Firing-rate models for neurons with a broad repertoire of spiking behaviors

Capturing the response behavior of spiking neuron models with rate-based models facilitates the investigation of neuronal networks using powerful methods for rate-based network dynamics. To this end, we investigate the responses of two widely used neuron model types, the Izhikevich and augmented multi-adapative threshold (AMAT) models, to a range of spiking inputs ranging from step responses to natural spike data. We find (i) that linear-nonlinear firing rate models fitted to test data can be used to describe the firing-rate responses of AMAT and Izhikevich spiking neuron models in many cases; (ii) that firing-rate responses are generally too complex to be captured by first-order low-pass filters but require bandpass filters instead; (iii) that linear-nonlinear models capture the response of AMAT models better than of Izhikevich models; (iv) that the wide range of response types evoked by current-injection experiments collapses to few response types when neurons are driven by stationary or sinusoidally modulated Poisson input; and (v) that AMAT and Izhikevich models show different responses to spike input despite identical responses to current injections. Together, these findings suggest that rate-based models of network dynamics may capture a wider range of neuronal response properties by incorporating second-order bandpass filters fitted to responses of spiking model neurons. These models may contribute to bringing rate-based network modeling closer to the reality of biological neuronal networks.     

Modeling nonstationary longitudinal data

An important theme of longitudinal data analysis in the past two decades has been the development and use of explicit parametric models for the data's variance-covariance structure. A variety of these models have been proposed, of which most are second-order stationary. A few are flexible enough to accommodate nonstationarity, i.e., nonconstant variances and/or correlations that are not a function solely of elapsed time between measurements. We review five nonstationary models that we regard as most useful: (1) the unstructured covariance model, (2) unstructured antedependence models, (3) structured antedependence models, (4) autoregressive integrated moving average and similar models, and (5) random coefficients models. We evaluate the relative strengths and limitations of each model, emphasizing when it is inappropriate or unlikely to be useful. We present three examples to illustrate the fitting and comparison of the models and to demonstrate that nonstationary longitudinal data can be modeled effectively and, in some cases, quite parsimoniously. In these examples, the antedependence models generally prove to be superior and the random coefficients models prove to be inferior. We conclude that antedependence models should be given much greater consideration than they have historically received.     

HR-pQCT-based homogenised finite element models provide quantitative predictions of experimental vertebral body stiffness and strength with the same accuracy as μFE models

This study validated two different high-resolution peripheral quantitative computer tomography (HR-pQCT)-based finite element (FE) approaches, enhanced homogenised continuum-level (hFE) and micro-finite element (μFE) models, by comparing them with compression test results of vertebral body sections. Thirty-five vertebral body sections were prepared by removing endplates and posterior elements, scanned with HR-pQCT and tested in compression up to failure. Linear hFE and μFE models were created from segmented and grey-level CT images, and apparent model stiffness values were compared with experimental stiffness as well as strength results. Experimental and numerical apparent elastic properties based on grey-level/segmented CT images (N=35) correlated well for μFE (r2=0.748/0.842) and hFE models (r2=0.741/0.864). Vertebral section stiffness values from the linear μFE/hFE models estimated experimental ultimate apparent strength very well (r2=0.920/0.927). Calibrated hFE models were able to predict quantitatively apparent stiffness with the same accuracy as μFE models. However, hFE models needed no back-calculation of a tissue modulus or any kind of fitting and were computationally much cheaper.     

Non-rigid deformation to include subject-specific detail in musculoskeletal models of CP children with proximal femoral deformity and its effect on muscle and contact forces during gait

To account for proximal femoral deformities in children with cerebral palsy (CP), subject-specific musculoskeletal models are needed. Non-rigid deformation (NRD) deforms generic onto personalized bone geometry and thereby transforms the muscle points. The goal of this study was to determine to what extent the models and simulation outcomes in CP patients differ when including subject-specific detail using NRD or Magnetic Resonance Imaging (MRI)-based models. The NRD models slightly overestimated hip contact forces compared to MRI models and differences in muscle point positions and moment arm lengths (MALs) remained, although differences were smaller than for the generic model.     

