Universality of J-shaped and U-shaped dose-response relations as emergent properties of stochastic transition systems

Dose-response data for many chemical carcinogens exhibit multiple apparent concentration thresholds. A relatively small increase in exposure concentration near such a threshold disproportionately increases incidence of a specific tumor type. Yet, many common mathematical models of carcinogenesis do not predict such threshold-like behavior when model parameters (e.g., describing cell transition rates) increase smoothly with dose, as often seems biologically plausible. For example, commonly used forms of both the traditional Armitage-Doll and multistage (MS) models of carcinogenesis and the Moolgavkar-Venzon-Knudson (MVK) two-stage stochastic model of carcinogenesis typically yield smooth dose-response curves without sudden jumps or thresholds when exposure is assumed to increase cell transition rates in proportion to exposure concentration.This paper introduces a general mathematical modeling framework that includes the MVK and MS model families as special cases, but that shows how abrupt transitions in cancer hazard rates, considered as functions of exposure concentrations and durations, can emerge naturally in large cell populations even when the rates of cell-level events increase smoothly (e.g., proportionally) with concentration. In this framework, stochastic transitions of stem cells among successive events represent exposure-related damage. Cell proliferation, cell killing and apoptosis can occur at different stages. Key components include: An effective number of stem cells undergoing active cycling and hence vulnerable to stochastic transitions representing somatically heritable transformations. (These need not occur in any special linear order, as in the MS model.)A random time until the first malignant stem cell is formed. This is the first order-statistic, T = min{T1, T2, ..., Tn} of n random variables, interpreted as the random times at which each of n initial stem cells or their progeny first become malignant.A random time for a normal stem cell to complete a full set of transformations converting it to a malignant one. This is interpreted very generally as the first passage time through a network of stochastic transitions, possibly with very many possible paths and unknown topology.In this very general family of models, threshold-like (J-shaped or multi-threshold) dose-response nonlinearities naturally emerge even without cytotoxicity, as consequences of stochastic phase transition laws for traversals of random transition networks. With cytotoxicity present, U-shaped as well as J-shaped dose-response curves can emerge. These results are universal, i.e., independent of specific biological details represented by the stochastic transition networks.     

Modeling heterogeneity of properties and random effects in drug dissolution

Purpose. To investigate new models characterizing dissolution data obtained for heterogenous materials (model I) and under randomly time-varying conditions (model II). Methods. In model I, the heterogeneity of the dissolving substance introduces variation of the fractional dissolution rate. In model II, the fractional dissolution rate evolves randomly, and thus the dissolution has the characteristics of a stochastic process. This situation is studied for the constant and time-dependent means of the dissolution rate. Results. The time dynamics of the dissolved fraction is presented for model I. The standard characteristics of dissolution are derived under general conditions and for several examples. One of them is in accordance with a function found empirically (1). A duality between the time-dependency of the fractional dissolution rate and the heterogeneity of the substance is investigated. The mean and variance of the dissolved fraction are calculated for model II. A method for estimating the mean dissolution rate is proposed and illustrated using Monte-Carlo experiments. Conclusions. It follows from model I that the heterogeneity, with the same mean properties, slows down the dissolution with respect to the homogeneous case. The second approach permits predictions about the role of the stochastic fluctuations of the dissolution rate and to establish the boundaries for the dissolution profiles.     

Integrated microfluidic bioprocessor for single-cell gene expression analysis

An integrated microdevice is developed for the analysis of gene expression in single cells. The system captures a single cell, transcribes and amplifies the mRNA, and quantitatively analyzes the products of interest. The key components of the microdevice include integrated nanoliter metering pumps, a 200-nL RT-PCR reactor with a single-cell capture pad, and an affinity capture matrix for the purification and concentration of products that is coupled to a microfabricated capillary electrophoresis separation channel for product analysis. Efficient microchip integration of these processes enables the sensitive and quantitative examination of gene expression variation at the single-cell level. This microdevice is used to measure siRNA knockdown of the GAPDH gene in individual Jurkat cells. Single-cell measurements suggests the presence of 2 distinct populations of cells with moderate (≈50%) or complete (≈0%) silencing. This stochastic variation in gene expression and silencing within single cells is masked by conventional bulk measurements.     

13C MRS of occipital and frontal lobes at 3 T using a volume coil for stochastic proton decoupling

Previously, we devised a novel strategy for in vivo ¹³C MRS using [2‐¹³C]glucose infusion and low‐power proton decoupling, and proposed that this strategy could be used to acquire ¹³C MR spectra from the frontal lobe of the human brain. Here, we demonstrate, for the first time, in vivo ¹³C MRS of human frontal lobe acquired at 3 T. Because the primary metabolites of [2‐¹³C]glucose can be decoupled using very‐low‐radiofrequency power, we used a volume coil for proton decoupling in this study. The homogeneous B₁ field of the volume coil was found to significantly enhance the decoupling efficiency of the stochastic decoupling sequence. Detailed specific absorption rates inside the human head were analyzed using the finite difference time domain method to ensure experimental safety. In vivo ¹³C spectra from the occipital and frontal lobes of the human brain were obtained. At a decoupling power of 30 W (time‐averaged power, 2.45 W), the spectra from the occipital lobe showed well‐resolved spectral resolution and excellent signal‐to‐noise ratio. Although frontal lobe ¹³C spectra were affected by local B₀ field inhomogeneity, we demonstrated that the spectral quality could be improved using post‐acquisition data processing. In particular, we showed that the frontal lobe glutamine C5 at 178.5 ppm and aspartate C4 at 178.3 ppm could be spectrally resolved with effective proton decoupling and B₀ field correction. Because of its large spatial coverage, volume coil decoupling provides the potential to acquire ¹³C MRS from more than one brain region simultaneously. Copyright © 2010 John Wiley & Sons, Ltd.     

