A new mathematical model for combining growth and energy intake in animals: The case of the growing pig

A simultaneous model for analysis of net energy intake and growth curves is presented, viewing the animal's responses as a two dimensional outcome. The model is derived from four assumptions: (1) the intake is a quadratic function of metabolic weight; (2) the rate of body energy accretion represents the difference between intake and maintenance; (3) the relationship between body weight and body energy is allometric and (4) animal intrinsic variability affects the outcomes so the intake and growth trajectories are realizations of a stochastic process. Data on cumulated net energy intake and body weight measurements registered from weaning to maturity were available for 13 pigs. The model was fitted separately to 13 datasets. Furthermore, slaughter data obtained from 170 littermates was available for validation of the model. The parameters of the model were estimated by maximum likelihood within a stochastic state space model framework where a transform-both-sides approach was adopted to obtain constant variance. A suitable autocorrelation structure was generated by the stochastic process formulation. The pigs’ capacity for intake and growth were quantified by eight parameters: body weight at maximum rate of intake (149-281 kg); maximum rate of intake (25.7-35.7 MJ/day); metabolic body size exponent (fixed: 0.75); the daily maintenance requirement per kg metabolic body size (0.232-0.303 MJ/(day×kg^0.75)); reciprocal scaled energy density ; a dimensional exponent, θ₆ (0.730-0.867); coefficient for animal intrinsic variability in intake (0.120-0.248 MJ^0.5) and coefficient for animal intrinsic variability in growth (0.029-0.065 kg^0.5). Model parameter values for maintenance requirements and body energy gains were in good agreement with those obtained from slaughter data. In conclusion, the model provides biologically relevant parameter values, which cannot be derived by traditional analysis of growth and energy intake data.     

Propagation of Fluctuations in Biochemical Systems,I: Linear SSC Networks

We investigate the propagation of random fluctuations through biochemical networks in which the number of molecules of each species is large enough so that the concentrations are well modeled by differential equations. We study the effect of network topology on the emergent properties of the reaction system by characterizing the behavior of variance as fluctuations propagate down chains and studying the effect of side chains and feedback loops. We also investigate the asymptotic behavior of the system as one reaction becomes fast relative to the others.     

An interacting particle system modelling aggregation behavior: from individuals to populations

In this paper we investigate the stochastic modelling of a spatially structured biological population subject to social interaction. The biological motivation comes from the analysis of field experiments on a species of ants which exhibits a clear tendency to aggregate, still avoiding overcrowding. The model we propose here provides an explanation of this experimental behavior in terms of long-ranged aggregation and short-ranged repulsion mechanisms among individuals, in addition to an individual random dispersal described by a Brownian motion. Further, based on a law of large numbers, we discuss the convergence, for large N, of a system of stochastic differential equations describing the evolution of N individuals (Lagrangian approach) to a deterministic integro-differential equation describing the evolution of the mean-field spatial density of the population (Eulerian approach).     

Mutation,selection, and ancestry in branching models: a variational approach

We consider the evolution of populations under the joint action of mutation and differential reproduction, or selection. The population is modelled as a finite-type Markov branching process in continuous time, and the associated genealogical tree is viewed both in the forward and the backward direction of time. The stationary type distribution of the reversed process, the so-called ancestral distribution, turns out as a key for the study of mutation–selection balance. This balance can be expressed in the form of a variational principle that quantifies the respective roles of reproduction and mutation for any possible type distribution. It shows that the mean growth rate of the population results from a competition for a maximal long-term growth rate, as given by the difference between the current mean reproduction rate, and an asymptotic decay rate related to the mutation process; this tradeoff is won by the ancestral distribution. We then focus on the case when the type is determined by a sequence of letters (like nucleotides or matches/mismatches relative to a reference sequence), and we ask how much of the above competition can still be seen by observing only the letter composition (as given by the frequencies of the various letters within the sequence). If mutation and reproduction rates can be approximated in a smooth way, the fitness of letter compositions resulting from the interplay of reproduction and mutation is determined in the limit as the number of sequence sites tends to infinity. Our main application is the quasispecies model of sequence evolution with mutation coupled to reproduction but independent across sites, and a fitness function that is invariant under permutation of sites. In this model, the fitness of letter compositions is worked out explicitly. In certain cases, their competition leads to a phase transition.      

