Stochastic models for regulatory networks of the genetic toggle switch

Bistability arises within a wide range of biological systems from the A phage switch in bacteria to cellular signal transduction pathways in mammalian cells. Changes in regulatory mechanisms may result in genetic switching in a bistable system. Recently, more and more experimental evidence in the form of bimodal population distributions indicates that noise plays a very important role in the switching of bistable systems. Although deterministic models have been used for studying the existence of bistability properties under various system conditions, these models cannot realize cell-to-cell fluctuations in genetic switching. However, there is a lag in the development of stochastic models for studying the impact of noise in bistable systems because of the lack of detailed knowledge of biochemical reactions, kinetic rates, and molecular numbers. in this work, we develop a previously undescribed general technique for developing quantitative stochastic models for large-scale genetic regulatory networks by introducing Poisson random variables into deterministic models described by ordinary differential equations. Two stochastic models have been proposed for the genetic toggle switch interfaced with either the SOS signaling pathway or a quorum-sensing signaling pathway, and we have successfully realized experimental results showing bimodal population distributions. Because the introduced stochastic models are based on widely used ordinary differential equation models, the success of this work suggests that this approach is a very promising one for studying noise in large-scale genetic regulatory networks.

Computational properties of min/max autocorrelation factors

Minimum/maximum autocorrelation factor (MAF) is a suitable algorithm for orthogonalization of a vector random field. Orthogonalization avoids the use of multivariate geostatistics during joint stochastic modeling of geological attributes. This manuscript demonstrates in a practical way that computation of MAF is the same as discriminant analysis of the nested structures. Mathematica software is used to illustrate MAF calculations from a linear model of coregionalization (LMC) model. The limitation of two nested structures in the LMC for MAF is also discussed and linked to the effects of anisotropy and support. The analysis elucidates the matrix properties behind the approach and clarifies relationships that may be useful for model-based approaches. (C) 2003 Elsevier Science Ltd. All rights reserved.

Fock-state dynamics in Raman photoassociation of Bose-Einstein condensates

By stochastic modeling of the process of Raman photoassociation of Bose-Einstein condensates, we show that, the farther the initial quantum state is from a coherent state, the farther the one-dimensional predictions are from those of the commonly used zero-dimensional approach. We compare the dynamics of condensates, initially in different quantum states, finding that, even when the quantum prediction for an initial coherent state is relatively close to the Gross-Pitaevskii prediction, an initial Fock state gives qualitatively different predictions. We also show that this difference is not present in a single-mode type of model, but that the quantum statistics assume a more important role as the dimensionality of the model is increased. This contrasting behavior in different dimensions, well known with critical phenomena in statistical mechanics, makes itself plainly visible here in a mesoscopic system and is a strong demonstration of the need to consider physically realistic models of interacting condensates.

Estimating variable returns to scale production frontiers with alternative stochastic assumptions

Two stochastic production frontier models are formulated within the generalized production function framework popularized by Zellner and Revankar (Rev. Econ. Stud. 36 (1969) 241) and Zellner and Ryu (J. Appl. Econometrics 13 (1998) 101). This framework is convenient for parsimonious modeling of a production function with returns to scale specified as a function of output. Two alternatives for introducing the stochastic inefficiency term and the stochastic error are considered. In the first the errors are added to an equation of the form h(log y, theta) = log f (x, beta) where y denotes output, x is a vector of inputs and (theta, beta) are parameters. In the second the equation h(log y,theta) = log f(x, beta) is solved for log y to yield a solution of the form log y = g[theta, log f(x, beta)] and the errors are added to this equation. The latter alternative is novel, but it is needed to preserve the usual definition of firm efficiency. The two alternative stochastic assumptions are considered in conjunction with two returns to scale functions, making a total of four models that are considered. A Bayesian framework for estimating all four models is described. The techniques are applied to USDA state-level data on agricultural output and four inputs. Posterior distributions for all parameters, for firm efficiencies and for the efficiency rankings of firms are obtained. The sensitivity of the results to the returns to scale specification and to the stochastic specification is examined. (c) 2004 Elsevier B.V. All rights reserved.

Output price subsidies in a stochastic world

This article studies the comparative statics of output subsidies for firms, with monotonic preferences over costs and returns, that face price and production uncertainty. The modeling of deficiency payments, support-price schemes, and stochastic supply shifts in a state-space framework is discussed. It is shown how these notions can be used, via a simple application of Shephard's lemma, to analyze input-demand shifts once comparative-static results for supply are available. A range of comparative-static results for supply are then developed and discussed.