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PubMed1985

Phasic ion channel blockade. A kinetic model and parameter estimation procedure.

For excitable membranes, use and frequency dependence represent a progressive incorporation of drug into gated ion channels with repetitive stimulation. In contrast to receptors where access to ligand is continuous in time, we define guarded receptors, such as gated ion channels, as receptors whose access to the ligand pool is transient and controlled by the channel-gating process. During repetitive stimulation, the fraction of ligand-bound channels (ion channel blockade) follows an exponential time course, determined by the interstimulus interval, channel-gating processes, drug concentration, and the forward and reverse rate coefficients characteristic of the binding process. Based on a first order model of ligand-receptor binding, we derive a characterization of ion channel blockade via a single diffusion path under conditions of repetitive phasic stimulation. Extension to multiple diffusion paths and multiple drugs leads to a more complex scheme, but these generalizations are straightforward. For the case of one diffusion path, we derive the steady state level of channel blockade for guarded receptors as a function of stimulus rate and develop a data analysis strategy suitable for characterizing ion channel-blocking agents such as local anesthetics and antiarrhythmic drugs. We show that as receptor access time increases, the transient and steady state properties of guarded receptors become equivalent to those derived from the standard continuous access ligand-receptor model. The analysis tools presented simplify the quantitative description of the functional properties of many ion channel blockers and appear to have general applicability to characterization of periodically accessible receptors.

Animals↗
PubMed1995

Recruitment-driven, spatially discontinuous communities: a null model for transferred patterns in target communities of intestinal helminths.

Populations and therefore communities of intestinal helminths of vertebrates are fueled by recruitment of new individuals from outside the host. The source of new individuals is often an intermediate host that harbors several infective propagules of 1 or more species. Hence these source communities are transmitted in packets of infective propagules to target communities in definitive hosts. Packets not only provide recruits to target communities, but, because a packet of propagules possesses its own structure, it may also transmit structure to the target community. We use this system to examine the contribution that structure in the source pool of propagules makes to the structure of recruitment-driven target populations and communities. By treating the dynamics of such target populations and communities as immigration-death processes, we conclude: (1) Unlike a birth-driven population a recruitment-driven target population will grow to an asymptotic limit even in the absence of density-dependent processes or reaching carrying capacity; (2) the frequency distribution of the number of recruits entering target populations will determine the frequency distribution of adults in target populations; (3) interspecific associations among species in the source community will be transmitted to target communities, but the magnitude of the transmitted associations will depend upon the relative survival rates of the species; and (4) for associations of equal magnitude in a source community, the magnitude of a transferred negative association will be less than the magnitude of a positive association in a target community. Two examples of source communities in salt marsh crabs reveal that source infracommunities exist with the hypothesized structure. Further, the source helminth communities display a greater number of positive than negative interspecific associations. The inequity in transfer and the existence of a greater proportion of positive associations in source communities may explain the widespread occurrence of excess positive associations that has been noted in recruitment-driven communities.

Animals↗
PubMed2004

LOR-OSEM: statistical PET reconstruction from raw line-of-response histograms.

Iterative statistical reconstruction methods are becoming the standard in positron emission tomography (PET). Conventional maximum-likelihood expectation-maximization (MLEM) and ordered-subsets (OSEM) algorithms act on data which have been pre-processed into corrected, evenly-spaced histograms; however, such pre-processing corrupts the Poisson statistics. Recent advances have incorporated attenuation, scatter and randoms compensation into the iterative reconstruction. The objective of this work was to incorporate the remaining pre-processing steps, including arc correction, to reconstruct directly from raw unevenly-spaced line-of-response (LOR) histograms. This exactly preserves Poisson statistics and full spatial information in a manner closely related to listmode ML, making full use of the ML statistical model. The LOR-OSEM algorithm was implemented using a rotation-based projector which maps directly to the unevenly-spaced LOR grid. Simulation and phantom experiments were performed to characterize resolution, contrast and noise properties for 2D PET. LOR-OSEM provided a beneficial noise-resolution tradeoff, outperforming AW-OSEM by about the same margin that AW-OSEM outperformed pre-corrected OSEM. The relationship between LOR-ML and listmode ML algorithms was explored, and implementation differences are discussed. LOR-OSEM is a viable alternative to AW-OSEM for histogram-based reconstruction with improved spatial resolution and noise properties.

