From spiking neuron models to linear-nonlinear models

Neurons transform time-varying inputs into action potentials emitted stochastically at a time dependent rate. The mapping from current input to output firing rate is often represented with the help of phenomenological models such as the linear-nonlinear (LN) cascade, in which the output firing rate is estimated by applying to the input successively a linear temporal filter and a static non-linear transformation. These simplified models leave out the biophysical details of action potential generation. It is not a priori clear to which extent the input-output mapping of biophysically more realistic, spiking neuron models can be reduced to a simple linear-nonlinear cascade. Here we investigate this question for the leaky integrate-and-fire (LIF), exponential integrate-and-fire (EIF) and conductance-based Wang-Buzsáki models in presence of background synaptic activity. We exploit available analytic results for these models to determine the corresponding linear filter and static non-linearity in a parameter-free form. We show that the obtained functions are identical to the linear filter and static non-linearity determined using standard reverse correlation analysis. We then quantitatively compare the output of the corresponding linear-nonlinear cascade with numerical simulations of spiking neurons, systematically varying the parameters of input signal and background noise. We find that the LN cascade provides accurate estimates of the firing rates of spiking neurons in most of parameter space. For the EIF and Wang-Buzsáki models, we show that the LN cascade can be reduced to a firing rate model, the timescale of which we determine analytically. Finally we introduce an adaptive timescale rate model in which the timescale of the linear filter depends on the instantaneous firing rate. This model leads to highly accurate estimates of instantaneous firing rates.     

Identifiability of single-index models and additive-index models

We provide a proof for the identifiability for both single-indexmodels and partially linear single-index models assuming onlythe continuity of the regression function, a condition muchweaker than the differentiability conditions assumed in theexisting literature. Our discussion is then extended to theidentifiability of the additive-index models.     

From continuum Fokker-Planck models to discrete kinetic models

Two theoretical formalisms are widely used in modeling mechanochemical systems such as protein motors: continuum Fokker-Planck models and discrete kinetic models. Both have advantages and disadvantages. Here we present a "finite volume" procedure to solve Fokker-Planck equations. The procedure relates the continuum equations to a discrete mechanochemical kinetic model while retaining many of the features of the continuum formulation. The resulting numerical algorithm is a generalization of the algorithm developed previously by Fricks, Wang, and Elston through relaxing the local linearization approximation of the potential functions, and a more accurate treatment of chemical transitions. The new algorithm dramatically reduces the number of numerical cells required for a prescribed accuracy. The kinetic models constructed in this fashion retain some features of the continuum potentials, so that the algorithm provides a systematic and consistent treatment of mechanical-chemical responses such as load-velocity relations, which are difficult to capture with a priori kinetic models. Several numerical examples are given to illustrate the performance of the method.     

Using network models to approximate spatial point-process models

Spatial effects are fundamental to ecological and epidemiological systems, yet the incorporation of space into models is potentially complex. Fixed-edge network models (i.e. networks where each edge has the same fixed strength of interaction) are widely used to study spatial processes but they make simplistic assumptions about spatial scale and structure. Furthermore, it can be difficult to parameterize such models with empirical data. By comparison, spatial point-process models are often more realistic than fixed-edge network models, but are also more difficult to analyze. Here we develop a moment closure technique that allows us to define a fixed-edge network model which predicts the prevalence and rate of epidemic spread of a continuous spatial point-process epidemic model. This approach provides a systematic method for accurate parameterization of network models using data from continuously distributed populations (such as data on dispersal kernels). Insofar as point-process models are accurate representations of real spatial biological systems, our example also supports the view that network models are realistic representations of space.     

Gamete-competition models

The gamete-competition model is an application of the Bradley-Terry model for ranking of sports teams. If allele i of a marker locus is assigned parameter taui>0, then the probability that a parent with heterozygous genotype i/j transmits allele i is Pr(i/j-->)=tau(i)/(tau(i) + tau(j). Mendelian segregation corresponds to the choice tau(i)=1 for all i. To test whether Mendelian segregation is true, one can estimate the tau(i) from pedigree data and perform a likelihood-ratio test under the constraint that one tau(i) equals 1. Although this procedure generates an interesting method for performance of segregation analysis with a marker locus, its real promise lies in generalization of the transmission/disequilibrium test. Quantitative as well as qualitative outcomes can be considered. The gamete-competition model uses full pedigree data and gives an estimate of the strength of transmission distortion to affected children for each allele. Covariates are incorporated by rewriting of tau(i)=exp(beta(t)x(k)), where beta is a parameter vector and xk is a covariate vector for the kth transmitted gamete. Examples of covariates include disease-severity indicators for the child, sex of the child, or repeat number for tandem-repeat alleles.     