Estimating the prevalence of infections in vector populations using pools of samples

Several statistical methods have been proposed for estimating the infection prevalence based on pooled samples, but these methods generally presume the application of perfect diagnostic tests, which in practice do not exist. To optimize prevalence estimation based on pooled samples, currently available and new statistical models were described and compared. Three groups were tested: (a) Frequentist models, (b) Monte Carlo Markov‐Chain (MCMC) Bayesian models, and (c) Exact Bayesian Computation (EBC) models. Simulated data allowed the comparison of the models, including testing the performance under complex situations such as imperfect tests with a sensitivity varying according to the pool weight. In addition, all models were applied to data derived from the literature, to demonstrate the influence of the model on real‐prevalence estimates. All models were implemented in the freely available R and OpenBUGS software and are presented in Appendix S1. Bayesian models can flexibly take into account the imperfect sensitivity and specificity of the diagnostic test (as well as the influence of pool‐related or external variables) and are therefore the method of choice for calculating population prevalence based on pooled samples. However, when using such complex models, very precise information on test characteristics is needed, which may in general not be available.     

What are the dielectric “constants” of proteins and how to validate electrostatic models?

Implicit models for evaluation of electrostatic energies in proteins include dielectric constants that represent effect of the protein environment. Unfortunately, the results obtained by such models are very sensitive to the value used for the dielectric constant. Furthermore, the factors that determine the optimal value of these constants are far from being obvious. This review considers the meaning of the protein dielectric constants and the ways to determine their optimal values. It is pointed out that typical benchmarks for validation of electrostatic models cannot discriminate between consistent and inconsistent models. In particular, the observed pK(a) values of surface groups can be reproduced correctly by models with entirely incorrect physical features. Thus, we introduce a discriminative benchmark that only includes residues whose pK(a) values are shifted significantly from their values in water. We also use the semimacroscopic version of the protein dipole Langevin dipole (PDLD/S) formulation to generate a series of models that move gradually from microscopic to fully macroscopic models. These include the linear response version of the PDLD/S models, Poisson Boltzmann (PB)-type models, and Tanford Kirkwwod (TK)-type models. Using our different models and the discriminative benchmark, we show that the protein dielectric constant, epsilon(p), is not a universal constant but simply a parameter that depends on the model used. It is also shown in agreement with our previous works that epsilon(p) represents the factors that are not considered explicitly. The use of a discriminative benchmark appears to help not only in identifying nonphysical models but also in analyzing effects that are not reproduced in an accurate way by consistent models. These include the effect of water penetration and the effect of the protein reorganization. Finally, we show that the optimal dielectric constant for self-energies is not the optimal constant for charge-charge interactions.     

The analysis of dependence in cross-classifications having ordered categories, using log-linear models for frequencies and log-linear models for odds

To analyse the dependence of a qualitative (dichotomous or polytomous) response variable upon one or more qualitative explanatory variables, log-linear models for frequencies are compared with log-linear models for odds, when the categories of the response variable are ordered and the categories of each explanatory variable may be either ordered or unordered. The log-linear models for odds express the odds (or log odds) pertaining to adjacent response categories in terms of appropriate multiplicative (or additive) factors. These models include the 'null log-odds model', the 'uniform log-odds model', the 'parallel log-odds model', and other log-linear models for the odds. With these models, the dependence of the response variable (with ordered categories) can be analyzed in a manner analogous to the usual multiple regression analysis and related analysis of variance and analysis of covariance. Application of log-linear models for the odds sheds light on earlier applications of log-linear models for the frequencies in contingency tables with ordered categories.     

Comparative modeling and protein-like features of hydrophobic-polar models on a two-dimensional lattice

Lattice models of proteins have been extensively used to study protein thermodynamics, folding dynamics, and evolution. Our study considers two different hydrophobic-polar (HP) models on the 2D square lattice: the purely HP model and a model where a compactness-favoring term is added. We exhaustively enumerate all the possible structures in our models and perform the study of their corresponding folds, HP arrangements in space and shapes. The two models considered differ greatly in their numbers of structures, folds, arrangements, and shapes. Despite their differences, both lattice models have distinctive protein-like features: (1) Shapes are compact in both models, especially when a compactness-favoring energy term is added. (2) The residue composition is independent of the chain length and is very close to 50% hydrophobic in both models, as we observe in real proteins. (3) Comparative modeling works well in both models, particularly in the more compact one. The fact that our models show protein-like features suggests that lattice models incorporate the fundamental physical principles of proteins. Our study supports the use of lattice models to study questions about proteins that require exactness and extensive calculations, such as protein design and evolution, which are often too complex and computationally demanding to be addressed with more detailed models.     

