Statistical reconstruction of transcription factor activity using Michaelis-Menten kinetics.

The basic building block of a gene regulatory network consists of a gene encoding a transcription factor (TF) and the gene(s) it regulates. Considerable efforts have been directed recently at devising experiments and algorithms to determine TFs and their corresponding target genes using gene expression and other types of data. The underlying problem is that the expression of a gene coding for the TF provides only limited information about the activity of the TF, which can also be controlled posttranscriptionally. In the absence of a reliable technology to routinely measure the activity of regulators, it is of great importance to understand whether this activity can be inferred from gene expression data. We here develop a statistical framework to reconstruct the activity of a TF from gene expression data of the target genes in its regulatory module. The novelty of our approach is that we embed the deterministic Michaelis-Menten model of gene regulation in this statistical framework. The kinetic parameters of the gene regulation model are inferred together with the profile of the TF regulator. We also obtain a goodness-of-fit test to verify the fit of the model. The model is applied to a time series involving the Streptomyces coelicolor bacterium. We focus on the transcriptional activator cdaR, which is partly responsible for the production of a particular type of antibiotic. The aim is to reconstruct the activity profile of this regulator. Our approach can be extended to include more complex regulatory relationships, such as multiple regulatory factors, competition, and cooperativity.

Reconstructing repressor protein levels from expression of gene targets in Escherichia coli.

The basic underlying problem in reverse engineering of gene regulatory networks from gene expression data is that the expression of a gene encoding the regulator provides only limited information about its protein activity. The proteins, which result from translation, are subject to stringent posttranscriptional control and modification. Often, it is only the modified version of the protein that is capable of activating or repressing its regulatory targets. At present there exists no reliable high-throughput technology to measure the protein activity levels in real-time, and therefore they are, so-to-say, lost in translation. However, these activity levels can be recovered by studying the gene expression of their targets. Here, we describe a computational approach to predict temporal regulator activity levels from the gene expression of its transcriptional targets in a network motif with one regulator and many targets. We consider an example of an SOS repair system, and computationally infer the regulator activity of its master repressor, LexA. The reconstructed activity profile of LexA exhibits a behavior that is similar to the experimentally measured profile of this repressor: after UV irradiation, the amount of LexA substantially decreases within a few minutes, followed by a recovery to its normal level. Our approach can easily be applied to known single-input motifs in other organisms.

An experimental evaluation of a loop versus a reference design for two-channel microarrays.

MOTIVATION: Despite theoretical arguments that so-called 'loop designs' for two-channel DNA microarray experiments are more efficient, biologists continue to use 'reference designs'. We describe two sets of microarray experiments with RNA from two different biological systems (TPA-stimulated mammalian cells and Streptomyces coelicolor). In each case, both a loop and a reference design were used with the same RNA preparations with the aim of studying their relative efficiency. RESULTS: The results of these experiments show that (1) the loop design attains a much higher precision than the reference design, (2) multiplicative spot effects are a large source of variability, and if they are not accounted for in the mathematical model, for example, by taking log-ratios or including spot effects, then the model will perform poorly. The first result is reinforced by a simulation study. Practical recommendations are given on how simple loop designs can be extended to more realistic experimental designs and how standard statistical methods allow the experimentalist to use and interpret the results from loop designs in practice. AVAILABILITY: The data and R code are available at http://exgen.ma.umist.ac.uk CONTACT: veronica.vinciotti@brunel.ac.uk.

A probabilistic model for the establishment of neuron polarity.

The main aim of this paper is to present a simple probabilistic model for the early stage of neuron growth: the specification on an axon out of several initially similar neurites. The model is a Markov process with competition between the growing neurites, wherein longer objects have more chances to grow, and parameter alpha determines the intensity of the competition. For alpha > 1 the model provides results which are qualitatively similar to the experimental ones, i.e. selection of one rapidly elongating axon out of several neurites while other less successful neurites stop growing at some random time. Rigorous mathematical proofs are given.

The diffusion of molecules in axonal plasma membranes: the sites of insertion of new membrane molecules and their distribution along the axon surface.

The neuronal cell surface consists of two domains, the somatodendritic and axonal plasma membranes. Each domain serves different functions, and has a different complement of membrane molecules. Since membrane molecules are able to diffuse in the plane of the plasma membrane lipid bilayer, with diffusion coefficients ranging from 10-8 cm 2 s-1 for lipids to 10-10 cm 2 s-1 for proteins, mechanisms must exist to prevent as intermixing of membrane molecules from each domain by diffusion. Presented here is a theoretical analysis of the distribution of axonal molecules in both growing and non-growing axons based on two models for the insertion of these molecules into the axonal membrane, namely insertion exclusively at the distal end of the axon, or insertion with equal probability all along the axon. In all cases, assuming that the molecules have a finite half-life in the axonal membrane, compositional differences between the axonal and somatodendritic membranes can be obtained that are similar to those observed in other polarized cells, even in the absence of a physical barrier to prevent the intermixing of membrane molecules. Moreover, our analyses demonstrate that the diffusion of membrane molecules in the plane of the axonal lipid bilayer is a sufficiently slow process to preclude the possibility that membrane molecules are inserted into axonal membranes at a site remote from their final location, and then move to their final locations for diffusion. Thus, in long axons, for membrane molecules that are localized all along the length of the axon, mechanisms must exist for their insertion in the axonal membrane at sites all along the axon, and not just at the distal end.

"First step" negative feedback accounts for inhibition of fast neurotransmitter release.

This paper is concerned with feedback inhibition of neurotransmitter release by the neurotransmitter itself. We put forward the idea that, similar to multistep biochemical processes, feedback inhibition acts on the initial step in the chain of events that lead to release. Using experimental results carried out on glutamatergic synapses in crayfish, we show that the "first step" hypothesis can account for all experimental results. Our modeling suggests that the biochemical implementation of this inhibition involves the formation of a second messenger, whose production is triggered by binding of transmitter to the autoreceptor. We argue that the autoreceptor is a key part of the release-inducing machinery.

A mechanism for discharge of charged excitatory neurotransmitter.

Excitatory neurotransmitter is charged, so that emptying of a transmitter-containing vesicle (discharge) would seem to require considerable energy. Even if the energy problem is surmounted and discharge thereby made possible, there is still a problem of making the discharge fast enough (considerably less than 1 ms). Proposed here is a mechanism wherein discharge of charged transmitter is accompanied by the influx of cocharged ions or coefflux of counter-charged particles (ion interchange). It is shown theoretically that ion interchange obviates the necessity for a separate energy source and can provide the observed rapid vesicle discharge.

Diffusion cannot govern the discharge of neurotransmitter in fast synapses.

In the present work we show that diffusion cannot provide the observed fast discharge of neurotransmitter from a synaptic vesicle during neurotransmitter release, mainly because it is not sufficiently rapid nor is it sufficiently temperature-dependent. Modeling the discharge from the vesicle into the cleft as a continuous point source, we have determined that discharge should occur in 50-75 microseconds, to provide the observed high concentrations of transmitter at the critical zone.