On schemes of combinatorial transcription logic

Abstract

Cells receive a wide variety of cellular and environmental signals, which are often processed combinatorially to generate specific genetic responses. Here we explore theoretically the potentials and limitations of combinatorial signal integration at the level of cis-regulatory transcription control. Our analysis suggests that many complex transcription-control functions of the type encountered in higher eukaryotes are already implementable within the much simpler bacterial transcription system. Using a quantitative model of bacterial transcription and invoking only specific protein-DNA interaction and weak glue-like interaction between regulatory proteins, we show explicit schemes to implement regulatory logic functions of increasing complexity by appropriately selecting the strengths and arranging the relative positions of the relevant protein-binding DNA sequences in the cis-regulatory region. The architectures that emerge are naturally modular and evolvable. Our results suggest that the transcription regulatory apparatus is a "programmable" computing machine, belonging formally to the class of Boltzmann machines. Crucial to our results is the ability to regulate gene expression at a distance. In bacteria, this can be achieved for isolated genes via DNA looping controlled by the dimerization of DNA-bound proteins. However, if adopted extensively in the genome, long-distance interaction can cause unintentional intergenic cross talk, a detrimental side effect difficult to overcome by the known bacterial transcription-regulation systems. This may be a key factor limiting the genome-wide adoption of complex transcription control in bacteria. Implications of our findings for combinatorial transcription control in eukaryotes are discussed.

Fig 1.

(a) Some possible gene responses (ON or OFF) according to the specific activation patterns of two TFs, A and B, as denoted by their cellular concentrations (high or low). The logical equivalents of these gene responses are listed above each column. (b) The cis-regulatory implementation for the response of gene g1, as adapted from the E. coli lac operon. To achieve the desired effects, the operator sites need to be strong (filled boxes) and the promoter needs to be weak (open box). In this and subsequent cis-regulatory constructs, we use the offset, overlapping boxes to indicate mutual repression and the dashed lines to indicate cooperative interaction. The logic function that this system implements is indicated above the construct, with the overline denoting the “inverse” of A, or NOT A.

Fig 2.

Cis-regulatory constructs and response characteristics of the AND (a), OR (b), and NAND (c) gates. Filled, hatched, and open boxes denote strong, moderate, and weak binding sites, respectively. Dashed lines indicate cooperative interaction with ω_i,j = 20, and overlapping boxes indicate repulsive interaction with ω_i,j = 0. Plotted to the right of each construct is the fold change in RNAP-binding probability, ΔP ≡ P([A], [B])/P_min for typical cellular TF concentrations [A] and [B] (in nM). See Supporting Text for the actual forms of P([A], [B]) and the strengths of the binding sites. Qualitative features of these plots are insensitive to the precise values of the parameters used.

Fig 3.

Various strategies of implementing the XOR function. (a) A gene cascade, where the intermediate gene products G3 and G4 themselves are TFs that can interact cooperatively. Alternative cis-regulatory constructs using a single promoter (b) or two promoters (c) are shown. Notations are the same as those used for Fig. 2, whereas the squiggles in c indicate that the two promoters can be at variable distances from one another.

Fig 4.

Cis-regulatory constructs for possible implementations of the EQ gate using a single promoter (a) or two promoters (b). Notations are the same as those used for Figs. 2 and 3. Both constructs illustrate the problem of promoter overcrowding, a situation that occurs when multiple repressive conditions are needed.

Fig 5.

(a) Illustration of distal regulation through “DNA looping,” mediated by a heterodimer formed between two subunits, R and S, each recognizing a distinct DNA-binding site. (b) The schematic construct and response characteristics of a regulatory region implementing the EQ gate (g6 of Fig. 1a): The operators labeled R1, R2, and S are the targets of the subunits R and S as shown in a. The solid lines indicate the relatively strong attraction between the subunits of the heterodimer. (c) An alternative implementation of the EQ gate using the distal activation mechanism.

Fig 6.

(a) Modular construct of a regulatory function involving three controlling TFs using the distal activation scheme. The operators labeled R1, R2, R3, and S are the targets of the recruited subunits R and the activating subunit S. Each module is bracketed with the corresponding logical syntax written above, and the squiggles indicate that these modules can be at variable distances from one another. (b) The same regulatory function using the distal repression scheme.

Fig 7.

The construct of Fig. 6b maps directly on a well studied model of neural network known as the “Boltzmann machine” (see Supporting Text). In this mapping, the binding sites are the neurons, the TF concentrations are the inputs, and the promoter is the output neuron. Cooperative/repressive molecular interactions between the TFs play the role of synapses and are denoted with arrows and bars, respectively. Note that the sites R1, R2, R3, and S are not connected to any inputs and are examples of hidden units.