Algorithms↗
PubMed1994

Predicting the number of herds infected with pseudorabies virus in the United States.

Epidemiologic modeling of the likely herd-to-herd transmission of pseudorabies virus (PRV) was developed to assess the progress and potential for the PRV-eradication program in the United States. The herd-to-herd transmission of PRV over a 20-year period (1993 to 2012) in the United States was simulated under various scenarios, which included variable program-funding levels and variable prevalences. A transition model (Markov process model) was used to predict yearly changes in herd prevalence of PRV infection. Five mutually exclusive states of nature for herds were assumed: uninfected and not vaccinated; uninfected and vaccinated; known to be infected and not vaccinated; known to be infected and vaccinated; and infected, but not known to be infected. Three prevalences for states in the United States were assumed: higher prevalence, moderate prevalence, and lower prevalence. Three funding levels were assumed: no eradication program, continued funding at the current level, and increased funding of 25%. Estimates made by an expert panel for determining probabilities in the state-transition matrices were used. A model also was developed, and was considered to be the most optimistic scenario likely under increased funding of 25%. The most optimistic estimates of the probabilities that still lay within the range of estimates made by the expert panel were used for this model. Only the optimistic transmission matrices allowed for total eradication of PRV.(ABSTRACT TRUNCATED AT 250 WORDS)

Animals↗
PubMed2003

Markov modelling of changes in HIV-specific cytotoxic T-lymphocyte responses with time in untreated HIV-1 infected patients.

HIV-specific cytotoxic CD8(+) T-lymphocytes (CTL) appear to be the cornerstone of the immune response to HIV infection. Recent studies show that CTL activity reflects patients' anti-HIV immune status and slows disease progression. However, the dynamics of the diversity of this response also appears as a key parameter for immune control but the dynamics of this diversity is largely undocumented. We modelled changes in CTL responses against the seven principal HIV proteins over time. We also studied the influence of plasma viral load on temporal changes in HIV protein recognition by memory CTL. The generic model we developed is based on a continuous time homogeneous Markov process with reversible states. Those states are defined by the number of proteins recognized by memory CTL in a given patient at a given time. This approach was developed within a Bayesian framework. Full Bayesian inference is implemented using Markov chain Monte Carlo simulations (MCMC). The Gibbs sampling algorithm was used to estimate the marginal posterior distributions of the transition intensities between stages of CTL responses. We applied our model to data of 152 HIV-infected patients included in the IMMUNOCO cohort. The model suggested that the diversity of HIV protein recognition by memory CTL in treatment-naive patients decreases as the disease progresses. Namely, the loss of T cytotoxic responses is globally faster than their acquisition. Indeed, these patients' T cytotoxic responses were characterized by marked individual turnover and a gradual loss of multiple protein recognition over time, this loss accelerating as viral load increased.

Adult↗
PubMed1998

Noise-induced spiral waves in astrocyte syncytia show evidence of self-organized criticality.

Long range (a few centimeters), long lived (many seconds), spiral chemical waves of calcium ions (Ca2+) are observed in cultured networks of glial cells for normal concentrations of the neurotransmitter kainate. A new method for quantitatively measuring the spatiotemporal size of the waves is described. This measure results in a power law distribution of wave sizes, meaning that the process that creates the waves has no preferred spatial or temporal (size or lifetime) scale. This power law is one signature of self-organized critical phenomena, a class of behaviors found in many areas of science. The physiological results for glial networks are fully supported by numerical simulations of a simple network of noisy, communicating threshold elements. By contrast, waves observed in astrocytes cultured from human epileptic foci exhibited radically different behavior. The background random activity, or "noise", of the network is controlled by the kainate concentration. The mean rate of wave nucleation is mediated by the network noise. However, the power law distribution is invariant, within our experimental precision, over the range of noise intensities tested. These observations indicate that spatially and temporally coherent Ca2+ waves, mediated by network noise may play and important role in generating correlated neural activity (waves) over long distances and times in the healthy vertebrate central nervous system.

