Optimizing static thermodynamic models of transcriptional regulation

Thermodynamic model of gene regulation for the Or59b olfactory receptor in Drosophila

Complex eukaryotic promoters normally contain multiple cis-regulatory sequences for different transcription factors (TFs). The binding patterns of the TFs to these sites, as well as the way the TFs interact with each other and with the RNA polymerase (RNAp), lead to combinatorial problems rarely understood in detail, especially under varying epigenetic conditions. The aim of this paper is to build a model describing how the main regulatory cluster of the olfactory receptor Or59b drives transcription of this gene in Drosophila. The cluster-driven expression of this gene is represented as the equilibrium probability of RNAp being bound to the promoter region, using a statistical thermodynamic approach. The RNAp equilibrium probability is computed in terms of the occupancy probabilities of the single TFs of the cluster to the corresponding binding sites, and of the interaction rules among TFs and RNAp, using experimental data of Or59b expression to tune the model parameters. The model reproduces correctly the changes in RNAp binding probability induced by various mutation of specific sites and epigenetic modifications. Some of its predictions have also been validated in novel experiments.

Parallel Simulated Annealing Using an Adaptive Resampling Interval

This paper presents a parallel simulated annealing algorithm that is able to achieve 90% parallel efficiency in iteration on up to 192 processors and up to 40% parallel efficiency in time when applied to a 5000-dimension Rastrigin function. Our algorithm breaks scalability barriers in the method of Chu et al. (1999) by abandoning adaptive cooling based on variance. The resulting gains in parallel efficiency are much larger than the loss of serial efficiency from lack of adaptive cooling. Our algorithm resamples the states across processors periodically. The resampling interval is tuned according to the success rate for each specific number of processors. We further present an adaptive method to determine the resampling interval based on the adoption rate. This adaptive method is able to achieve nearly identical parallel efficiency but higher success rates compared to the fixed interval one using the best interval found.

An algebra-based method for inferring gene regulatory networks

BACKGROUND

The inference of gene regulatory networks (GRNs) from experimental observations is at the heart of systems biology. This includes the inference of both the network topology and its dynamics. While there are many algorithms available to infer the network topology from experimental data, less emphasis has been placed on methods that infer network dynamics. Furthermore, since the network inference problem is typically underdetermined, it is essential to have the option of incorporating into the inference process, prior knowledge about the network, along with an effective description of the search space of dynamic models. Finally, it is also important to have an understanding of how a given inference method is affected by experimental and other noise in the data used.

RESULTS

This paper contains a novel inference algorithm using the algebraic framework of Boolean polynomial dynamical systems (BPDS), meeting all these requirements. The algorithm takes as input time series data, including those from network perturbations, such as knock-out mutant strains and RNAi experiments. It allows for the incorporation of prior biological knowledge while being robust to significant levels of noise in the data used for inference. It uses an evolutionary algorithm for local optimization with an encoding of the mathematical models as BPDS. The BPDS framework allows an effective representation of the search space for algebraic dynamic models that improves computational performance. The algorithm is validated with both simulated and experimental microarray expression profile data. Robustness to noise is tested using a published mathematical model of the segment polarity gene network in Drosophila melanogaster. Benchmarking of the algorithm is done by comparison with a spectrum of state-of-the-art network inference methods on data from the synthetic IRMA network to demonstrate that our method has good precision and recall for the network reconstruction task, while also predicting several of the dynamic patterns present in the network.

CONCLUSIONS

Boolean polynomial dynamical systems provide a powerful modeling framework for the reverse engineering of gene regulatory networks, that enables a rich mathematical structure on the model search space. A C++ implementation of the method, distributed under LPGL license, is available, together with the source code, at http://www.paola-vera-licona.net/Software/EARevEng/REACT.html.

Predicting gene-regulation functions: lessons from temperate bacteriophages

Gene-regulation functions (GRF) provide a unique characteristic of a cis-regulatory module (CRM), relating the concentrations of transcription factors (input) to the promoter activities (output). The challenge is to predict GRFs from the sequence. Here we systematically consider the lysogeny-lysis CRMs of different temperate bacteriophages such as the Lactobacillus casei phage A2, Escherichia coli phages lambda, and 186 and Lactococcal phage TP901-1. This study allowed explaining a recent experimental puzzle on the role of Cro protein in the lambda switch. Several general conclusions have been drawn: 1), long-range interactions, multilayer assembly and DNA looping may lead to complex GRFs that cannot be described by linear functions of binding site occupancies; 2), in general, GRFs cannot be described by the Boolean logic, whereas a three-state non-Boolean logic suffices for the studied examples; 3), studied CRMs of the intact phages seemed to have a similar GRF topology (the number of plateaus and peaks corresponding to different expression regimes); we hypothesize that functionally equivalent CRMs might have topologically equivalent GRFs for a larger class of genetic systems; and 4) within a given GRF class, a set of mechanistic-to-mathematical transformations has been identified, which allows shaping the GRF before carrying out a system-level analysis.