Biomimetic oxidation of nonphenolic lignin models by Mn(III): new observations on the oxidizability of guaiacyl and syringyl substructures

Mn(III) is a one-electron oxidant, produced in vivo by the Mn peroxidases of white-rot fungi, and thought to be involved in lignin degradation by these organisms. However, Mn(III) has not been shown to oxidize the major nonphenolic substructures of lignin under mild conditions. We have used Mn(III) acetate as a biomimetic model for enzymatically generated Mn(III), and report that low concentrations of this oxidant suffice to oxidize nonphenolic lignin models at physiological temperatures and pH values. Under these conditions, the monomeric lignin model veratryl alcohol was oxidized to veratraldehyde, and the diarylpropane model 1-(3,4-dimethoxyphenyl)-2-phenylpropanol was oxidatively cleaved to veratraldehyde, 1-phenylethanol, and acetophenone. In an attempt to identify other lignin models that might be oxidized by Mn(III) more rapidly, we compared the rates at which Mn(III) was reduced by two guaiacyl models, veratryl alcohol and 1-(3-methoxy-4-isopropoxyphenyl)ethanol, vs two syringyl models, 3,4,5-trimethoxybenzyl alcohol and 1-(3,5-dimethoxy-4-isopropoxyphenyl)ethanol. The results were the opposite of those predicted: the syringyl models were oxidized slower than the guaiacyl models by Mn(III). To investigate the basis for this unexpected result, we recorded the visible absorption spectra of charge-transfer complexes prepared between each of the lignin models and an electron acceptor, tetracyanoethylene or p-chloranil. The results, in general agreement with the kinetic findings, showed that the nonphenolic syringyl lignin models had higher ionization potentials than the guaiacyl models.     

Five Hierarchical Levels of Sequence-Structure Correlation in Proteins

This article reviews recent work towards modelling protein folding pathways using a bioinformatics approach. Statistical models have been developed for sequence-structure correlations in proteins at five levels of structural complexity: (i) short motifs; (ii) extended motifs; (iii) nonlocal pairs of motifs; (iv) 3-dimensional arrangements of multiple motifs; and (v) global structural homology. We review statistical models, including sequence profiles, hidden Markov models (HMMs) and interaction potentials, for the first four levels of structural detail. The I-sites (folding Initiation sites) Library models short local structure motifs. Each succeeding level has a statistical model, as follows: HMMSTR (HMM for STRucture) is an HMM for extended motifs; HMMSTR-CM (Contact Maps) is a model for pairwise interactions between motifs; and SCALI-HMM (HMMs for Structural Core ALIgnments) is a set of HMMs for the spatial arrangements of motifs. The parallels between the statistical models and theoretical models for folding pathways are discussed in this article; however, global sequence models are not discussed because they have been extensively reviewed elsewhere. The data used and algorithms presented in this article are available at http://www.bioinfo.rpi.edu/~bystrc/ (click on "servers" or "downloads") or by request to bystrc@rpi.edu .     

Efficiencies of maximum likelihood methods of phylogenetic inferences when different substitution models are used

Choice of a substitution model is a crucial step in the maximum likelihood (ML) method of phylogenetic inference, and investigators tend to prefer complex mathematical models to simple ones. However, when complex models with many parameters are used, the extent of noise in statistical inferences increases, and thus complex models may not produce the true topology with a higher probability than simple ones. This problem was studied using computer simulation. When the number of nucleotides used was relatively large (1000 bp), the HKY+Gamma model showed smaller d(T) topological distance between the inferred and the true trees) than the JC and Kimura models. In the cases of shorter sequences (300 bp) simpler model and search algorithm such as JC model and SA+NNI search were found to be as efficient as more complicated searches and models in terms of topological distances, although the topologies obtained under HKY+Gamma model had the highest likelihood values. The performance of relatively simple search algorithm SA+NNI was found to be essentially the same as that of more extensive SA+TBR search under all models studied. Similarly to the conclusions reached by Takahashi and Nei [Mol. Biol. Evol. 17 (2000) 1251], our results indicate that simple models can be as efficient as complex models, and that use of complex models does not necessarily give more reliable trees compared with simple models.     