Translational models of tumor angiogenesis: A nexus of in silico and in vitro models

Emerging evidence shows that endothelial cells are not only the building blocks of vascular networks that enable oxygen and nutrient delivery throughout a tissue but also serve as a rich resource of angiocrine factors. Endothelial cells play key roles in determining cancer progression and response to anti-cancer drugs. Furthermore, the endothelium-specific deposition of extracellular matrix is a key modulator of the availability of angiocrine factors to both stromal and cancer cells. Considering tumor vascular network as a decisive factor in cancer pathogenesis and treatment response, these networks need to be an inseparable component of cancer models. Both computational and in vitro experimental models have been extensively developed to model tumor-endothelium interactions. While informative, they have been developed in different communities and do not yet represent a comprehensive platform. In this review, we overview the necessity of incorporating vascular networks for both in vitro and in silico cancer models and discuss recent progresses and challenges of in vitro experimental microfluidic cancer vasculature-on-chip systems and their in silico counterparts. We further highlight how these two approaches can merge together with the aim of presenting a predictive combinatorial platform for studying cancer pathogenesis and testing the efficacy of single or multi-drug therapeutics for cancer treatment.     

Effects of transmural electrical heterogeneities and electrotonic interactions on the dispersion of cardiac repolarization and action potential duration: A simulation study

It has been shown in the literature that myocytes isolated from the ventricular walls at various intramural depths have different action potential durations (APDs). When these myocytes are embedded in the ventricular wall, their inhomogeneous properties affect the sequence of repolarization and the actual distribution of the APDs in the entire wall. In this article, we implement a mathematical model to simulate the combined effect of (a) the non-homogeneous intrinsic membrane properties (in particular the non-homogeneous APDs) and (b) the electrotonic currents that modulate the APDs when the myocytes are embedded in the ventricular myocardium. In particular, we study the effect of (a) and (b) on the excitation and repolarization sequences and on the distribution of APDs in the ventricles. We implement a Monodomain tissue representation that includes orthotropic anisotropy, transmural fiber rotation and homogeneous or heterogeneous transmural intrinsic membrane properties, modeled according to the phase I Luo-Rudy membrane ionic model. Three-dimensional simulations are performed in a cartesian slab with a parallel finite element solver employing structured isoparametric trilinear finite elements in space and a semi-implicit adaptive method in time. Simulations of excitation and repolarization sequences elicited by epicardial or endocardial pacing show that in a homogeneous slab the repolarization pathways approximately follow the activation sequence. Conversely, in the heterogeneous cases considered in this study, we observed two repolarization wavefronts that started from the epi and the endocardial faces respectively and collided in the thickness of the wall and in one case an additional repolarization wave starting from an intramural site. Introducing the heterogeneities along the transmural epi-endocardial direction affected both the repolarization sequence and the APD dispersion, but these effects were clearly discernible only in transmural planes. By contrast, in planes parallel to epi- and endocardium the APD distribution remained remarkably similar to that observed in the homogeneous model. Therefore, the patterns of the repolarization sequence and APD dispersion on the epicardial surface (or any other intramural surface parallel to it) do not reveal the uniform transmural heterogeneity.     

A four-state cross bridge model for muscle contraction. Mathematical study and validation

A mathematical model of contracting skeletal muscle is studied. The model is composed by an elastic element (SE) in series with a contractile element (CE) that describes the cross bridge kinetics with a formulation derived by that proposed by Eisenberg and Hill (1978). An analytical study of the system of nonlinear partial differential equations of the model allows the existence and the uniqueness of the solution to be proved. A suitable approach to the numerical solution is defined and a series of numerical tests are performed. These tests lead to select an appropriate set of parameters and allow to compare model predictions and experimental observations on frog skeletal muscle. Work partially supported by M.P.I., by CNR through I.A.N. of Pavia and by HUSPI Project     

Anorexia dreaming: A case study.

