An infinitesimal model for quantitative trait genomic value prediction

We developed a marker based infinitesimal model for quantitative trait analysis. In contrast to the classical infinitesimal model, we now have new information about the segregation of every individual locus of the entire genome. Under this new model, we propose that the genetic effect of an individual locus is a function of the genome location (a continuous quantity). The overall genetic value of an individual is the weighted integral of the genetic effect function along the genome. Numerical integration is performed to find the integral, which requires partitioning the entire genome into a finite number of bins. Each bin may contain many markers. The integral is approximated by the weighted sum of all the bin effects. We now turn the problem of marker analysis into bin analysis so that the model dimension has decreased from a virtual infinity to a finite number of bins. This new approach can efficiently handle virtually unlimited number of markers without marker selection. The marker based infinitesimal model requires high linkage disequilibrium of all markers within a bin. For populations with low or no linkage disequilibrium, we develop an adaptive infinitesimal model. Both the original and the adaptive models are tested using simulated data as well as beef cattle data. The simulated data analysis shows that there is always an optimal number of bins at which the predictability of the bin model is much greater than the original marker analysis. Result of the beef cattle data analysis indicates that the bin model can increase the predictability from 10% (multiple marker analysis) to 33% (multiple bin analysis). The marker based infinitesimal model paves a way towards the solution of genetic mapping and genomic selection using the whole genome sequence data.     

Estimating a binary character's effect on speciation and extinction

Determining whether speciation and extinction rates depend on the state of a particular character has been of long-standing interest to evolutionary biologists. To assess the effect of a character on diversification rates using likelihood methods requires that we be able to calculate the probability that a group of extant species would have evolved as observed, given a particular model of the character's effect. Here we describe how to calculate this probability for a phylogenetic tree and a two-state (binary) character under a simple model of evolution (the "BiSSE" model, binary-state speciation and extinction). The model involves six parameters, specifying two speciation rates (rate when the lineage is in state 0; rate when in state 1), two extinction rates (when in state 0; when in state 1), and two rates of character state change (from 0 to 1, and from 1 to 0). Using these probability calculations, we can do maximum likelihood inference to estimate the model's parameters and perform hypothesis tests (e.g., is the rate of speciation elevated for one character state over the other?). We demonstrate the application of the method using simulated data with known parameter values.     

Can a Species Keep Pace with a Shifting Climate?

Consider a patch of favorable habitat surrounded by unfavorable habitat and assume that due to a shifting climate, the patch moves with a fixed speed in a one-dimensional universe. Let the patch be inhabited by a population of individuals that reproduce, disperse, and die. Will the population persist? How does the answer depend on the length of the patch, the speed of movement of the patch, the net population growth rate under constant conditions, and the mobility of the individuals? We will answer these questions in the context of a simple dynamic profile model that incorporates climate shift, population dynamics, and migration. The model takes the form of a growth-diffusion equation. We first consider a special case and derive an explicit condition by glueing phase portraits. Then we establish a strict qualitative dichotomy for a large class of models by way of rigorous PDE methods, in particular the maximum principle. The results show that mobility can both reduce and enhance the ability to track climate change that a narrow range can severely reduce this ability and that population range and total population size can both increase and decrease under a moving climate. It is also shown that range shift may be easier to detect at the expanding front, simply because it is considerably steeper than the retreating back.     

Modeling Spatial Spread of Infectious Diseases with a Fixed Latent Period in a Spatially Continuous Domain

In this paper, with the assumptions that an infectious disease in a population has a fixed latent period and the latent individuals of the population may diffuse, we formulate an SIR model with a simple demographic structure for the population living in a spatially continuous environment. The model is given by a system of reaction-diffusion equations with a discrete delay accounting for the latency and a spatially non-local term caused by the mobility of the individuals during the latent period. We address the existence, uniqueness, and positivity of solution to the initial-value problem for this type of system. Moreover, we investigate the traveling wave fronts of the system and obtain a critical value c ^* which is a lower bound for the wave speed of the traveling wave fronts. Although we can not prove that this value is exactly the minimal wave speed, numeric simulations seem to suggest that it is. Furthermore, the simulations on the PDE model also suggest that the spread speed of the disease indeed coincides with c ^*. We also discuss how the model parameters affect c ^*.     