Combining genotype, environment and attribute variables in regression models for predicting the cell-means of multi-environment cultivar trials

 The main objectives of this study were: (1) to develop models which combine variables of genotype, environment and attribute in regression models (GEAR) for increasing the accuracy of predicted cell-means of the genotype×environment two-way table, and (2) to compare GEAR models with the additive main effects and multiplicative interaction (AMMI) model. GEAR models were developed by regressing the observed values on principal components of genotypes (PCG) and environments (PCE). Genetic and environmental attributes were also added to the GEAR models. GEAR and AMMI models were applied to multi-environment trials of triticale (trial 1), maize (trial 2) and broad beans (trial 3). The random data-splitting and cross-validation procedure was used and the root mean square-predicted difference (RMSPD) was computed to validate each model. GEAR models increased the accuracy of predicted cell-means. Attribute variables, such as soil pH, rainfall, altitude and class of genotype, did not improve the best GEAR model of trial 1, but they increased the predictive value of other models. Two iterations of the computer program further refined the best GEAR model. Based on the RMSPD criterion, GEAR models were as good as, or better than, some AMMI truncated models for predicting cell-means. The approximate accuracy gain factors (GF) of the best GEAR model over the raw data were 2.08, 3.02 and 2.22, for trials 1, 2 and 3, respectively. The GF of the best AMMI model were 1.74, 2.28 and 2.32 for trials 1, 2 and 3, respectively. The analysis of variance of the predicted cell means showed that the genotype×environment interaction (GEI) variance was reduced by about 20% in trial 1 and 81% in trial 2. A bias associated with the predicted cell reduced the GEI variability. Advantages of using GEAR models in muti-environment cultivar trials are that they: (1) increase the precision of cell-mean estimates and (2) reduce the GEI variance and increase trait heritability. Received: 15 August 1997 / Accepted: 28 October 1997     

宏观植物生态模型的研究现状与展望

概述了3种主要植物生态模型的发展现状1)种群动态模型,主要模拟在一个生态系统中单个种的植物个体发芽、成长和死亡过程,及其种内竞争和种间相互作用,是研究开发最早的一类生态模型之一.该类模型主要应用于分析植物种群之间相互作用.2)演替模型,主要模拟植物种类(动物与此相伴)在整个生态系统发展过程的变化,包括植被类型的转变和相关的生物地球化学循环过程的改变.可用于研究生物群落对气候变化的响应.3)生态系统模型,是把生态系统当作一个功能整体来模拟的一类模型,主要有以下3类(1)SVAT模型,主要模拟地表生态系统过程,以BATS、SiB、SiB2和LEAF为代表,多用于气候研究;(2)BGC模型,主要模拟3个关键循环碳,水和营养物质循环.常用的BGC模型有FOREST-BGC、BIOME-BGC、CENTURY、TEM、DOLY以及由它们衍生而来的整合模型组;(3)BG模型,模拟群落、生物群区中植物分布,比较具有代表性的 BGMs包括BIOME2和MAPSS,它们主要用于研究因气候变化而引起的生物分布的变迁.最后,结合我们的实际工作展望了生态模型在未来几年内的几个发展方向1)与基础学科相结合,比如把物候学引入生态模型研究中来,以寻求新的支撑点;2)与现代非线性理论相结合,重新评价模型的假设基础;3)与现代科学技术相结合,利用3S技术和计算机技术为模型的发展提供更强大的技术支持;4)在研究方法上,从还原论转向整体论,尽可能地把生态系统当作一个功能整体来模拟研究.     

Aposematism and crypsis are not enough to explain dorsal polymorphism in the Iberian adder

Aposematic organisms can show phenotypic variability across their distributional ranges. The ecological advantages of this variability have been scarcely studied in vipers. We explored this issue in Vipera seoanei, a species that exhibits five geographically structured dorsal colour phenotypes across Northern Iberia: two zigzag patterned (Classic and Cantabrica), one dorsal-strip patterned (Bilineata), one even grey (Uniform), and one melanistic (Melanistic). We compared predation rates (raptors and mammals) on plasticine models resembling each colour phenotype in three localities. Visual modelling techniques were used to infer detectability (i.e. conspicuousness) of each model type for visually guided predators (i.e. diurnal raptors). We hypothesize that predation rates will be lower for the two zigzag models (aposematism hypothesis) and that models with higher detectability would show higher predation rates (detectability hypothesis). Classic and Bilineata models were the most conspicuous, while Cantabrica and Uniform were the less. Melanistic presented an intermediate conspicuousness. Predation rate was low (3.24% of models) although there was variation in attack frequency among models. Zigzag models were scarcely predated supporting the aposematic role of the zigzag pattern in European vipers to reduce predation (aposematism hypothesis). From the non-zigzag models, high predation occurred on Bilineata and Melanistic models, and low on Uniform models, partially supporting our detectability hypothesis. These results suggest particular evolutionary advantages for non-zigzag phenotypes such as better performance of Melanistic phenotypes in cold environments or better crypsis of Uniform phenotypes. Polymorphism in V. seoanei may respond to a complex number of forces acting differentially across an environmental gradient.     