Astrocytes↗
PubMed1982

Processes influencing the distribution of parasite numbers within host populations with special emphasis on parasite-induced host mortalities.

The paper examines the factors which generate various patterns of dispersion in the distribution of parasites within their host populations. Particular emphasis is placed on the role played by chance elements in the growth and decay of parasite populations and on the influence of different types of demographic processes. It is argued that observed distributions are dynamic, rather than static, entities generated by opposing forces, some acting to create over-dispersion and others acting to generate under-dispersion. Monte Carlo simulation experiments, based on probability models of the growth and decay of host and parasite populations, are used to study the dynamics of parasite dispersion. Attention is specifically focused on the role played by parasite-induced host mortality. It is shown that, for certain types of host-parasite associations, convex curves of mean parasite abundance in relation to age (age-intensity curves), concomitant with a decline in the degree of dispersion in the older age, classes of hosts, may be evidence of the induction in host mortality by parasite infection. Empirical evidence is examined in light of this prediction. In general, however, simulation studies highlight the technical difficulties inherent in establishing clear evidence of parasite-induced host mortality from ecological studies of hosts and parasites in their natural habitats.

Aging↗
PubMedDate not supplied

A model for evaluating the effect of son or daughter preference on population size.

This paper develops a micro probabilistic model to describe the family extension process. The parameters are: the probability that a newborn is a boy (P), the number of desired boys (B), the number of desired girls (G), and the maximum possible number of children (N). This maximum is a stopping rule rather than a biological maximum. The variables are the ultimate number of boys and girls. According to this model, each couple determines B, G, and N, at the beginning of the reproductive period and continues to reproduce until at least B and at least G are achieved, or until the total number of children reaches N. The probability distribution of the ultimate number of boys and girls in the population is derived for this model. Simulation techniques are used to generate offspring. The results showed that the population size increases with the absolute differences, [B-G] for fixed N. They also suggested that son or daughter preference may be an important factor in fertility determinants, which may have important implications in population policies.

Computer Simulation↗
PubMed2002

A direct approach to estimating surfaces in tomographic data.

Under ideal circumstances, the inverse of the radon transform is computable, and sequences of measured projections are sufficient to obtain accurate estimates of volume densities. In situations where the sinogram data is incomplete, the radon transform is noninvertable, and attempts to reconstruct greyscale density values result in reconstruction artifacts that can undermine the effectiveness of subsequent processing. This paper presents a direct approach to the segmentation of incomplete tomographic data. The strategy is to impose a fairly simple model on the data, and treat segmentation as a problem of estimating the interface between two substances of somewhat homogeneous density. The segmentation is achieved by simultaneously deforming a surface model and updating density parameters in order to achieve a best fit between the projected model and the measured sinograms. The deformation is implemented with level-set surface models, calculated at the resolution of the input data. Relative to previous work, this paper makes several contributions. First is a proper derivation of the deformation of surface models that move according to a gradient descent on a likelihood measure. We also present a series of computational innovations that make this direct surface-fitting approach feasible with state-of-the-art computers. Another contribution is the demonstration of the effectiveness of this approach on under-constrained tomographic problems, using both simulated and real datasets.

Algorithms↗
PubMed2002

Membrane stretch accelerates activation and slow inactivation in Shaker channels with S3-S4 linker deletions.

