A rapid and effective method for obtaining thermodynamic quantities for Hamiltonians whose configurational space has not been examined through a direct simulation has been developed. This approach extends the scope of the weighted histogram analysis method and is applied to the exploration of the balance of forces within the off-lattice Honeycutt–Thirumalai 46-mer beta-barrel model. Specificity is introduced into the long range hydrophobic interactions by scaling back the non-native attractive component of the hydrophobic interactions through a scaling factor λ (0<λ<1). Thermodynamic properties for incremental values of λ are extrapolated from the sampling of the original (λ=1) Hamiltonian. The results were found to be in good agreement with the thermodynamic signatures obtained by direct simulations. Decreasing the strength of the non-native attractive hydrophobic interactions leads to a more cooperative folding with the folding and collapse temperatures nearly coinciding at λ=0.0. The free energy surfaces were also seen to become progressively smoother while retaining a pronounced native well. Thus, this methodology may be used in the development, refinement, and exploration of folding for off-lattice protein models.

Decomposing transcriptional regulatory networks into functional modules and determining logical relations between them is the first step toward understanding transcriptional regulation at the system level. Modules based on analysis of genome-scale data can serve as the basis for inferring combinatorial regulation and for building mathematical models to quantitatively describe the behavior of the networks. We present here an algorithm called MODEM to identify target genes of a transcription factor (TF) from a single expression experiment, based on a joint probabilistic model for promoter sequence and gene expression data. We show how this method can facilitate the discovery of specific instances of combinatorial regulation and illustrate this for a specific case of transcriptional networks that regulate sporulation in the yeast Saccharomyces cerevisiae. Applying this method to analyze two crucial TFs in sporulation, Ndt80p and Sum1p, we were able to delineate their overlapping binding sites. We proposed a mechanistic model for the competitive regulation by the two TFs on a defined subset of sporulation genes. We show that this model accounts for the temporal control of the ''middle'' sporulation genes and suggest a similar regulatory arrangement can be found in developmental programs in higher organisms.eciphering regulatory networks is a key step toward understanding gene regulation at a genomic scale. Both top-down and bottom-up approaches have been introduced. The top-down approach focuses on characterizing topologies of the networks from genome-wide measurements, such as large-scale surveys of network arrangements (1, 2), and is very useful in studying the organization of networks. The complementary bottom-up approach builds mechanistic models for each individual case, e.g., identifying the binding sites and target genes of a transcription factor (TF) (reviewed in ref. 3 and references therein), then specifies the roles of each TF in the networks, e.g., predicting under which cellular conditions a TF is activated (3-8). This approach next seeks to determine higher-order regulatory logic, e.g., how TFs cooperate with each other, and finally organizes all these pieces into functional networks. The bottom-up approach aims to explain the molecular basis of regulatory mechanisms. After a number of solid network structures are revealed, common regulatory rules are expected to emerge and, guided by the top-down approach, eventually general regulatory principles may be discovered.We present here a bottom-up approach to decipher transcriptional regulatory networks (9), in which a key step is to accurately identify the binding sites and regulatory targets of transcription factors systematically. For the convenience of discussion, we use the term transcription module as an abbreviation for a TF, its binding sites, and target genes (9) throughout this article. To accurately reconstruct transcription modules, we have developed a computational algorithm called MODEM (Module construction using gene Expression and sequence M...

Deciphering the design principles for regulatory networks is fundamental to an understanding of biological systems. We have explored the mapping from the space of network topologies to the space of dynamical phenotypes for small networks. Using exhaustive enumeration of a simple model of three-and four-node networks, we demonstrate that certain dynamical phenotypes can be generated by an atypically broad spectrum of network topologies. Such dynamical outputs are highly designable, much like certain protein structures can be designed by an unusually broad spectrum of sequences. The network topologies that encode a highly designable dynamical phenotype possess two classes of connections: a fully conserved core of dedicated connections that encodes the stable dynamical phenotype and a partially conserved set of variable connections that controls the transient dynamical flow. By comparing the topologies and dynamics of the three-and four-node network ensembles, we observe a large number of instances of the phenomenon of ''mutational buffering,'' whereby addition of a fourth node suppresses phenotypic variation amongst a set of three-node networks.designability ͉ dynamical phenotype ͉ enumeration ͉ mutational buffering ͉ regulatory network D iscerning the structure and function of cellular networks is essential to the development of a true understanding of biological systems. Experimental and theoretical studies are steadily advancing our knowledge of the wiring and input-output characteristics of a variety of natural and designed biological networks. These efforts have focused on characterizing the components and interactions for specific biological networks and their dynamical behaviors, by using standard genetic and biochemical approaches in conjunction with mathematical analysis of discovered circuits (1-7). Valuable insights into certain design features of biological networks have emerged through these efforts (8-13) and are used to guide the design of synthetic systems (14-16). The choice of which synthetic circuits to build is often a matter of careful hand-picking guided by experimental restrictions.Reverse-engineering and modeling of specific experimental systems on a case-by-case basis is necessary and meritorious. However, the space of networks and associated dynamics is potentially very large, and parallel approaches that consider broad ensembles of networks may advance our understanding of general design principles in ways that the serial strategies may have difficulty revealing. Therefore, we have chosen to explore general design principles by using a global strategy. We expect that exploration of an entire ensemble of networks and associated dynamics will reveal statistical signatures connecting network architectures to categories of dynamical phenotypes. In particular, we analyze the relationship between the space of topology and the space of dynamics by employing an analogy to the protein ''designability principle,'' which states that compact protein structures that can be encoded by a wide array of ...

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