pubmed.ncbi.nlm.nih.gov

AIM for Allostery: Using the Ising Model to Understand Information Processing and Transmission in Allosteric Biomolecular Systems - PubMed

. 2015 May;17(5):2895-2918.

doi: 10.3390/e17052895. Epub 2015 May 7.

Affiliations

AIM for Allostery: Using the Ising Model to Understand Information Processing and Transmission in Allosteric Biomolecular Systems

Michael V LeVine et al. Entropy (Basel). 2015 May.

Abstract

In performing their biological functions, molecular machines must process and transmit information with high fidelity. Information transmission requires dynamic coupling between the conformations of discrete structural components within the protein positioned far from one another on the molecular scale. This type of biomolecular "action at a distance" is termed allostery. Although allostery is ubiquitous in biological regulation and signal transduction, its treatment in theoretical models has mostly eschewed quantitative descriptions involving the system's underlying structural components and their interactions. Here, we show how Ising models can be used to formulate an approach to allostery in a structural context of interactions between the constitutive components by building simple allosteric constructs we termed Allosteric Ising Models (AIMs). We introduce the use of AIMs in analytical and numerical calculations that relate thermodynamic descriptions of allostery to the structural context, and then show that many fundamental properties of allostery, such as the multiplicative property of parallel allosteric channels, are revealed from the analysis of such models. The power of exploring mechanistic structural models of allosteric function in more complex systems by using AIMs is demonstrated by building a model of allosteric signaling for an experimentally well-characterized asymmetric homodimer of the dopamine D2 receptor.

Keywords: G protein coupled receptors (GPCRs); Ising model; allostery; biophysics; dopamine D2 receptor; functional selectivity; information theory; signal transduction; statistical mechanics.

PubMed Disclaimer

Conflict of interest statement

Conflicts of Interest: The authors declare no conflict of interest.

Figures

Figure 1
Figure 1

Thermodynamic cycle of a two-state ligand/receptor activation reaction. The receptor (blue circle) has an on and an off state (square and triangle indentations, respectively), both of which can bind a ligand (red triangle). The kinetic parameters are shown for the two equilibria of interest.

Figure 2
Figure 2

Schematic representations of Allosteric Ising models (AIMs). In the four AIMs analyzed here the ligand, L, is represented as a red triangle, and the protein is the blue circle subdivided into various constituent structural components. Lines separating ligand from protein or protein structural components from each other are labeled with the appropriate interaction energy term (as used in the text). Allosteric effective interactions are represented with green dotted lines. (A): The simple two-component ligand/receptor system. (B): A three-component ligand/receptor system with two allosteric sites, A1 and A2. (C): A three-component ligand/receptor system with one channel, C, coupling the ligand and the allosteric site A. (D): A four-component ligand/receptor system with two channels, C1 and C2, coupling the ligand and the allosteric site A.

Figure 3
Figure 3

The effective interaction energy through serial channels. Effective interaction energies of the first and last components of one-dimensional Ising chains are plotted as a function of chain length for conditional allosteric efficacy values of 10 (black), 100 (blue), 1000 (purple) 10,000 (red) and 100,000 (orange). The inset shows detail for short chain lengths. The effective interaction energy is seen to decay exponentially with channel length.

Figure 4
Figure 4

Using the Ising model to estimate effective interaction energies in non-Ising three-component/two-state systems. The exact effective interaction energies of 100,000 three-component/two-state non-Ising systems are plotted against the effective interaction energy estimated using the equations derived for the three-component Ising model (see (42)). The systems are generated using energy terms sampled from a normal distribution of mean 0 and standard deviation of 1/β (A), 3/β (B), and 5/β (C) and the points are plotted with 10% opacity.

Figure 5
Figure 5

Calculated mutual information between the channel and allosteric sites sets a lower bound on the allosteric efficacy. The symmetric uncertainty between the two components is plotted against the absolute effective interaction energy for 100,000 two-component/two-state non-Ising models (A), and two-component Ising models (B). The systems are generated using energy terms sampled from a normal distribution of mean 0 and standard deviation of 1/β, and the points are plotted with 10% opacity.

Figure 6
Figure 6

Relation of effective interaction energies in non-Ising two-state systems with multiple independent channels to estimates from the corresponding Ising model. The exact effective interaction energies of 100,000 two-state non-Ising system is plotted against the effective interaction energy estimated using the equations derived for the n-channel Ising model (Equation (51)) for two (A), and three (B) independent channels. The systems are generated using energy terms sampled from a normal distribution of mean 0 and standard deviation of 1/β, and the points are plotted with 10% opacity.

Figure 7
Figure 7

The effective interaction energy of a two-channel AIM as a function of the interaction energy between the channels. (A): The two-channel system in which each channel contributes to positive allosteric modulation is shown for a ligand that interacts with one channel (blue) or both channels (black). (B): A two-channel system with one positive allosteric channel and one negative allosteric channel is shown for a ligand that interacts only with the positive channel (blue), only with the negative channel (red), or both channels (black). The effect of interactions between channels is seen to modify significantly the allosteric signal transduction.

Figure 8
Figure 8

Analysis of the AIM for a well-characterized asymmetric D2 homodimer of the dopamine D2 receptor (D2R). (A): The D2R monomer AIM. (B): The effective interaction energy calculated for the D2R monomer AIM is presented for ligands that are agonists, antagonists, and inverse agonists, and also for the mutation of either IL3 or the conserved binding motifs (CBMs). (C): A molecular model of the homodimer obtained as described in the text, is shown with each AIM domain labeled in white on the structural representation. Protomer A is in blue, protomer B is in orange, and the G protein is in red. (D): The effective interaction energy for the D2R homodimer AIM is presented for different combinations of the states of protomer A (indicated by A in the top row) and those of protomer B in the dimer (B, bottom row).

Similar articles

Cited by

References

    1. Shi Y. A Glimpse of Structural Biology through X-Ray Crystallography. Cell. 2014;4:995–1014. - PubMed
    1. Markwick PRL, Malliavin T, Nilges M. Structural biology by NMR: Structure, dynamics, and interactions. PLoS Comput Biol. 2008;4:e1000168. - PMC - PubMed
    1. Bai X, McMullan G, Scheres SH. How cryo-EM is revolutionizing structural biology. Trends Biochem Sci. 2015;40:49–57. - PubMed
    1. Ha T. Single-molecule fluorescence resonance energy transfer. Methods. 2001;25:78–86. - PubMed
    1. Sahu ID, McCarrick RM, Lorigan GA. Use of electron paramagnetic resonance to solve biochemical problems. Biochemistry. 2013;52:5967–5984. - PMC - PubMed

LinkOut - more resources