible during the stance phase of normal gait. The contact surfaces between the parts within the knee were modelled as bonded. Weak springs were attached to the distal tibia for numerical reasons.

Results

Hip joint reaction forces from the RB model and those from the FE model were similar in magnitude with relative differences less than 16%. The forces of the weak spring were negligible compared to the applied muscle forces. The maximal strain was 0.23% in the proximal region of the femoral diaphysis and 1.7% in the contact zone between the tibia and the fibula.

Conclusions

The presented approach based on FE modelling by including muscle forces from inverse dynamic analysis of musculoskeletal RB model can be used to perform analyses of the lower limb with very realistic boundary conditions. In the present form, this model can be used to better understand the loading, stresses and strains of bones in the knee area and hence to analyse osteotomy fixation devices.