Modelling in molecular biology: describing transcription regulatory networks at different scales

Abstract

Approaches to describe gene regulation networks can be categorized by increasing detail, as network parts lists, network topology models, network control logic models or dynamic models. We discuss the current state of the art for each of these approaches. We study the relationship between different topology models, and give examples how they can be used to infer functional annotations for genes of unknown function. We introduce a new simple way of describing dynamic models called finite state linear model (FSLM). We discuss the gap between the parts list and topology models on one hand, and network logic and dynamic models, on the other hand. The first two classes of models have reached a genome-wide scale, while for the other model classes high-throughput technologies are yet to make a major impact.

Figure 1

(a) The building blocks of the finite state linear model: binding sites are represented by triangles, control functions by boxes and substance generators by diamonds. Dotted lines represent cases where the discrete output of one element is the input for another element. (b, c) Switching behaviour of the binding sites. The curve (b) is typical for processes with hysteresis characteristics of a system that does not instantly follow the forces applied to it, but reacts slowly, or does not return completely to its original state: that is, systems whose states depend on their immediate history. The threshold for switching the states of the binding sites in FSLM is state-dependent and results in a similar curve (c). [c] concentration of substance binding to binding site j; asso_j, disso_j, association and dissociation constants for binding site j; u, binding site not occupied; o, binding site occupied.

Figure 2

Example for the dynamics of a simple network: (a) in this negative feedback loop the substance generator produces a substance which acts as a repressor of its own control function. (b) Environment change graph recording the changes in repressor concentration during time. From the initial concentration the repressor accumulates with rate r⁺ until the association constant of the binding site b_rep is reached at time t₁. Then the substance generator is switched off and the repressor degrades with rate r⁻ until the dissociation constant is reached at time t_2. The substance generator then produces the repressor until the association constant is reached again (¬ means Boolean ‘not’).

Figure 3

A network consisting of two genes and four binding sites. (a) The control functions of both genes have two inputs each. One input is from a binding site for its own substance, thus each gene is autoregulated by a negative feedback loop. Gene 1 has an additional negative feedback on gene 2, while gene 2 has an additional positive feedback on gene 1. (b) Result of the simulation of this network in FSLM. a1 association constant of binding site 1, d1 is the corresponding dissociation constant; a2, d2, a3, d3, a4, d4 correspondingly; ¬ Boolean ‘not’, & Boolean ‘and’.

Figure 4

Description of phage λ using the elements of FSLM. Phage λ is a bacteriovirus that can infect Escherichia coli cells (Ptashne 1992). Depending on the growth conditions it either integrates into the host genome and stays dormant (lysogenic), or causes production of new phage particles and lysis of the host cell, to allow infecting neighbouring cells. The decision for one or the other alternative (lysis versus lysogeny) is made by the so-called lambda switch, which is based on competitive binding of two transcription factors to overlapping regions in the genome of phage λ. If the repressor is bound, the phage stays dormant, if the repressor is degraded and the activator can bind, new virus particles are being made. In the FSLM model for phage λ the substance generators highlighted in grey produce substances, which bind to binding sites on the left (the connections have been omitted to improve the readability of the figure). The promoters P_L1, P_L2, P_R1 and P_R2 are used to model the behaviour of the λ terminator sites t_L1, t_L2, t_R1 and t_R2. The substance generators connected to them are only active if n is bound to the respective binding sites. The substance ‘Struc’ represents the structural proteins of the phage particles. The shaded grey boxes indicate the number of different states that the corresponding control functions can have. A simulation of phage λ using this model leads to lysogenic behaviour or lytic behaviour. In the lysogenic mode the initially active genes are inactivated, and the substance concentrations decrease rapidly, only the repressor cI is produced. The fluctuations of the cI concentration are due to the negative feedback loop involving the binding site O_R3. In the lytic mode, cI and cII are not produced, but the other substance generators are active. The concentrations of int, N and Q increase infinitely because of the lack of a negative feedback control. The inset describes the effect of the stress response of the host cell using elements not yet implemented in the FSLM simulator. For a more detailed description of the model see Brazma & Schlitt (2003). Summary of λ gene functions: cI, λ repressor; cII, cIII, establishment of lysogeny; N, Q, anti-terminators for early and delayed early genes; O, P, origin recognition in DNA replication; int, integration and excision of phage DNA; xis, excision of phage DNA; R, S, host lysis; O_R, operator sites; P, promoters; T, terminators (see Ptashne 1992).

Figure 5

Log–log plot of the node connectivity in different topological networks. The genes with the highest connectivity are ABF1 in the ChIP-network, SWI5 in the in-silico-network, and TUP1 in the mutant network.

Figure 6

Intersection of the in-silico network with the mutant network and the ChIP network. Only 34 connections (red) can be found in all three of them. In addition this figure shows all connections between SWI4, SWI6 and MBP1 present in two of the networks (green). Box-shaped nodes indicate all genes with unknown function. SWI4 interacts with either SWI6 to form the SBF complex or with MBP1 to form the MBF complex (Ho et al. 1997). Genes connected to SWI4 and SWI6 (highlighted green) are likely to interact with SBF, genes connected to SWI4 and MBP1 (highlighted in blue) are likely to interact with MBF. Some genes might interact with both MBF and SBF (highlighted in yellow). Genes connected to MBP1 and SWI6 are highlighted in red.

Figure 7

Illustration of the target set comparison. (a) In the ChIP network transcription factors are connected to their target genes (regulation set); in the mutant network the deleted genes are linked to all genes with differential expression in this particular mutant background (effectual set). (b) Some transcription factors are present in both networks (ChIP and mutant network); we can, therefore, compare the genomic localization (regulation set) with the expression changes in the mutant cell (effectual set).

Figure 8

The Venn diagrams illustrate the overlap between the in-silico, the mutant and the ChIP network. (a) Number of source genes shared by several networks, in brackets number of source genes with significantly similar target sets in the different networks (^*SWI5, YAP1, MBP1, ARG80, ^**GCN4, STE12, ^***ABF1, BAS1, GAL4, HAP4, LEU3, MBP1, MCM1, RAP1, REB1, SWI6, YAP1, ZAP1). (b) Number of connections shared by the networks.

Figure 9

(a) The deletion of transcription factor X may affect gene Z, because X controls the expression of Z (direct effect). It is also possible that the deletion of transcription factor X affects gene Z indirectly, via a direct effect on transcription factor Y. (b) The single input motif as defined by Shen-Orr et al. for a Escherichia coli network and Lee et al. for the ChIP network. (c–f) All cases where a single connection in the mutant network corresponds to two connections in the ChIP network. (c) and (d) resemble the single input motif, with an additional top layer of regulation, whereas (e) and (f) correspond to more complex combinations of network motifs. dashed green, connections in the mutant network; solid red, connections in the ChIP network.

Figure 10

Example for network logics: genes A, B and C control the activity of gene D; D is active if A and B are bound, but not C; (b) shows the FSLM representation for such a promoter.

Figure 11

Example for a small Boolean network consisting of three genes X, Y and Z. There are different ways for representing the network: (a) as a graph, (b) Boolean rules for state transitions, (c) a complete table of all possible states before and after transition, or (d) as a graph representing the state transitions.