Genetic prediction of complex traits: integrating infinitesimal and marked genetic effects

Genetic prediction for complex traits is usually based on models including individual (infinitesimal) or marker effects. Here, we concentrate on models including both the individual and the marker effects. In particular, we develop a “Mendelian segregation” model combining infinitesimal effects for base individuals and realized Mendelian sampling in descendants described by the available DNA data. The model is illustrated with an example and the analyses of a public simulated data file. Further, the potential contribution of such models is assessed by simulation. Accuracy, measured as the correlation between true (simulated) and predicted genetic values, was similar for all models compared under different genetic backgrounds. As expected, the segregation model is worthwhile when markers capture a low fraction of total genetic variance.     

Learning by structural remodeling in a class of single cell models

Changes in neural connectivity are thought to underlie the most permanent forms of memory in the brain. We consider two models, derived from the clusteron (Mel, Adv Neural Inf Process Syst 4:35-42, 1992), to study this method of learning. The models show a direct relationship between the speed of memory acquisition and the probability of forming appropriate synaptic connections. Moreover, the strength of learned associations grows with the number of fibers that have taken part in the learning process. We provide simple and intuitive explanations of these two results by analyzing the distribution of synaptic activations. The obtained insights are then used to extend the model to perform novel tasks: feature detection, and learning spatio-temporal patterns. We also provide an analytically tractable approximation to the model to put these observations on a firm basis. The behavior of both the numerical and analytical models correlate well with experimental results of learning tasks which are thought to require a reorganization of neuronal networks.     

Reconstructing genetic ancestry blocks in admixed individuals

A chromosome in an individual of recently admixed ancestry resembles a mosaic of chromosomal segments, or ancestry blocks, each derived from a particular ancestral population. We consider the problem of inferring ancestry along the chromosomes in an admixed individual and thereby delineating the ancestry blocks. Using a simple population model, we infer gene-flow history in each individual. Compared with existing methods, which are based on a hidden Markov model, the Markov-hidden Markov model (MHMM) we propose has the advantage of accounting for the background linkage disequilibrium (LD) that exists in ancestral populations. When there are more than two ancestral groups, we allow each ancestral population to admix at a different time in history. We use simulations to illustrate the accuracy of the inferred ancestry as well as the importance of modeling the background LD; not accounting for background LD between markers may mislead us to false inferences about mixed ancestry in an indigenous population. The MHMM makes it possible to identify genomic blocks of a particular ancestry by use of any high-density single-nucleotide-polymorphism panel. One application of our method is to perform admixture mapping without genotyping special ancestry-informative-marker panels.     

A QTL on chromosome 3q23 influences processing speed in humans

Processing speed is a psychological construct that refers to the speed with which an individual can perform any cognitive operation. Processing speed correlates strongly with general cognitive ability, declines sharply with age and is impaired across a number of neurological and psychiatric disorders. Thus, identifying genes that influence processing speed will likely improve understanding of the genetics of intelligence, biological aging and the etiologies of numerous disorders. Previous genetics studies of processing speed have relied on simple phenotypes (eg, mean reaction time) derived from single tasks. This strategy assumes, erroneously, that processing speed is a unitary construct. In the present study, we aimed to characterize the genetic architecture of processing speed by using a multidimensional model applied to a battery of cognitive tasks. Linkage and QTL‐specific association analyses were performed on the factors from this model. The randomly ascertained sample comprised 1291 Mexican‐American individuals from extended pedigrees. We found that performance on all three distinct processing‐speed factors (Psychomotor Speed; Sequencing and Shifting and Verbal Fluency) were moderately and significantly heritable. We identified a genome‐wide significant quantitative trait locus (QTL) on chromosome 3q23 for Psychomotor Speed (LOD = 4.83). Within this locus, we identified a plausible and interesting candidate gene for Psychomotor Speed (Z = 2.90, P = 1.86 × 10^?03).     