Effects of choice of DNA sequence model structure on gene identification accuracy

MOTIVATION: Markov chain models of DNA sequences have frequently been used in gene finding algorithms. Performance of the algorithm critically depends on the model structure and parameters. Still, the issue of choosing the model structure has not been studied with sufficient attention. RESULTS: We have assessed performance of several types of Markov chain models, both fixed order (FO) models and models with interpolation, within the framework of the GeneMark algorithm. The performance was measured in two ways: (i) the accuracy of detection of protein-coding potential in artificial DNA sequences and (ii) the accuracy of identifying genes in real prokaryotic genomes. We observed that the models built by deleted interpolation (DI) slightly outperformed other models in detecting protein-coding potential in artificial DNA sequences with GC content in the medium range and also in detecting genes in real genomes with medium GC content. For artificial and real genomic DNA with high or low GC content, we observed that the models built by DI were in some cases slightly outperformed by FO models.     

What Is the Most Realistic Single-Compartment Model of Spike Initiation?

A large variety of neuron models are used in theoretical and computational neuroscience, and among these, single-compartment models are a popular kind. These models do not explicitly include the dendrites or the axon, and range from the Hodgkin-Huxley (HH) model to various flavors of integrate-and-fire (IF) models. The main classes of models differ in the way spikes are initiated. Which one is the most realistic? Starting with some general epistemological considerations, I show that the notion of realism comes in two dimensions: empirical content (the sort of predictions that a model can produce) and empirical accuracy (whether these predictions are correct). I then examine the realism of the main classes of single-compartment models along these two dimensions, in light of recent experimental evidence.     

Current trends in mathematical simulation of the function of semicircular canals

The review covers new trends in the simulation of the processes associated with the functioning of the semicircular canal (SC) system, i.e., the component of the vestibular apparatus responsible for the detection of angular movement of the head. The basic factor determining these trends is an increasing role of computers both in the research of mathematical models and in the direct simulation (imitation) of the SC structure, processes proceeding in SCs and conditions of the experiment. As shown by the analysis of the literature, at present, it is possible to distinguish the following trends in the development of SC simulation: (1) reconstruction models; (2) micro-simulation; (3) integrated models; (4) simulation models; (5) alternative models of SC functioning. Examples are given of publications presenting the present-day research in these fields.     

Molecular dynamics simulations of solvated crystal models of cellulose I(alpha) and III(I)

Swelling behaviors of cellulose I(alpha) and III(I) crystals have been studied using molecular dynamics simulations of the solvated finite-crystal models. The typical crystal models consisted of 48 x 10-mer chains. For the cellulose I(alpha) crystal, models consisting of different numbers of chains and chain lengths were also studied. The structural features of the swollen crystal models, including the cellulose I(beta) crystal model reported previously, were compared. A distinct right-handed twist was observed for models of the native cellulose crystals (cellulose I(alpha) and I(beta)), with a greater amount of twisting observed for the I(alpha) crystal model. Although the amount of twist decreased with increasing dimensions of the cellulose I(alpha) crystal model, the relative changes in twist angle suggest that considerable twist would arise in a crystal model of the actual dimensions. In contrast to the swelling behavior of crystal models of the native cellulose, the cellulose III(I) crystal model exhibited local, gradual disordering at the corner of the reducing end. Comparison of the lattice energies indicated that the cellulose chains of the I(beta) crystal were packed in the most stable fashion, whereas those of the I(alpha) and III(I) crystals were in a metastable state, which is consistent with the crystallization behaviors observed. Upon heating of the native cellulose crystal models, the chain sheets of the I(alpha) model showed a continuous increase in twist angle, suggesting weaker intersheet interactions in this model. The swollen crystal models of cellulose I(alpha) and III(I) reproduce well the representative structural features observed in the corresponding crystal structures. The crystal model twist thus characterizes the swelling behavior of the native cellulose crystal models, which seems to be related to the insolubility of the crystals.