At low P(open)(V) Shaker exhibits pronounced stretch-activation. Possible explanations for Shaker's sensitivity to tension include 1) Shaker channels are sufficiently distensible that stretch produces novel channel states and 2) Shaker channels expand in the plane of the membrane during voltage gating. For channels expressed in oocytes, we compared effects of patch stretch on Shaker and mutants that retain their voltage-gating ability but activate sluggishly because all or most of the S3-S4 linker has been deleted. Deletants had 10, 5, or 0 amino acid (aa) linkers, whereas wild-type is 31 aa. In deletants, though activation is exceptionally slow, slow inactivation is exceptionally quick; the resulting kinetic match was a bonus that allowed effects of stretch to be followed simultaneously in both processes. With the intact linker, an approximately 3 orders of magnitude mismatch in the two processes makes this impracticable. Standard stretch stimuli increased the rates and extent of activation by about the same degree in wild type and deletants, with effects especially pronounced near the foot of G(V). In deletants (where slow inactivation is strongly coupled to activation) stretch also accelerated slow inactivation. Maximum conductances were unaffected by stretch in all variants. In ramp clamp dose experiments, near-lytic patch stretch acted, for all variants, like a approximately 10 mV hyperpolarizing shift. These results suggested that, whether basal rates were high (wild type) or low (deletants), stretch acted by facilitating voltage-dependent activation. Channel activity was therefore simulated with/without "tension," tension being simulated via rate changes at voltage-dependent closed-closed transitions that might involve in-plane expansion (explanation 2). Simulated Delta P(open) arising from approximately 2 kT of "mechanical gating energy" mimicked experimental effects seen with comfortably sub-lytic stretch.

Animals↗
PubMed2003

A comparison of normalization methods for high density oligonucleotide array data based on variance and bias.

MOTIVATION: When running experiments that involve multiple high density oligonucleotide arrays, it is important to remove sources of variation between arrays of non-biological origin. Normalization is a process for reducing this variation. It is common to see non-linear relations between arrays and the standard normalization provided by Affymetrix does not perform well in these situations. RESULTS: We present three methods of performing normalization at the probe intensity level. These methods are called complete data methods because they make use of data from all arrays in an experiment to form the normalizing relation. These algorithms are compared to two methods that make use of a baseline array: a one number scaling based algorithm and a method that uses a non-linear normalizing relation by comparing the variability and bias of an expression measure. Two publicly available datasets are used to carry out the comparisons. The simplest and quickest complete data method is found to perform favorably. AVAILABILITY: Software implementing all three of the complete data normalization methods is available as part of the R package Affy, which is a part of the Bioconductor project http://www.bioconductor.org. SUPPLEMENTARY INFORMATION: Additional figures may be found at http://www.stat.berkeley.edu/~bolstad/normalize/index.html

Algorithms↗
PubMed2004

Fully Bayesian spatio-temporal modeling of FMRI data.

We present a fully Bayesian approach to modeling in functional magnetic resonance imaging (FMRI), incorporating spatio-temporal noise modeling and haemodynamic response function (HRF) modeling. A fully Bayesian approach allows for the uncertainties in the noise and signal modeling to be incorporated together to provide full posterior distributions of the HRF parameters. The noise modeling is achieved via a nonseparable space-time vector autoregressive process. Previous FMRI noise models have either been purely temporal, separable or modeling deterministic trends. The specific form of the noise process is determined using model selection techniques. Notably, this results in the need for a spatially nonstationary and temporally stationary spatial component. Within the same full model, we also investigate the variation of the HRF in different areas of the activation, and for different experimental stimuli. We propose a novel HRF model made up of half-cosines, which allows distinct combinations of parameters to represent characteristics of interest. In addition, to adaptively avoid over-fitting we propose the use of automatic relevance determination priors to force certain parameters in the model to zero with high precision if there is no evidence to support them in the data. We apply the model to three datasets and observe matter-type dependence of the spatial and temporal noise, and a negative correlation between activation height and HRF time to main peak (although we suggest that this apparent correlation may be due to a number of different effects).