Dynamic Artificial Neural Networks with Affective Systems

Artificial neural networks (ANNs) are processors that are trained to perform particular tasks. We couple a computational ANN with a simulated affective system in order to explore the interaction between the two. In particular, we design a simple affective system that adjusts the threshold values in the neurons of our ANN. The aim of this paper is to demonstrate that this simple affective system can control the firing rate of the ensemble of neurons in the ANN, as well as to explore the coupling between the affective system and the processes of long term potentiation (LTP) and long term depression (LTD), and the effect of the parameters of the affective system on its performance. We apply our networks with affective systems to a simple pole balancing example and briefly discuss the effect of affective systems on network performance.     

A dynamical model of kinesin-microtubule motility assays

A two-dimensional stochastic model for the dynamics of microtubules in gliding-assay experiments is presented here, which includes the viscous drag acting on the moving fiber and the interaction with the kinesins. For this purpose, we model kinesin as a spring, and explicitly use parameter values to characterize the model from experimental data. We numerically compute the mean attachment lifetimes of all motors, the total force exerted on the microtubules at all times, the effects of a distribution in the motor speeds, and also the mean velocity of a microtubule in a gliding assay. We find quantitative agreement with the results of J. Howard, A. J. Hudspeth, and R. D. Vale, Nature. 342:154-158. We perform additional numerical analysis of the individual motors, and show how cancellation of the forces exerted by the many motors creates a resultant longitudinal force much smaller than the maximum force that could be exerted by a single motor. We also examine the effects of inhomogeneities in the motor-speeds. Finally, we present a simple theoretical model for microtubules dynamics in gliding assays. We show that the model can be analytically solved in the limit of few motors attached to the microtubule and in the opposite limit of high motor density. We find that the speed of the microtubule goes like the mean speed of the motors in good quantitative agreement with the experimental and numerical results.     

Wide-field motion integration in fly VS cells: insights from an inverse approach

Fly lobula plate tangential cells are known to perform wide-field motion integration. It is assumed that the shape of these neurons, and in particular the shape of the subclass of VS cells, is responsible for this type of computation. We employed an inverse approach to investigate the morphology-function relationship underlying wide-field motion integration in VS cells. In the inverse approach detailed, model neurons are optimized to perform a predefined computation: here, wide-field motion integration. We embedded the model neurons to be optimized in a biologically plausible model of fly motion detection to provide realistic inputs, and subsequently optimized model neuron with and without active conductances (g(Na), g(K), g(K(Na))) along their dendrites to perform this computation. We found that both passive and active optimized model neurons perform well as wide-field motion integrators. In addition, all optimized morphologies share the same blueprint as real VS cells. In addition, we also found a recurring blueprint for the distribution of g(K) and g(Na) in the active models. Moreover, we demonstrate how this morphology and distribution of conductances contribute to wide-field motion integration. As such, by using the inverse approach we can predict the still unknown distribution of g(K) and g(Na) and their role in motion integration in VS cells.     

Fast, DNA-sequence independent translocation by FtsK in a single-molecule experiment

Escherichia coli FtsK is an essential cell division protein, which is thought to pump chromosomal DNA through the closing septum in an oriented manner by following DNA sequence polarity. Here, we perform single-molecule measurements of translocation by FtsK50C, a derivative that functions as a DNA translocase in vitro. FtsK50C translocation follows Michaelis-Menten kinetics, with a maximum speed of approximately 6.7 kbp/s. We present results on the effect of applied force on the speed, distance translocated, and the mean times during and between protein activity. Surprisingly, we observe that FtsK50C can spontaneously reverse its translocation direction on a fragment of E. coli chromosomal DNA, indicating that DNA sequence is not the sole determinant of translocation direction. We conclude that in vivo polarization of FtsK translocation could require the presence of cofactors; alternatively, we propose a model in which tension in the DNA directs FtsK translocation.     