A case study is presented focusing on a dream of a severely anorectic woman. The dream occurred at a point when the disorder had become life threatening. The dream is discussed in terms of its significance in the dreamer's experience, its implications for the use of dreams in psychotherapy, and its relevance for the broader literature on psychopathology and dreams. Archetypal psychology's aesthetic, and phenomenological approach to dreams is presented as a framework for understanding the ongoing significance of significant dreams such as the one presented here. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Latent antithrombin does not affect physiological angiogenesis: an in vivo study on vascularization of grafted ovarian follicles

Latent antithrombin (L-AT), a heat-denatured form of native antithrombin (AT), is a potent inhibitor of pathological tumor angiogenesis. In the present study, we have investigated whether L-AT has comparable antiangiogenic effects on physiological angiogenesis of ovarian tissue. For this purpose, preovulatory follicles of Syrian golden hamsters were mechanically isolated and transplanted into dorsal skinfold chambers chronically implanted in L-AT- or AT-treated hamsters. Non-treated animals served as controls. Over 14 days after transplantation neovascularization of the follicular grafts was assessed in vivo by quantitative analysis of the newly developed microvascular network, its microvessel density, the diameter of the microvessels, their red blood cell velocity and volumetric blood flow as well as leukocyte-endothelial cell interaction using fluorescence microscopic techniques. In each group, all of the grafted follicles were able to induce angiogenesis. At day 3 after transplantation, sinusoidal sacculations and capillary sprouts could be observed, finally developing complete glomerulum-like microvascular networks within 5 to 7 days. Overall revascularization of grafted follicles did not differ between the groups studied. Interestingly, follicular grafts in L-AT- and AT-treated hamsters presented with higher values of microvessel diameters and volumetric blood flow, when compared to non-treated controls, which may be best interpreted as a reactive response to an increased release of vasoactive mediators. In conclusion, the present study demonstrates, that L-AT has no adverse effects on physiological angiogenesis of freely transplanted ovarian follicles. Thus, L-AT may be an effective drug in tumor therapy, which blocks tumor growth by selective suppression of tumor vascularization without affecting new vessel formation in the female reproductive system.     

Human microvascular endothelial cells immortalized with human telomerase catalytic protein: a model for the study of in vitro angiogenesis

Human microvascular endothelial cell-1 (HMEC-1) generated by transfection with SV40 large T antigen has been the prevailing model for in vitro studies on endothelium. However, the transduction of SV40 may lead to unwanted cell behaviors which are absent in primary cells. Thus, establishing a new microvascular endothelial cell line, which is capable of maintaining inherent features of primary endothelial cells, appears to be extremely important. Here, we immortalized primary human microvascular endothelial cells (pHMECs) by engineering the human telomerase catalytic protein (hTERT) into the cells. Endothelial cell-specific markers were examined and the angiogenic responses were characterized in these cells (termed as HMVECs, for human microvascular endothelial cells). We found that VEGF receptor 2 (Flk-1/KDR), tie1, and tie2 expression is preserved in HMVEC, whereas Flk-1/KDR is absent in HMEC-1. In addition, HMVEC showed similar angiogenic responses to VEGF as HMEC-1. Furthermore, the HMVEC line was found to generate a prominent angiogenic response to periostin, a potent angiogenic factor identified recently. The data indicate that HMVEC may serve as a suitable in vitro endothelium model.     

Management of drug resistance in the population: influenza as a case study

The rise of drug resistance remains a major impediment to the treatment of some diseases caused by fast-evolving pathogens that undergo genetic mutations. Models describing the within-host infectious dynamics suggest that the resistance is unlikely to emerge if the pathogen-specific immune responses are maintained above a certain threshold during therapy. However, emergence of resistance in the population involves both within-host and between-host infection mechanisms. Here, we employ a mathematical model to identify an effective treatment strategy for the management of drug resistance in the population. We show that, in the absence of pre-existing immunity, the population-wide spread of drug-resistant pathogen strains can be averted if a sizable portion of susceptible hosts is depleted before drugs are used on a large scale. The findings, based on simulations for influenza infection as a case study, suggest that the initial prevalence of the drug-sensitive strain under low pressure of drugs, followed by a timely implementation of intensive treatment, can minimize the total number of infections while preventing outbreaks of drug-resistant infections.     

