A system for generating transcription regulatory networks with combinatorial control of transcription

Abstract

Summary: We have developed a new software system, REgulatory Network generator with COmbinatorial control (RENCO), for automatic generation of differential equations describing pre-transcriptional combinatorics in artificial regulatory networks. RENCO has the following benefits: (a) it explicitly models protein–protein interactions among transcription factors, (b) it captures combinatorial control of transcription factors on target genes and (c) it produces output in Systems Biology Markup Language (SBML) format, which allows these equations to be directly imported into existing simulators. Explicit modeling of the protein interactions allows RENCO to incorporate greater mechanistic detail of the transcription machinery compared to existing models and can provide a better assessment of algorithms for regulatory network inference.

Availability: RENCO is a C++ command line program, available at http://sourceforge.net/projects/renco/

Contact: terran@cs.unm.edu

Supplementary information: Supplementary data are available at Bioinformatics online.

1 INTRODUCTION

With the increasing availability of genome-scale data, a plethora of algorithms are being developed to infer regulatory networks. Examples of such algorithms include Bayesian networks, ARACNE (Bansal et al., 2007). Because of the absence of “ground truth” of regulatory network topology, these algorithms are evaluated on artificial networks generated via network simulators (Kurata et al., 2003; Margolin et al., 2005; Mendes et al., 2003; Schilstra and Bolouri, 2002).

Since gene regulation is a dynamic process, existing network simulations employ systems of ordinary differential equations (ODEs) that describe the kinetics of mRNA and protein concentrations as a function of time. Some approaches construct highly detailed models, but require large amounts of user-specified information (Kurata et al., 2003; Schilstra and Bolouri, 2002). Other approaches generate large networks but use simpler models by making the mRNA concentration of target genes dependent upon mRNA concentration, rather than on protein concentration of transcription factors (Mendes et al., 2003). In real biological systems, protein expression does not correlate with gene expression, especially at steady state, due to different translation and degradation rates (Belle et al., 2006). These approaches also do not model protein interactions edges and, therefore, combinatorics resulting from these interactions.

We describe a regulatory network generator, RENCO, that models genes and proteins as separate entities, incorporates protein–protein interations among the transcription factor proteins, and generates ODEs that explicitly capture the combinatorial control of transcription factors. RENCO accepts either pre-specified network topologies or gene counts, in which case it generates a network topology. The network topology is used to generate ODEs that capture combinatorial control among transcription factor proteins. The output from RENCO is in SBML format, compatible with existing simulators such as Copasi (Hoops et al., 2006) and RANGE (Long and Roth, 2007). Time-series and steady-state expression data produced from the ODEs from our generator can be leveraged for comparative analysis of different network inference algorithms.

2 TRANSCRIPTIONAL REGULATORY NETWORK GENERATOR

RENCO works in two steps: (a) generate/read the network topology and (b) generate the ODEs specifying the transcription kinetics (see RENCO manual for details). For (a) proteins are connected to each other via a scale-free network (Albert and Barabasi, 2000), and to genes via a network with exponential degree distribution (Maslov and Sneppen, 2005).

2.1 Modeling combinatorial control of gene regulation

We model combinatorial control by first identifying the set of cliques, , up to a maximum of size t in the protein interaction network. Each clique represents a protein complex that must function together to produce the desired target regulation. A target gene, g_i is regulated by k randomly selected such cliques, where k is the indegree of the gene. These k cliques regulate g_i by binding in different combinations, thus exercising combinatorial gene regulation. We refer to the set of cliques in a combination as a transcription factor complex (TFC). At any time there can be several such TFCs regulating g_i. The mRNA concentration of a target gene is, therefore, a function of three types of regulation: within-clique, within-complex and across-complex regulation. Within-clique regulation captures the contribution of one clique on a target gene. The within-complex regulation captures the combined contribution of all cliques in one TFC. Finally, the across-complex regulation specifies the combined contribution of different TFCs.

We now introduce the notation for ODEs generated by RENCO. M_i (t) and P_i(t) denote the mRNA and protein concentrations, respectively, of gene g_i, at time t. V_i^M and v_i^M denote the rate constants of mRNA synthesis and degradation of and denote the rate constants of protein synthesis and degradation. C_ij and T_ij denote a protein clique and a TFC, respectively, associated with g_i. Q_i denotes the set of TFCs associated with g_i. X_ij, Y_ij and S_i specify the within-clique, within-complex and across-complex regulation on g_i.

Based on existing work (Mendes et al., 2003; Schilstra and Bolouri, 2002), the rate of change of mRNA concentration is the difference of synthesis and degradation of . Similarly for protein concentration, .

The across-complex regulation, S_i is a weighted sum of contributions from |Q_i| TFCs: , where w_q denotes the TFC weight. The sum models ‘or’ behavior of the different TFCs because all TFCs need not be active simultaneously. The within-complex regulation, Y_ij is a product of within-clique actions in the TFC T_ij, . The product models ‘and’ behavior of a single TFC because all proteins within a TFC must be active at the same time. Finally, the cliques per gene C_ij are randomly assigned activating or repressing roles on g_i. If C_ij is activating,

otherwise,

Ka_ip and Ki_ip are equilibrium dissociation constants of the pth activator or repressor of g_i. All degradation, synthesis and dissociation constants are initialized uniformly at random from [0.01,V_max], where V_max is user specified.

3 EXAMPLE NETWORK

We used RENCO to analyze : (a) mRNA and protein steady-state measurements and (b) combinatorial gene regulation, in a small example network (Supplementary Material has details).

3.1 Importance of modeling protein expression

The example network has five genes and five proteins (Fig. 1a). The gene G₄ is regulated via different combinations of the cliques {P₂},{P₀,P₁}. We find that the wild-type time courses of individual mRNA expressions are correlated with corresponding proteins (Fig. 1b and c). But because different genes and proteins have different degradation and synthesis rate constants, the mRNA population as a whole does not correlate with the protein population (Spearman's; correlation =0.3). Because of the dissimilarity in the steady-state mRNA and protein expression populations, genes appearing to be differentially expressed at the mRNA level may not be differentially expressed at the protein level. This highlights the importance of modeling mRNA and protein expression as separate entities in the network.

Fig. 1.

(a) Example network. Dashed edges indicate regulatory actions. Wild-type gene (b) and protein (c) time courses.

3.2 Combinatorics of gene regulation

We analyzed combinatorial control in our network by generating the G₄ time course under different knockout combinations of the G₄ activators, P₀,P₁ and P₂ (Fig. 2). Because all the regulators are activating, G₄ is downregulated here compared to wild-type. We note that each knock out combination yields different time courses. In particular, knocking out either G₀ or G₁ in combination with G₂ is sufficient to drive the G₄ expression to 0. This phenomenon is because of the clique, P₀,P₁. This illustrates a possible combinatorial regulation process to produce a range of expression dynamics using a few transcription factors.

Fig. 2.

G₄ time course under knock out combinations of G₀, G₁ and G₂.

4 CONCLUSION

We have described RENCO, a generator for artificial regulatory networks and their ODEs. RENCO models the transcriptional machinery more faithfully by explicitly capturing protein interactions and provides a good testbed for network structure inference algorithms.