Bayes Theorem↗
PubMed2005

Correction methods for random coincidences in fully 3D whole-body PET: impact on data and image quality.

UNLABELLED: With the advantages of the increased sensitivity of fully 3-dimensional (3D) PET for whole-body imaging come the challenges of more complicated quantitative corrections and, in particular, an increase in the number of random coincidences. The most common method of correcting for random coincidences is the real-time subtraction of a delayed coincidence channel, which does not add bias but increases noise. An alternative approach is the postacquisition subtraction of a low-noise random coincidence estimate, which can be obtained either from a smoothed delayed coincidence sinogram or from a calibration scan or directly estimated. Each method makes different trade-offs between noise amplification, bias, and data-processing requirements. These trade-offs are dependent on activity injected, the local imaging environment (e.g., near the bladder), and the reconstruction algorithm. METHODS: Using fully 3D whole-body simulations and phantom studies, we investigate how the gains in noise equivalent count (NEC) rates from using a noiseless random coincidence estimation method are translated to improvements in image signal-to-noise ratio (SNR). The image SNR, however, depends on the image reconstruction method and the local imaging environment. RESULTS: We show that for fully 3D whole-body imaging using a particular set of scanners and clinical protocols, a low-noise estimate of random coincidences improves sinogram and image SNRs by approximately 15% compared with online subtraction of delayed coincidences. CONCLUSION: A 15% improvement in image SNR arises from a 32% increase in the NEC rate. Thus, scan duration can be reduced by 25% while still maintaining a constant total acquired NEC.

Algorithms↗
PubMed2006

A Brownian Dynamics model of kinesin in three dimensions incorporating the force-extension profile of the coiled-coil cargo tether.

The kinesin family of motor proteins are involved in a variety of cellular processes that transport materials and generate force. With recent advances in experimental techniques, such as optical tweezers can probe individual molecules, there has been an increasing interest in understanding the mechanisms by which motor proteins convert chemical energy into mechanical work. Here we present a mathematical model for the chemistry and three dimensional mechanics of the kinesin motor protein which captures many of the force dependent features of the motor. For the elasticity of the tether that attaches cargo to the motor we develop a method for deriving the non-linear force-extension relationship from optical trap data. For the kinesin heads, cargo, and microscope stage we formulate a three dimensional Brownian Dynamics model that takes into account excluded volume interactions. To efficiently compute statistics from the model, an algorithm is proposed which uses a two step protocol that separates the simulation of the mechanical features of the model from the chemical kinetics of the model. Using this approach for a bead transported by the motor, the force dependent average velocity and randomness parameter are computed and compared with the experimental data.

Algorithms↗
PubMed1998

Hypothetical neural mechanism that may play a role in mental rotation: an attractor neural network model.

We propose an attractor neural network (ANN) model that performs rotation-invariant pattern recognition in such a way that it can account for a neural mechanism being involved in the image transformation accompanying the experience of mental rotation. We compared the performance of our ANN model with the results of the chronometric psychophysical experiments of Cooper and Shepard (Cooper L A and Shepard R N 1973 Visual Information Processing (New York: Academic) pp 204-7) on discrimination of alphanumeric characters presented in various angular departures from their canonical upright position. Comparing the times required for pattern retrieval in its canonical upright position with the reaction times of human subjects, we found agreement in that (i) retrieval times for clockwise and anticlockwise departures of the same angular magnitude (up to 180 degrees) were not different, (ii) retrieval times increased with departure from upright and (iii) increased more sharply as departure from upright approached 180 degrees. The rotation-invariant retrieval of the activity pattern has been accomplished by means of the modified algorithm of Dotsenko (Dotsenko V S 1988 J. Phys. A: Math. Gen. 21 L783-7) proposed for translation-, rotation- and size-invariant pattern recognition, which uses relaxation of neuronal firing thresholds to guide the evolution of the ANN in state space towards the desired memory attractor. The dynamics of neuronal relaxation has been modified for storage and retrieval of low-activity patterns and the original gradient optimization of threshold dynamics has been replaced with optimization by simulated annealing.