Time-varying Markov regression random-effect model with Bayesian estimation procedures: Application to dynamics of functional recovery in patients with stroke

The rates of functional recovery after stroke tend to decrease with time. Time-varying Markov processes (TVMP) may be more biologically plausible than time-invariant Markov process for modeling such data. However, analysis of such stochastic processes, particularly tackling reversible transitions and the incorporation of random effects into models, can be analytically intractable. We make use of ordinary differential equations to solve continuous-time TVMP with reversible transitions. The proportional hazard form was used to assess the effects of an individual’s covariates on multi-state transitions with the incorporation of random effects that capture the residual variation after being explained by measured covariates under the concept of generalized linear model. We further built up Bayesian directed acyclic graphic model to obtain full joint posterior distribution. Markov chain Monte Carlo (MCMC) with Gibbs sampling was applied to estimate parameters based on posterior marginal distributions with multiple integrands. The proposed method was illustrated with empirical data from a study on the functional recovery after stroke.     

A numerical study of the nonsteady transport of gases in the pulmonary capillaries

A mathematical model is formulated for simulating the unsteady transport of gases in the blood flowing through the pulmonary capillaries. The formulation takes into account the transport mechanisms of molecular diffusion, convection and facilitated diffusion of the species due to haemoglobin. A time dependent situation is created by allowing to vary suddenly the partial pressures of the gases either in the venous blood or in the alveolar air. A numerical technique is described to solve the resulting time-dependent system of nonlinear coupled partial differential equations with the physiologically relevant boundary, entrance and initial conditions. The time required by the gases to achieve equilibrium is computed. It is shown that the dissolved oxygen takes longest in reaching equilibration whereas the carbon dioxide is the fastest. The various physiologically relevant unsteady situations have been examined.     

Self-fighting syndrome in macaques: I. A representative case study

Spontaneously occurring self-fighting behaviour in a male Stumptail macaqueMacaca arctoides with a history of prior social deprivation was studied clinically. Experimental interventions showed external aggression to be a triggering factor when the animal aggressed against could neither escape nor defend itself. Syndrome: a precisely defined ensemble of symptoms which can be observed in several different pathological states but which as such do not shed light on the cause or the nature of an illness.     

Joint generalized models for multidimensional outcomes: A case study of neuroscience data from multimodalities

This paper is motivated from the analysis of neuroscience data in a study of neural and muscular mechanisms of muscle fatigue. Multidimensional outcomes of different natures were obtained simultaneously from multiple modalities, including handgrip force, electromyography (EMG), and functional magnetic resonance imaging (fMRI). We first study individual modeling of the univariate response depending on its nature. A mixed‐effects beta model and a mixed‐effects simplex model are compared for modeling the force/EMG percentages. A mixed‐effects negative‐binomial model is proposed for modeling the fMRI counts. Then, I present a joint modeling approach to model the multidimensional outcomes together, which allows us to not only estimate the covariate effects but also to evaluate the strength of association among the multiple responses from different modalities. A simulation study is conducted to quantify the possible benefits by the new approaches in finite sample situations. Finally, the analysis of the fatigue data is illustrated with the use of the proposed methods.     

The effect of volcanism on postglacial migration and seed dispersal. A case study in southern South America

During the Quaternary, southern South American temperate forests were confined to small and isolated refugia. Recolonization could be related not only with location of refugia but also with postglacial phenomena like volcanism, which could have interrupted the expansion of the forests. The aim of this study was to analyze the local effect of volcanism during the postglacial migration of Nothofagus nervosa in a particular region of Argentina were convergence of two migratory routes was suggested. The main question is whether admixture occurred or not and if the current populations are connected by pollen or seed gene flow. Two populations separated by a 3-km-width lava flow were sampled. Buds from 30 individuals of each of the two populations and from a total of 142 juveniles were analyzed. Genetic variation was detected through maternally inherited chloroplast deoxyribonucleic acid (cpDNA; polymerase chain reaction restriction fragment length polymorphisms of two fragments) and nuclear markers like isozymes (six loci) and simple sequence repeats (three loci). Population genetic parameters were estimated and the existence of a genetic structure was tested with an analysis of molecular variance. Historical gene flow was estimated through the indirect method of the genetic differentiation (F _ST). Chloroplast DNA revealed a total genetic differentiation between the two populations indicating completely isolation respecting seed gene flow. On the contrary, the degree of genetic differentiation for the nuclear markers was significantly lower, and moderate levels of historical gene flow through pollen were inferred. The results suggest that in this area, volcanism has played an important local role during the expansion of N. nervosa maintaining these two populations separated. Communicated by A. Kremer     

