Identification and estimation algorithm for stochastic neural system

An algorithm for the estimation of stochastic processes in a neural system is presented. This process is defined here as the continuous stochastic process reflecting the dynamics of the neural system which has some inputs and generates output spike trains. The algorithm proposed here is to identify the system parameters and then estimate the stochastic process called neural system process here. These procedures carried out on the basis of the output spike trains which are supposed to be the data observed in the randomly missing way by the threshold time function in the neural system. The algorithm is constructed with the well-known Kalman filters and realizes the estimation of the neural system process by cooperating with the algorithm for the parameter estimation of the threshold time function presented previously (Nakao et al., 1983). The performance of the algorithm is examined by applying it to the various spike trains simulated by some artificial models and also to the neural spike trains recorded in cat's optic tract fibers. The results in these applications are thought to prove the effectiveness of the algorithm proposed here to some extent. Such attempts, we think, will serve to improve the characterizing and modelling techniques of the stochastic neural systems.     

Synaptic transmission in a model for stochastic neural activity.

A stochastic model equation for nerve membrane depolarization is derived which incorporates properties of synaptic transmission with a Rail-Eccles circuit for a trigger zone. If input processes are Poisson the depolarization is a Markov process for which equations for the moments of the interspike interval can be written down. An analytic result for the mean interval is obtained in a special case. The effect of the excitatory reversal potential is considerable if it is not too far from threshold and if the interspike interval is long. Computer simulations were performed when inhibitory and excitatory inputs are active. A substantial amount of inhibition leads to an exceedingly long tail in the density of the interspike time. With excitation only the interspike interval is often an approximately lognormal random variable. A coefficient of variation greater than one is often a consequence of relatively strong inhibition. Inferences can be made on the nature of the synaptic input from the statistics and density of the time between spikes. The inhibitory reversal potential usually has a relatively small effect except when the frequency of inhibition is large. An appendix contains the model equations in the case of an arbitrary distribution of postsynaptic potential amplitudes.     

NN-align. An artificial neural network-based alignment algorithm for MHC class II peptide binding prediction

Background  

The major histocompatibility complex (MHC) molecule plays a central role in controlling the adaptive immune response to infections. MHC class I molecules present peptides derived from intracellular proteins to cytotoxic T cells, whereas MHC class II molecules stimulate cellular and humoral immunity through presentation of extracellularly derived peptides to helper T cells. Identification of which peptides will bind a given MHC molecule is thus of great importance for the understanding of host-pathogen interactions, and large efforts have been placed in developing algorithms capable of predicting this binding event.     

Identification of sparse neural functional connectivity using penalized likelihood estimation and basis functions

One key problem in computational neuroscience and neural engineering is the identification and modeling of functional connectivity in the brain using spike train data. To reduce model complexity, alleviate overfitting, and thus facilitate model interpretation, sparse representation and estimation of functional connectivity is needed. Sparsities include global sparsity, which captures the sparse connectivities between neurons, and local sparsity, which reflects the active temporal ranges of the input-output dynamical interactions. In this paper, we formulate a generalized functional additive model (GFAM) and develop the associated penalized likelihood estimation methods for such a modeling problem. A GFAM consists of a set of basis functions convolving the input signals, and a link function generating the firing probability of the output neuron from the summation of the convolutions weighted by the sought model coefficients. Model sparsities are achieved by using various penalized likelihood estimations and basis functions. Specifically, we introduce two variations of the GFAM using a global basis (e.g., Laguerre basis) and group LASSO estimation, and a local basis (e.g., B-spline basis) and group bridge estimation, respectively. We further develop an optimization method based on quadratic approximation of the likelihood function for the estimation of these models. Simulation and experimental results show that both group-LASSO-Laguerre and group-bridge-B-spline can capture faithfully the global sparsities, while the latter can replicate accurately and simultaneously both global and local sparsities. The sparse models outperform the full models estimated with the standard maximum likelihood method in out-of-sample predictions.     

Non-invasive algorithm for bowel motility estimation using a back-propagation neural network model of bowel sounds

Background

Although cardiac auscultation remains important to detect abnormal sounds and murmurs indicative of cardiac pathology, the application of electronic methods remains seldom used in everyday clinical practice. In this report we provide preliminary data showing how the phonocardiogram can be analyzed using color spectrographic techniques and discuss how such information may be of future value for noninvasive cardiac monitoring.

Methods

We digitally recorded the phonocardiogram using a high-speed USB interface and the program Gold Wave http://www.goldwave.com in 55 infants and adults with cardiac structural disease as well as from normal individuals and individuals with innocent murmurs. Color spectrographic analysis of the signal was performed using Spectrogram (Version 16) as a well as custom MATLAB code.

Results

Our preliminary data is presented as a series of seven cases.

Conclusions

We expect the application of spectrographic techniques to phonocardiography to grow substantially as ongoing research demonstrates its utility in various clinical settings. Our evaluation of a simple, low-cost phonocardiographic recording and analysis system to assist in determining the characteristic features of heart murmurs shows promise in helping distinguish innocent systolic murmurs from pathological murmurs in children and is expected to useful in other clinical settings as well.     

