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Stochastic accumulator models account for response times and errors in perceptual decision making by assuming a noisy accumulation of perceptual evidence to a threshold. Previously, we explained saccade visual search decision making by macaque monkeys with a stochastic multiaccumulator model in which accumulation was driven by a gated feed-forward integration to threshold of spike trains from visually responsive neurons in frontal eye field that signal stimulus salience. This neurally constrained model quantitatively accounted for response times and errors in visual search for a target among varying numbers of distractors and replicated the dynamics of presaccadic movement neurons hypothesized to instantiate evidence accumulation. This modeling framework suggested strategic control over gate or over threshold as two potential mechanisms to accomplish speed-accuracy tradeoff (SAT). Here, we show that our gated accumulator model framework can account for visual search performance under SAT instructions observed in a milestone neurophysiological study of frontal eye field. This framework captured key elements of saccade search performance, through observed modulations of neural input, as well as flexible combinations of gate and threshold parameters necessary to explain differences in SAT strategy across monkeys. However, the trajectories of the model accumulators deviated from the dynamics of most presaccadic movement neurons. These findings demonstrate that traditional theoretical accounts of SAT are incomplete descriptions of the underlying neural adjustments that accomplish SAT, offer a novel mechanistic account of decision-making mechanisms during speed-accuracy tradeoff, and highlight questions regarding the identity of model and neural accumulators. NEW & NOTEWORTHY A gated accumulator model is used to elucidate neurocomputational mechanisms of speed-accuracy tradeoff. Whereas canonical stochastic accumulators adjust strategy only through variation of an accumulation threshold, we demonstrate that strategic adjustments are accomplished by flexible combinations of both modulation of the evidence representation and adaptation of accumulator gate and threshold. The results indicate how model-based cognitive neuroscience can translate between abstract cognitive models of performance and neural mechanisms of speed-accuracy tradeoff.
Emerging techniques now allow for precise quantification of distributions of biological molecules in single cells. These rapidly advancing experimental methods have created a need for more rigorous and efficient modeling tools. Here, we derive new bounds on the likelihood that observations of single-cell, single-molecule responses come from a discrete stochastic model, posed in the form of the chemical master equation. These strict upper and lower bounds are based on a finite state projection approach, and they converge monotonically to the exact likelihood value. These bounds allow one to discriminate rigorously between models and with a minimum level of computational effort. In practice, these bounds can be incorporated into stochastic model identification and parameter inference routines, which improve the accuracy and efficiency of endeavors to analyze and predict single-cell behavior. We demonstrate the applicability of our approach using simulated data for three example models as well as for experimental measurements of a time-varying stochastic transcriptional response in yeast.
The production and degradation of RNA transcripts is inherently subject to biological noise that arises from small gene copy numbers in individual cells. As a result, cellular RNA levels can exhibit large fluctuations over time and from one cell to the next. This article presents a range of precise single-molecule experimental techniques, based upon RNA fluorescence in situ hybridization, which can be used to measure the fluctuations of RNA at the single-cell level. A class of models for gene activation and deactivation is postulated in order to capture complex stochastic effects of chromatin modifications or transcription factor interactions. A computational tool, known as the finite state projection approach, is introduced to accurately and efficiently analyze these models in order to predict how probability distributions of RNA change over time in response to changing environmental conditions. These single-molecule experiments, discrete stochastic models, and computational analyses are systematically integrated to identify models of gene regulation dynamics. To illustrate the power and generality of our integrated experimental and computational approach, we explore cases that include different models for three different RNA types (sRNA, mRNA and nascent RNA), three different experimental techniques and three different biological species (bacteria, yeast and human cells).
Copyright © 2015. Published by Elsevier Inc.
Experiments have shown that, even in a homogeneous population of cells, the distribution of division times is highly variable. In addition, a homogeneous population of cells will exhibit a heterogeneous response to drug therapy. We present a simple stochastic model of the cell cycle as a multistep stochastic process. The model, which is based on our conception of the cell cycle checkpoint, is used to derive an analytical expression for the distribution of cell cycle times. We demonstrate that this distribution provides an accurate representation of cell cycle time variability and show how the model relates drug-induced changes in basic biological parameters to variability in response to drug treatment.
Copyright © 2014 Elsevier Ltd. All rights reserved.
In Saccharomyces cerevisiae, Hog1 MAPK is activated and induces a transcriptional program in response to hyperosmotic stress. Several Hog1-responsive genes exhibit stochastic transcription, resulting in cell-to-cell variability in mRNA and protein levels. However, the mechanisms governing stochastic gene activity are not fully defined. Here we uncover a novel role for casein kinase II (CK2) in the cellular response to hyperosmotic stress. CK2 interacts with and phosphorylates the Hot1 transcription factor; however, Hot1 phosphorylation is not sufficient for controlling the stochastic response. The CK2 protein itself is required to negatively regulate mRNA expression of Hot1-responsive genes and Hot1 enrichment at target promoters. Single-cell gene expression analysis reveals altered activation of Hot1-targeted STL1 in ck2 mutants, resulting in a bimodal to unimodal shift in expression. Together, this work reveals a novel CK2 function during the hyperosmotic stress response that promotes cell-to-cell variability in gene expression.