Thermodynamics-based models of transcriptional regulation by enhancers: the roles of synergistic activation, cooperative binding and short-range repression

Quantitative models of cis-regulatory activity have the potential to improve our mechanistic understanding of transcriptional regulation. However, the few models available today have been based on simplistic assumptions about the sequences being modeled, or heuristic approximations of the underlying regulatory mechanisms. We have developed a thermodynamics-based model to predict gene expression driven by any DNA sequence, as a function of transcription factor concentrations and their DNA-binding specificities. It uses statistical thermodynamics theory to model not only protein-DNA interaction, but also the effect of DNA-bound activators and repressors on gene expression. In addition, the model incorporates mechanistic features such as synergistic effect of multiple activators, short range repression, and cooperativity in transcription factor-DNA binding, allowing us to systematically evaluate the significance of these features in the context of available expression data. Using this model on segmentation-related enhancers in Drosophila, we find that transcriptional synergy due to simultaneous action of multiple activators helps explain the data beyond what can be explained by cooperative DNA-binding alone. We find clear support for the phenomenon of short-range repression, where repressors do not directly interact with the basal transcriptional machinery. We also find that the binding sites contributing to an enhancer's function may not be conserved during evolution, and a noticeable fraction of these undergo lineage-specific changes. Our implementation of the model, called GEMSTAT, is the first publicly available program for simultaneously modeling the regulatory activities of a given set of sequences.

The development of complex multicellular organisms requires genes to be expressed at specific stages and in specific tissues. Regulatory DNA sequences, often called cis-regulatory modules, drive the desired gene expression patterns by integrating information about the environment in the form of the activities of transcription factors. The rules by which regulatory sequences read this type of information, however, are unclear. In this work, we developed quantitative models based on physicochemical principles that directly map regulatory sequences to the expression profiles they generate. We evaluated these models on the segmentation network of the model organism Drosophila melanogaster. Our models incorporate mechanistic features that attempt to capture how activating and repressing transcription factors work in the segmentation system. By evaluating the importance of these features, we were able to gain insights on the quantitative regulatory rules. We found that two different mechanisms may contribute to cooperative gene activation and that repressors often have a short range of influence in DNA sequences. Combining the quantitative modeling with comparative sequence analysis, we also found that even functional sequences may be lost during evolution.

Dual-functioning transcription factors in the developmental gene network of Drosophila melanogaster

Background

Quantitative models for transcriptional regulation have shown great promise for advancing our understanding of the biological mechanisms underlying gene regulation. However, all of the models to date assume a transcription factor (TF) to have either activating or repressing function towards all the genes it is regulating.

Results

In this paper we demonstrate, on the example of the developmental gene network in D. melanogaster, that the data-fit can be improved by up to 40% if the model is allowing certain TFs to have dual function, that is, acting as activator for some genes and as repressor for others. We demonstrate that the improvement is not due to additional flexibility in the model but rather derived from the data itself. We also found no evidence for the involvement of other known site-specific TFs in regulating this network. Finally, we propose SUMOylation as a candidate biological mechanism allowing TFs to switch their role when a small ubiquitin-like modifier (SUMO) is covalently attached to the TF. We strengthen this hypothesis by demonstrating that the TFs predicted to have dual function also contain the known SUMO consensus motif, while TFs predicted to have only one role lack this motif.

Conclusions

We argue that a SUMOylation-dependent mechanism allowing TFs to have dual function represents a promising area for further research and might be another step towards uncovering the biological mechanisms underlying transcriptional regulation.

Comparison of evolutionary algorithms in gene regulatory network model inference

BACKGROUND

The evolution of high throughput technologies that measure gene expression levels has created a data base for inferring GRNs (a process also known as reverse engineering of GRNs). However, the nature of these data has made this process very difficult. At the moment, several methods of discovering qualitative causal relationships between genes with high accuracy from microarray data exist, but large scale quantitative analysis on real biological datasets cannot be performed, to date, as existing approaches are not suitable for real microarray data which are noisy and insufficient.

RESULTS

This paper performs an analysis of several existing evolutionary algorithms for quantitative gene regulatory network modelling. The aim is to present the techniques used and offer a comprehensive comparison of approaches, under a common framework. Algorithms are applied to both synthetic and real gene expression data from DNA microarrays, and ability to reproduce biological behaviour, scalability and robustness to noise are assessed and compared.

CONCLUSIONS

Presented is a comparison framework for assessment of evolutionary algorithms, used to infer gene regulatory networks. Promising methods are identified and a platform for development of appropriate model formalisms is established.