Parameter estimation for bursting neural models

This paper presents work on parameter estimation methods for bursting neural models. In our approach we use both geometrical features specific to bursting, as well as general features such as periodic orbits and their bifurcations. We use the geometry underlying bursting to introduce defining equations for burst initiation and termination, and restrict the estimation algorithms to the space of bursting periodic orbits when trying to fit periodic burst data. These geometrical ideas are combined with automatic differentiation to accurately compute parameter sensitivities for the burst timing and period. In addition to being of inherent interest, these sensitivities are used in standard gradient-based optimization algorithms to fit model burst duration and period to data. As an application, we fit Butera et al.'s (Journal of Neurophysiology 81, 382-397, 1999) model of preB?tzinger complex neurons to empirical data both in control conditions and when the neuromodulator norepinephrine is added (Viemari and Ramirez, Journal of Neurophysiology 95, 2070-2082, 2006). The results suggest possible modulatory mechanisms in the preB?tzinger complex, including modulation of the persistent sodium current.     

Maximum likelihood estimation for stochastic first order reactions

Small sample properties of the maximum likelihood estimator for the rate constant of a stochastic first order reaction are investigated. The approximate bias and variance of the maximum likelihood estimator are derived and tabulated. If observations of the system are made at timesiτ,i=1, 2, ...,N; τ>0, the observational spacing τ which minimizes the approximate variance of the maximum likelihood estimator is found. The non-applicability of large sample theory to confidence interval derivation is demonstrated by examination of the relative likelihood. Bartlett’s method is employed to derive approximate confidence limits, and is illustrated by using simulated kinetic runs.     

Approximate maximum likelihood estimation for stochastic chemical kinetics

Recent experimental imaging techniques are able to tag and count molecular populations in a living cell. From these data mathematical models are inferred and calibrated. If small populations are present, discrete-state stochastic models are widely-used to describe the discreteness and randomness of molecular interactions. Based on time-series data of the molecular populations, the corresponding stochastic reaction rate constants can be estimated. This procedure is computationally very challenging, since the underlying stochastic process has to be solved for different parameters in order to obtain optimal estimates. Here, we focus on the maximum likelihood method and estimate rate constants, initial populations and parameters representing measurement errors.     

Global parameter estimation methods for stochastic biochemical systems

Background  

The importance of stochasticity in cellular processes having low number of molecules has resulted in the development of stochastic models such as chemical master equation. As in other modelling frameworks, the accompanying rate constants are important for the end-applications like analyzing system properties (e.g. robustness) or predicting the effects of genetic perturbations. Prior knowledge of kinetic constants is usually limited and the model identification routine typically includes parameter estimation from experimental data. Although the subject of parameter estimation is well-established for deterministic models, it is not yet routine for the chemical master equation. In addition, recent advances in measurement technology have made the quantification of genetic substrates possible to single molecular levels. Thus, the purpose of this work is to develop practical and effective methods for estimating kinetic model parameters in the chemical master equation and other stochastic models from single cell and cell population experimental data.     

An algorithm for angiographic estimation of blood vessel diameter.

This study was carried out in an attempt to develop an objective and robust method for measuring changes in the diameters of small blood vessels from X-ray angiographic images. Recognizing potential problems with edge detection methods applied to cylindrical vessels in which the contrast diminishes as the boundary is approached, we have attempted to utilize the X-ray absorbance data across the entire cross section of the vessel. Then, assuming a cylindrical geometry, the absorbance data are fit to the cylindrical absorbance function by use of nonlinear regression analysis. The method was tested and calibrated using glass tubes filled with various concentrations of contrast medium. The diameters of small pulmonary arteries were estimated by applying the method of angiograms obtained from an isolated dog lung lobe. The structure of the residuals obtained after the fitting procedure was analyzed to test the appropriateness of the model for use with images of vessels. The results suggest that this approach will have utility for systematically quantifying vessel dimensions.     

A modified particle swarm optimization algorithm for parameter estimation of a biological system

Background

Mathematical modeling has achieved a broad interest in the field of biology. These models represent the associations among the metabolism of the biological phenomenon with some mathematical equations such that the observed time course profile of the biological data fits the model. However, the estimation of the unknown parameters of the model is a challenging task. Many algorithms have been developed for parameter estimation, but none of them is entirely capable of finding the best solution. The purpose of this paper is to develop a method for precise estimation of parameters of a biological model.

Methods

In this paper, a novel particle swarm optimization algorithm based on a decomposition technique is developed. Then, its root mean square error is compared with simple particle swarm optimization, Iterative Unscented Kalman Filter and Simulated Annealing algorithms for two different simulation scenarios and a real data set related to the metabolism of CAD system.

Results

Our proposed algorithm results in 54.39% and 26.72% average reduction in root mean square error when applied to the simulation and experimental data, respectively.

Conclusion

The results show that the metaheuristic approaches such as the proposed method are very wise choices for finding the solution of nonlinear problems with many unknown parameters.