Long-term genomic selection for heterosis without dominance in multiplicative traits: case study of bunch production in oil palm

Background

To study the potential of genomic selection for heterosis resulting from multiplicative interactions between additive and antagonistic components, we focused on oil palm, where bunch production is the product of bunch weight and bunch number. We simulated two realistic breeding populations and compared current reciprocal recurrent selection (RRS) with reciprocal recurrent genomic selection (RRGS) over four generations. All breeding strategies aimed at selecting the best individuals in parental populations to increase bunch production in hybrids. For RRGS, we obtained the parental genomic estimated breeding values using GBLUP with hybrid phenotypes as data records and population specific allele models. We studied the effects of four RRGS parameters on selection response and genetic parameters: (1) the molecular data used to calibrate the GS model: in RRGS_PAR, we used parental genotypes and in RRGS_HYB we also used hybrid genotypes; (2) frequency of progeny tests (model calibration); (3) number of candidates and (4) number of genotyped hybrids in RRGS_HYB.

Results

We concluded that RRGS could increase the annual selection response compared to RRS by decreasing the generation interval and by increasing the selection intensity. With 1700 genotyped hybrids, calibration every four generations and 300 candidates per generation and population, selection response of RRGS_HYB was 71.8 % higher than RRS. RRGS_PAR with calibration every two generations and 300 candidates was a relevant alternative, as a good compromise between the annual response, risk around the expected response, increased inbreeding and cost. RRGS required inbreeding management because of a higher annual increase in inbreeding than RRS.

Conclusions

RRGS appeared as a valuable method to achieve a long-term increase in the performance for a trait showing heterosis due to the multiplicative interaction between additive and negatively correlated components, such as oil palm bunch production.     

A Two-Patch Model of Gambian Sleeping Sickness: Application to Vector Control Strategies in a Village and Plantations

A compartmental model is described for the spread of Gambian sleeping sickness in a spatially heterogeneous environment in which vector and human populations migrate between two "patches": the village and the plantations. The number of equilibrium points depends on two "summary parameters": gr the proportion removed among human infectives, and R0, the basic reproduction number. The origin is stable for R0 <1 and unstable for R0 >1. Control strategies are assessed by studying the mix of vector control between the two patches that bring R0 below 1. The results demonstrate the importance of vector control in the plantations. For example if 20 percent of flies are in the village and the blood meal rate in the village is 10 percent, then a 20 percent added vector mortality in the village must be combined with a 9 percent added mortality in the plantations in order to bring R0 below 1. The results are quite insentive to the blood meal rate in the village. Optimal strategies (that minimize the total number of flies trapped in both patches) are briefly discussed.     

A chronology of plankton dynamics in silico: how computer models have been used to study marine ecosystems

Research on plankton ecology in the oceans has traditionally been conducted via two scientific approaches: in situ (in the field) and in vitro (in the laboratory). There is, however, a third approach: exploring plankton dynamics in silico, or using computer models as tools to study marine ecosystems. Models have been used for this purpose for over 60 years, and the innovations and implementations of historical studies provide a context for how future model applications can continue to advance our understanding. To that end, this paper presents a chronology of the in silico approach to plankton dynamics, beginning with modeling pioneers who worked in the days before computers. During the first 30 years of automated computation, plankton modeling focused on formulations for biological processes and investigations of community structure. The changing technological context and conceptual paradigms of the late-1970s and 1980s resulted in simulations becoming more widespread research tools for biological oceanographers. This period saw rising use of models as hypothesis-testing tools, and means of exploring the effects of circulation on spatial distributions of organisms. Continued computer advances and increased availability of data in the 1990s allowed old approaches to be applied to old and new problems, and led to developments of new approaches. Much of the modeling in the new millennium so far has incorporated these sophistications, and many cutting-edge applications have come from a new generation of plankton scientists who were trained by modeling gurus of previous eras. The future directions for modeling plankton dynamics are rooted in the historical studies.