Algorithms↗
PubMed2005

Statistical-mechanical theory of DNA looping.

The lack of a rigorous analytical theory for DNA looping has caused many DNA-loop-mediated phenomena to be interpreted using theories describing the related process of DNA cyclization. However, distinctions in the mechanics of DNA looping versus cyclization can have profound quantitative effects on the thermodynamics of loop closure. We have extended a statistical mechanical theory recently developed for DNA cyclization to model DNA looping, taking into account protein flexibility. Notwithstanding the underlying theoretical similarity, we find that the topological constraint of loop closure leads to the coexistence of multiple classes of loops mediated by the same protein structure. These loop topologies are characterized by dramatic differences in twist and writhe; because of the strong coupling of twist and writhe within a loop, DNA looping can exhibit a complex overall helical dependence in terms of amplitude, phase, and deviations from uniform helical periodicity. Moreover, the DNA-length dependence of optimal looping efficiency depends on protein elasticity, protein geometry, and the presence of intrinsic DNA bends. We derive a rigorous theory of loop formation that connects global mechanical and geometric properties of both DNA and protein and demonstrates the importance of protein flexibility in loop-mediated protein-DNA interactions.

Binding Sites↗
PubMedDate not supplied

Supervised and unsupervised learning with two sites of synaptic integration.

Many learning rules for neural networks derive from abstract objective functions. The weights in those networks are typically optimized utilizing gradient ascent on the objective function. In those networks each neuron needs to store two variables. One variable, called activity, contains the bottom-up sensory-fugal information involved in the core signal processing. The other variable typically describes the derivative of the objective function with respect to the cell's activity and is exclusively used for learning. This variable allows the objective function's derivative to be calculated with respect to each weight and thus the weight update. Although this approach is widely used, the mapping of such two variables onto physiology is unclear, and these learning algorithms are often considered biologically unrealistic. However, recent research on the properties of cortical pyramidal neurons shows that these cells have at least two sites of synaptic integration, the basal and the apical dendrite, and are thus appropriately described by at least two variables. Here we discuss whether these results could constitute a physiological basis for the described abstract learning rules. As examples we demonstrate an implementation of the backpropagation of error algorithm and a specific self-supervised learning algorithm using these principles. Thus, compared to standard, one-integration-site neurons, it is possible to incorporate interesting properties in neural networks that are inspired by physiology with a modest increase of complexity.

Action Potentials↗
PubMed2005

Nonlinear software sensor for monitoring genetic regulation processes with noise and modeling errors.

Nonlinear control techniques by means of a software sensor that are commonly used in chemical engineering could be also applied to genetic regulation processes. We provide here a realistic formulation of this procedure by introducing an additive white Gaussian noise, which is usually found in experimental data. Besides, we include model errors, meaning that we assume we do not know the nonlinear regulation function of the process. In order to illustrate this procedure, we employ the Goodwin dynamics of the concentrations [B. C. Goodwin, (Academic, New York, 1963)] in the simple form recently applied to single gene systems and some operon cases [H. De Jong, J. Comput. Biol. 9, 67 (2002)], which involves the dynamics of the mRNA, given protein and metabolite concentrations. Further, we present results for a three gene case in coregulated sets of transcription units as they occur in prokaryotes. However, instead of considering their full dynamics, we use only the data of the metabolites and a designed software sensor. We also show, more generally, that it is possible to rebuild the complete set of nonmeasured concentrations despite the uncertainties in the regulation function or, even more, in the case of not knowing the mRNA dynamics. In addition, the rebuilding of concentrations is not affected by the perturbation due to the additive white Gaussian noise and also we managed to filter the noisy output of the biological system.

Algorithms↗

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