Limitations of perturbative techniques in the analysis of rhythms and oscillations

Perturbation theory is an important tool in the analysis of oscillators and their response to external stimuli. It is predicated on the assumption that the perturbations in question are “sufficiently weak”, an assumption that is not always valid when perturbative methods are applied. In this paper, we identify a number of concrete dynamical scenarios in which a standard perturbative technique, based on the infinitesimal phase response curve (PRC), is shown to give different predictions than the full model. Shear-induced chaos, i.e., chaotic behavior that results from the amplification of small perturbations by underlying shear, is missed entirely by the PRC. We show also that the presence of “sticky” phase–space structures tend to cause perturbative techniques to overestimate the frequencies and regularity of the oscillations. The phenomena we describe can all be observed in a simple 2D neuron model, which we choose for illustration as the PRC is widely used in mathematical neuroscience.     

An SEI model for sarcoptic mange among chamois

We consider a simple model to study the dynamics of sarcoptic mange in a population of chamois. The epidemiological patterns observed during an epidemic in Italy are reconstructed and key parameters of the model are estimated from field data. In particular, we calculate the basic reproductive ratio R (0), a threshold value for chamois density for the occurrence of an epidemic and the speed of propagation of the epidemic wave. The model is then used to obtain indications on the effect of culling as a possible control measure in a closed population and extended to analyse the spatial diffusion of the epidemic. Our results are in agreement with mange epidemiology and observations, and suggest that intervention could be efficacious in reducing the impact of an epidemic.     

Neural correlates of the difference between working memory speed and simple sensorimotor speed: an fMRI study

The difference between the speed of simple cognitive processes and the speed of complex cognitive processes has various psychological correlates. However, the neural correlates of this difference have not yet been investigated. In this study, we focused on working memory (WM) for typical complex cognitive processes. Functional magnetic resonance imaging data were acquired during the performance of an N-back task, which is a measure of WM for typical complex cognitive processes. In our N-back task, task speed and memory load were varied to identify the neural correlates responsible for the difference between the speed of simple cognitive processes (estimated from the 0-back task) and the speed of WM. Our findings showed that this difference was characterized by the increased activation in the right dorsolateral prefrontal cortex (DLPFC) and the increased functional interaction between the right DLPFC and right superior parietal lobe. Furthermore, the local gray matter volume of the right DLPFC was correlated with participants' accuracy during fast WM tasks, which in turn correlated with a psychometric measure of participants' intelligence. Our findings indicate that the right DLPFC and its related network are responsible for the execution of the fast cognitive processes involved in WM. Identified neural bases may underlie the psychometric differences between the speed with which subjects perform simple cognitive tasks and the speed with which subjects perform more complex cognitive tasks, and explain the previous traditional psychological findings.     

An SEI model for sarcoptic mange among chamois

We consider a simple model to study the dynamics of sarcoptic mange in a population of chamois. The epidemiological patterns observed during an epidemic in Italy are reconstructed and key parameters of the model are estimated from field data. In particular, we calculate the basic reproductive ratio R ₀, a threshold value for chamois density for the occurrence of an epidemic and the speed of propagation of the epidemic wave. The model is then used to obtain indications on the effect of culling as a possible control measure in a closed population and extended to analyse the spatial diffusion of the epidemic. Our results are in agreement with mange epidemiology and observations, and suggest that intervention could be efficacious in reducing the impact of an epidemic.     

Effects of genetic architecture on the evolution of assortative mating under frequency-dependent disruptive selection

We consider a model of sympatric speciation due to frequency-dependent competition, in which it was previously assumed that the evolving traits have a very simple genetic architecture. In the present study, we numerically analyze the consequences of relaxing this assumption. First, previous models assumed that assortative mating evolves in infinitesimal steps. Here, we show that the range of parameters for which speciation is possible increases when mutational steps are large. Second, it was assumed that the trait under frequency-dependent selection is determined by a single locus with two alleles and additive effects. As a consequence, the resultant intermediate phenotype is always heterozygous and can never breed true. To relax this assumption, here we add a second locus influencing the trait. We find three new possible evolutionary outcomes: evolution of three reproductively isolated species, a monomorphic equilibrium with only the intermediate phenotype, and a randomly mating population with a steep unimodal distribution of phenotypes. Both extensions of the original model thus increase the likelihood of competitive speciation.