Glioma models

Gliomas are primary central nervous system tumors that arise from astrocytes, oligodendrocytes or their precursors. Gliomas can be classified into several groups according to their histologic characteristics, the most malignant of the gliomas is glioblastoma multiforme. In contrast to the long-standing and well-defined histopathology, the underlying molecular and genetic bases for gliomas are only just emerging. Many genetic alterations have been identified in human gliomas, however, establishing unequivocal correlation between these genetic alterations and gliomagenesis requires accurate animal models for this disease. Here we are reviewing the existing animal models for gliomas with different strategies and our current knowledge on the important issues about this disease, such as activation of signal transduction pathways, disruption of cell cycle arrest pathways, cell-of-origin of gliomas, and therapeutic strategies.     

Parameterization of individual-based models: comparisons with deterministic mean-field models

The relating of deterministic, mean-field models into network models, where epidemic spread occurs between interconnected susceptible and infectious individuals or populations, requires careful consideration. Here, we discuss models that consider differently the manner in which contact rate and infectiousness change over time, with different algorithms suitable for different underlying processes. Though these models give coincidental results to the mean-field in the case of large, highly connected networks, the results when sparsely connected networks are considered may differ. Different subsets of the parameters from the mean-field epidemic (R(0), generation time, infectiousness, etc.) are preserved in each case. Despite these differences, simulated epidemics generated under some model architectures are insensitive to the average degree of contact amongst nodes, k. Model-based estimates of k may be model dependent, and must therefore be viewed with caution.     

Calibrating E-values for hidden Markov models using reverse-sequence null models

MOTIVATION: Hidden Markov models (HMMs) calculate the probability that a sequence was generated by a given model. Log-odds scoring provides a context for evaluating this probability, by considering it in relation to a null hypothesis. We have found that using a reverse-sequence null model effectively removes biases owing to sequence length and composition and reduces the number of false positives in a database search. Any scoring system is an arbitrary measure of the quality of database matches. Significance estimates of scores are essential, because they eliminate model- and method-dependent scaling factors, and because they quantify the importance of each match. Accurate computation of the significance of reverse-sequence null model scores presents a problem, because the scores do not fit the extreme-value (Gumbel) distribution commonly used to estimate HMM scores' significance. RESULTS: To get a better estimate of the significance of reverse-sequence null model scores, we derive a theoretical distribution based on the assumption of a Gumbel distribution for raw HMM scores and compare estimates based on this and other distribution families. We derive estimation methods for the parameters of the distributions based on maximum likelihood and on moment matching (least-squares fit for Student's t-distribution). We evaluate the modeled distributions of scores, based on how well they fit the tail of the observed distribution for data not used in the fitting and on the effects of the improved E-values on our HMM-based fold-recognition methods. The theoretical distribution provides some improvement in fitting the tail and in providing fewer false positives in the fold-recognition test. An ad hoc distribution based on assuming a stretched exponential tail does an even better job. The use of Student's t to model the distribution fits well in the middle of the distribution, but provides too heavy a tail. The moment-matching methods fit the tails better than maximum-likelihood methods. AVAILABILITY: Information on obtaining the SAM program suite (free for academic use), as well as a server interface, is available at http://www.soe.ucsc.edu/research/compbio/sam.html and the open-source random sequence generator with varying compositional biases is available at http://www.soe.ucsc.edu/research/compbio/gen_sequence     

Selection models and pattern-mixture models for incomplete data with covariates

Most models for incomplete data are formulated within the selection model framework. This paper studies similarities and differences of modeling incomplete data within both selection and pattern-mixture settings. The focus is on missing at random mechanisms and on categorical data. Point and interval estimation is discussed. A comparison of both approaches is done on side effects in a psychiatric study.