流体随机Petri网的一阶混杂Petri网模型

为了借用一阶混杂Petri网(First-Order Hybrid Petri Nets)的建模原语和分析方法来分析流体随机Petri网(Fluid Stochastic Petri Nets)以克服流体随机Petri网数值分析方法的局限性,本文提出了一种流体随机Petri网转换成一阶混杂Petri网的形式化描述方法,并对其转换的正确性进行了证明,最后通过实例分析了流体随机Petri网转换成一阶混杂Petri网的必要性.     

随机返混对颗粒反应的影响

针对多级返混流系统,比较了Markov过程模型与Monte Carlo方法的区别。采用Monte Carlo方法模拟了返混的波动对反应率的影响,给出了几种常见反应过程中返混对颗粒反应率影响的模拟结果。     

Determination of cell fate selection during phage lambda infection

Bacteriophage lambda infection of Escherichia coli can result in distinct cell fate outcomes. For example, some cells lyse whereas others survive as lysogens. A quantitative biophysical model of lambda infection supports the hypothesis that spontaneous differences in the timing of individual molecular events during lambda infection leads to variation in the selection of cell fates. Building from this analysis, the lambda lysis–lysogeny decision now serves as a paradigm for how intrinsic molecular noise can influence cellular behavior, drive developmental processes, and produce population heterogeneity. Here, we report experimental evidence that warrants reconsidering this framework. By using cell fractioning, plating, and single-cell fluorescent microscopy, we find that physical differences among cells present before infection bias lambda developmental outcomes. Specifically, variation in cell volume at the time of infection can be used to help predict cell fate: a ≈2-fold increase in cell volume results in a 4- to 5-fold decrease in the probability of lysogeny. Other cell fate decisions now thought to be stochastic might also be determined by pre-existing variation.     

Stochastic approximation EM for large-scale exploratory IRT factor analysis

A stochastic approximation EM algorithm (SAEM) is described for exploratory factor analysis of dichotomous or ordinal variables. The factor structure is obtained from sufficient statistics that are updated during iterations with the Robbins-Monro procedure. Two large-scale simulations are reported that compare accuracy and CPU time of the proposed SAEM algorithm to the Metropolis-Hasting Robbins-Monro procedure and to a generalized least squares analysis of the polychoric correlation matrix. A smaller-scale application to real data is also reported, including a method for obtaining standard errors of rotated factor loadings. A simulation study based on the real data analysis is conducted to study bias and error estimates. The SAEM factor algorithm requires minimal lines of code, no derivatives, and no large-matrix inversion. It is programmed entirely in R.     

具有输入时滞的随机非线性系统的自适应神经网络控制

考虑一类具有输入时滞的随机非线性系统的自适应神经网络控制问题。通过定义含输入积分项的设计变量,将输入时滞系统转变为非时滞系统。结合神经网络控制、积分中值定理与Decoupled Backstepping技巧,针对该类系统提出一套自适应控制策略。所提出的控制器保证闭环系统的所有信号皆4阶矩半全局一致最终有界, 并且跟踪误差收敛于原点附近的小邻域内。仿真实验结果验证了所提出控制策略的有效性。     

Inhibition dominates in shaping spontaneous CA3 hippocampal network activities in vitro

We have assessed the balance of excitation and inhibition in in vitro rodent hippocampal slices exhibiting spontaneous, basal sharp waves (bSPWs). A defining signature of a network exhibiting bSPWs is the rise and fall in local field activities with frequencies ranging from 0.5 to 4.5 Hz. This variation of extracellular local field activities manifests at the intracellular level as postsynaptic potentials (PSPs). In correspondence with the local field bSPWs, we consider "sparse" and "synchronous" parts of bSPWs at the intracellular level. We have used intracellular data of bSPW-associated PSPs together with mathematical extraction techniques to quantify the mean and variance of synaptic conductances that a neuron experiences during bSPW episodes. We find that inhibitory conductances dominate in pyramidal cells and in a putative interneuron, and that inhibitory variances are much greater than excitatory ones during synchronous parts of bSPWs. Specifically, we find that there is at least a twofold increase in inhibitory conductance dominance from "sparse" to "synchronous" bSPW states and that this transition is associated with inhibitory fluctuations of greater than 10% of the change in mean inhibitory conductance. On the basis of our findings, we suggest that such inhibitory fluctuations during transition may be a physiological feature of systems expressing such population activities. In summary, our results provide a quantified basis for understanding the interaction of excitatory and inhibitory neuronal subpopulations in bSPW activities.