© 2014 by The American Society for Biochemistry and Molecular Biology, Inc.
Regeneration of central nervous system (CNS) lesions requires movement of progenitor cells and production of their differentiated progeny. Although damage to the CNS clearly promotes these two processes, the interplay between these complex events and how it affects a response remains elusive. Here, we use spatial stochastic modeling to show that tradeoffs arise between production and recruitment during regeneration. Proper spatial control of cell cycle timing can mitigate these tradeoffs, maximizing recruitment, improving infiltration into the lesion, and reducing wasteful production outside of it. Feedback regulation of cell lineage dynamics alone however leads to spatial defects in cell recruitment, suggesting a novel, to our knowledge, hypothesis for the aggregation of cells to the periphery of a lesion in multiple sclerosis. Interestingly, stronger chemotaxis does not correct this aggregation and instead, substantial random cell motions near the site of the lesion are required to improve CNS regeneration.
Copyright © 2014 Biophysical Society. Published by Elsevier Inc. All rights reserved.
Decision-making is explained by psychologists through stochastic accumulator models and by neurophysiologists through the activity of neurons believed to instantiate these models. We investigated an overlooked scaling problem: How does a response time (RT) that can be explained by a single model accumulator arise from numerous, redundant accumulator neurons, each of which individually appears to explain the variability of RT? We explored this scaling problem by developing a unique ensemble model of RT, called e pluribus unum, which embodies the well-known dictum "out of many, one." We used the e pluribus unum model to analyze the RTs produced by ensembles of redundant, idiosyncratic stochastic accumulators under various termination mechanisms and accumulation rate correlations in computer simulations of ensembles of varying size. We found that predicted RT distributions are largely invariant to ensemble size if the accumulators share at least modestly correlated accumulation rates and RT is not governed by the most extreme accumulators. Under these regimes the termination times of individual accumulators was predictive of ensemble RT. We also found that the threshold measured on individual accumulators, corresponding to the firing rate of neurons measured at RT, can be invariant with RT but is equivalent to the specified model threshold only when the rate correlation is very high.
The stochastic accumulation framework provides a mechanistic, quantitative account of perceptual decision-making and how task performance changes with experimental manipulations. Importantly, it provides an elegant account of the speed-accuracy trade-off (SAT), which has long been the litmus test for decision models, and also mimics the activity of single neurons in several key respects. Recently, we developed a paradigm whereby macaque monkeys trade speed for accuracy on cue during visual search task. Single-unit activity in frontal eye field (FEF) was not homomorphic with the architecture of models, demonstrating that stochastic accumulators are an incomplete description of neural activity under SAT. This paper summarizes and extends this work, further demonstrating that the SAT leads to extensive, widespread changes in brain activity never before predicted. We will begin by reviewing our recently published work that establishes how spiking activity in FEF accomplishes SAT. Next, we provide two important extensions of this work. First, we report a new chronometric analysis suggesting that increases in perceptual gain with speed stress are evident in FEF synaptic input, implicating afferent sensory-processing sources. Second, we report a new analysis demonstrating selective influence of SAT on frequency coupling between FEF neurons and local field potentials. None of these observations correspond to the mechanics of current accumulator models.
We present a parameter sensitivity analysis method that is appropriate for stochastic models, and we demonstrate how this analysis generates experimentally testable predictions about the factors that influence local Ca(2+) release in heart cells. The method involves randomly varying all parameters, running a single simulation with each set of parameters, running simulations with hundreds of model variants, then statistically relating the parameters to the simulation results using regression methods. We tested this method on a stochastic model, containing 18 parameters, of the cardiac Ca(2+) spark. Results show that multivariable linear regression can successfully relate parameters to continuous model outputs such as Ca(2+) spark amplitude and duration, and multivariable logistic regression can provide insight into how parameters affect Ca(2+) spark triggering (a probabilistic process that is all-or-none in a single simulation). Benchmark studies demonstrate that this method is less computationally intensive than standard methods by a factor of 16. Importantly, predictions were tested experimentally by measuring Ca(2+) sparks in mice with knockout of the sarcoplasmic reticulum protein triadin. These mice exhibit multiple changes in Ca(2+) release unit structures, and the regression model both accurately predicts changes in Ca(2+) spark amplitude (30% decrease in model, 29% decrease in experiments) and provides an intuitive and quantitative understanding of how much each alteration contributes to the result. This approach is therefore an effective, efficient, and predictive method for analyzing stochastic mathematical models to gain biological insight.
Copyright © 2013 Biophysical Society. Published by Elsevier Inc. All rights reserved.
Although much has been done to elucidate the biochemistry of signal transduction and gene regulatory pathways, it remains difficult to understand or predict quantitative responses. We integrate single-cell experiments with stochastic analyses, to identify predictive models of transcriptional dynamics for the osmotic stress response pathway in Saccharomyces cerevisiae. We generate models with varying complexity and use parameter estimation and cross-validation analyses to select the most predictive model. This model yields insight into several dynamical features, including multistep regulation and switchlike activation for several osmosensitive genes. Furthermore, the model correctly predicts the transcriptional dynamics of cells in response to different environmental and genetic perturbations. Because our approach is general, it should facilitate a predictive understanding for signal-activated transcription of other genes in other pathways or organisms.