     

Accelerated maximum likelihood parameter estimation for stochastic biochemical systems

ABSTRACT: BACKGROUND: A prerequisite for the mechanistic simulation of a biochemical system is detailed knowledge of its kinetic parameters. Despite recent experimental advances, the estimation of unknown parameter values from observed data is still a bottleneck for obtaining accurate simulation results. Many methods exist for parameter estimation in deterministic biochemical systems; methods for discrete stochastic systems are less well developed. Given the probabilistic nature of stochastic biochemical models, a natural approach is to choose parameter values that maximize the probability of the observed data with respect to the unknown parameters, a.k.a. the maximum likelihood parameter estimates (MLEs). MLE computation for all but the simplest models requires the simulation of many system trajectories that are consistent with experimental data. For models with unknown parameters, this presents a computational challenge, as the generation of consistent trajectories can be an extremely rare occurrence. RESULTS: We have developed Monte Carlo Expectation-Maximization with Modified Cross-Entropy Method (MCEM2): an accelerated method for calculating MLEs that combines advances in rare event simulation with a computationally efficient version of the Monte Carlo expectation-maximization (MCEM) algorithm. Our method requires no prior knowledge regarding parameter values, and it automatically provides a multivariate parameter uncertainty estimate. We applied the method to five stochastic systems of increasing complexity, progressing from an analytically tractable pure-birth model to a computationally demanding model of yeast-polarization. Our results demonstrate that MCEM2 substantially accelerates MLE computation on all tested models when compared to a stand-alone version of MCEM. Additionally, we show how our method identifies parameter values for certain classes of models more accurately than two recently proposed computationally efficient methods. CONCLUSIONS: This work provides a novel, accelerated version of a likelihood-based parameter estimation method that can be readily applied to stochastic biochemical systems. In addition, our results suggest opportunities for added efficiency improvements that will further enhance our ability to mechanistically simulate biological processes.     

Robust parameter estimation techniques for stochastic within-host macroparasite models

We present a stochastic model of the within-host population dynamics of lymphatic filariasis, and use a simulated goodness-of-fit (GOF) method to estimate immunological parameters and their confidence intervals from experimental data. A variety of deterministic moment closure approximations to the stochastic system are explored and compared with simulation results. For the maximum GOF parameter estimates, none of the methods of closure accurately reproduce the behaviour of the stochastic model. However, direct analysis of the stochastic model demonstrates that the high levels of variation observed in the data can be reproduced without requiring parameters to vary between hosts. This indicates that the observed aggregation of parasite load may be dynamically generated by random variation in the development of an effective immune response against parasite larvae.     

The need for stochastic replication of ecological neural networks

Artificial neural networks are becoming increasingly popular as predictive statistical tools in ecosystem ecology and as models of signal processing in behavioural and evolutionary ecology. We demonstrate here that a commonly used network in ecology, the three-layer feed-forward network, trained with the backpropagation algorithm, can be extremely sensitive to the stochastic variation in training data that results from random sampling of the same underlying statistical distribution, with networks converging to several distinct predictive states. Using a random walk procedure to sample error-weight space, and Sammon dimensional reduction of weight arrays, we demonstrate that these different predictive states are not artefactual, due to local minima, but lie at the base of major error troughs in the error-weight surface. We further demonstrate that various gross weight compositions can produce the same predictive state, suggesting the analogy of weight space as a 'patchwork' of multiple predictive states. Our results argue for increased inclusion of stochastic training replication and analysis into ecological and behavioural applications of artificial neural networks.     

Parameter estimation of the threshold time function in the neural system

An algorithm for parameter estimation is presented for the neural system model. Because of its firing mechanism analogous to that of the model based on the first time crossing problem, this problem is solved numerically for our model according to the results of Kostyukov et al. (1981). We propose the algorithm that estimates the parameters of the model considering the equivalence between the probability density function of the 1st crossing time and that of the interspike interval, which is derived from the interspike interval histogram by making use of the spline function technique. The ability of the algorithm is ensured by the application to the simulated interspike interval data. The parameter estimation is carried out also for the practical neural data recorded in the cat's optic tract fibers in both the spontaneous and the stimulated cases. These applications will show the effectiveness of the algorithm in practical cases.     

A fast, stochastic threading algorithm for proteins

MOTIVATION: Sequences for new proteins are being determined at a rapid rate, as a result of the Human Genome Project, and related genome research. The ability to predict the three-dimensional structure of proteins from sequence alone would be useful in discovering and understanding their function. Threading, or fold recognition, aims to predict the tertiary structure of a protein by aligning its amino acid sequence with a large number of structures, and finding the best fit. This approach depends on obtaining good performance from both the scoring function, which simulates the free energy for given trial alignments, and the threading algorithm, which searches for the lowest-score alignment. It appears that current scoring functions and threading algorithms need improvement. RESULTS: This paper presents a new threading algorithm. Numerical tests demonstrate that it is more powerful than two popular approximate algorithms, and much faster than exact methods.