Allosteric conformational ensembles have unlimited capacity for integrating information

Abstract

Integration of binding information by macromolecular entities is fundamental to cellular functionality. Recent work has shown that such integration cannot be explained by pairwise cooperativities, in which binding is modulated by binding at another site. Higher-order cooperativities (HOCs), in which binding is collectively modulated by multiple other binding events, appear to be necessary but an appropriate mechanism has been lacking. We show here that HOCs arise through allostery, in which effective cooperativity emerges indirectly from an ensemble of dynamically interchanging conformations. Conformational ensembles play important roles in many cellular processes but their integrative capabilities remain poorly understood. We show that sufficiently complex ensembles can implement any form of information integration achievable without energy expenditure, including all patterns of HOCs. Our results provide a rigorous biophysical foundation for analysing the integration of binding information through allostery. We discuss the implications for eukaryotic gene regulation, where complex conformational dynamics accompanies widespread information integration.

The linear framework: using graph theory to reveal the algebra and thermodynamics of biomolecular systems

“…Such outputs are often measures of the overall state of the system that are appropriate for the specific biological context, as in the treatment of figure 3b in §4. Examples include receptors or allosteric systems responding to ligands, where the output could be the average number of bound sites [19],…”

“…Here, the quantity Q is chosen arbitrarily to ensure the dimension of the label is (time) −1 but it plays no essential role, as we will see. It is shown in [19] that, with the labelling given by equation (5.2), C(G) satisfies the cycle condition, even when G does not, and, furthermore, that the following coarse-graining equation is satisfied: It is important to note that the prescription above is not a coarse graining of the dynamics. There is no reason to expect that C(G) will approximate the dynamics of G, only that it reaches the expected steady state under the coarse graining.…”

“…Figure 3 a shows the structure that we denote scriptC2+1, reflecting two ligands, one of which binds at 2 sites and the other at 1 site. Hypercube graphs can be used to model a receptor [68], an allosteric system [19] or a gene-regulation system [14]. Such graphs enable higher-order cooperativities (HOCs) to be defined at thermodynamic equilibrium, in which binding of a ligand at one site can be modulated by the ligand binding status of multiple other sites [7,14,19].…”

“…Here, the system is represented by a linear framework graph, G ; the input is the concentration, x , of some interacting ligand; and the output is any non-negative linear combination of steady-state probabilities,f false(xfalse)=∑1≤i≤Nλiui∗false(Gfalse),1emλi≥0.Such outputs are often measures of the overall state of the system that are appropriate for the specific biological context, as in the treatment of figure 3 b in §4. Examples include receptors or allosteric systems responding to ligands, where the output could be the average number of bound sites [19], and gene-regulation systems responding to transcription factors, where the output could be the probability of RNA Polymerase being bound to the gene promoter. The latter kind of input–output response has been widely used to study gene regulation [7], where it represents Mark Ptashne’s concept of regulated recruitment [74].…”

“…Finally, C ( G ) has labels given byℓfalse(w→Cfalse(Gfalse)zfalse)=Q(∑ j∈Gzρj(G)).Here, the quantity Q is chosen arbitrarily to ensure the dimension of the label is (time) −1 but it plays no essential role, as we will see. It is shown in [19] that, with the labelling given by equation (5.2), C ( G ) satisfies the cycle condition, even when G does not, and, furthermore, that the following coarse-graining equation is satisfied:uw∗false(Cfalse(Gfalse)false)=∑i∈Gwui∗false(Gfalse).In other words, the steady-state probability of being at w in C ( G ) is the same as the steady-state probability of being at any of the vertices of G w in G . This is exactly what we would expect from a coarse graining.…”