Emerging Methods and Applications to Decrypt Allostery in Proteins and Nucleic Acids

Abstract

Many large protein-nucleic acid complexes exhibit allosteric regulation. In these systems, the propagation of the allosteric signaling is strongly coupled to conformational dynamics and catalytic function, challenging state-of-the-art analytical methods. Here, we review established and innovative approaches used to elucidate allosteric mechanisms in these complexes. Specifically, we report network models derived from graph theory and centrality analyses in combination with molecular dynamics (MD) simulations, introducing novel schemes that implement the synergistic use of graph theory with enhanced simulations methods and ab-initio MD. Accelerated MD simulations are used to construct "enhanced network models", describing the allosteric response over long timescales and capturing the relation between allostery and conformational changes. "Ab-initio network models" combine graph theory with ab-initio MD and quantum mechanics/molecular mechanics (QM/MM) simulations to describe the allosteric regulation of catalysis by following the step-by-step dynamics of biochemical reactions. This approach characterizes how the allosteric regulation changes from reactants to products and how it affects the transition state, revealing a tense-to-relaxed allosteric regulation along the chemical step. Allosteric models and applications are showcased for three paradigmatic examples of allostery in protein-nucleic acid complexes: (i) the nucleosome core particle, (ii) the CRISPR-Cas9 genome editing system and (iii) the spliceosome. These methods and applications create innovative protocols to determine allosteric mechanisms in protein-nucleic acid complexes that show tremendous promise for medicine and bioengineering.

Keywords: CRISPR-Cas9; graph theory; molecular dynamics; nucleosome core particle; spliceosome.

Figure 1.. Overview of three allosteric protein and nucleic acid complexes.

(a) The nucleosome core particle, composed of chromosomal DNA wrapped around an octamer of four core histone proteins (H3, H4, H2A and H2B, PDB: 1AOI).[14] (b) The CRISPR-Cas9 gene editing system (PDB: 5F9R),[46] composed of the Cas9 protein bound to RNA (orange) and DNA (purple). The HNH and RuvC catalytic domains are shown in green and blue, respectively. (c) The pre-catalytic spliceosome, composed of several proteins and five small nuclear ribonucleoprotein particles (snRNPs: U1, U2, U4, U5, and U6) (B complex, PDB ID: 5NRL).[47]

Figure 2.. Violin and domino models for biomolecular allostery.

[58] (a) In a violin model, the binding of an allosteric effector triggers a pattern of vibrations, similar to the player’s pitch on a string, leading to the activation of the system at distal sites. In CRISPR-Cas9, the binding of the PAM recognition sequence (i.e., the allosteric effector) leads to a change in the conformational dynamics, as indicated by a shift in the free energy basin and in the correlated motions (bottom panel).[10] (b) In a domino model, the allosteric effector triggers a sequential set of local events propagating via a well-defined pathway, similar to the effect of a hand touch to a domino. In the nucleosome core particle, the biding of RAPTA-T induces a local kink, that is dynamically coupled to a path of adjacent α-helices (shown using arrows), allowing the transfer of information to the auranofin site.[49]

Figure 3.. Correlation analysis.

(a) Coupled motions in the CRISPR-Cas12a system, suggesting an “open-to-close” conformational transition for nucleic acid binding.[45] Cross-Correlation (CC, upper triangles) and Generalized Correlations (GC, lower triangles) matrices, computed for Cas12a in the RNA-bound (left) and DNA-bound (right) states (color-coded according to the scales on the right). DNA binding induces a sensible increase in GCs. Adapted with permission from Saha et al. (2020).[65] Copyright 2020 American Chemical Society. https://pubs.acs.org/doi/full/10.1021/acs.jcim.0c00929. Further permissions related to the material excerpted should be directed to the American Chemical Society. (b) Per-domain CC histogram of the spliceosome dynamics.[46] The inter-domain cross-correlations reveal domains moving in lockstep (blue) and through opposite motions (red). Adapted with permission from Casalino et al. (2018). [65] Copyright 2018 National Academy of Sciences.

Figure 4.

Network models for biomolecular allostery, shown for the CRISPR-Cas9 system. The biomolecule (a) can be described as a network of residue nodes and edges whose length is weighted by the strength of the residues’ correlations (b), and as a network of communities connected by bonds measuring their intercommunication strength (c).[9] The network model builds on correlation analysis (d), whereby the Generalized Correlations (GC = $r_{MI}\left[x_i,x_j\right]$) are used to weight the edges connecting nodes ($w_{ij}=-logGC$), such placing strongly correlated nodes close to each other. (e) From the network model, the shortest pathways crossing the edges between distal sites can be computed as efficient communication routes among allosteric sites. This is shown for the L1/L2 loops in CRISPR-Cas9, connecting the HNH and RuvC domains as shortest pathways.[10]

Figure 5.

Circular network of the allosteric communication, reporting the mutation-induced Edge Betweenness change (ΔEB), a measure of communication gain or loss between couples of communities upon mutation.[44] The communities are displayed in a circle and are connected by links with thickness proportional to ΔEB. Communities connecting allosteric sites (A1–A3) display a loss of communication (negative ΔEB, red), while the non-allosteric sites (NA1–NA4) gain in communication (positive ΔEB, blue). Circular network adapted from Nierzwicki et al. (2021),[44] published in eLife under a Creative Commons Attribution license. https://elifesciences.org/articles/73601.

Figure 6.. Shortest paths connecting allosteric sites.

(a) Dijkstra algorithm for shortest path calculation. The algorithm defines a starting and a destination point (i.e., nodes A and C) and optimizes iteratively a path from the former to the latter. In each iteration, the closest unvisited node is designated as the current node, updating the remaining unvisited nodes until the destination is reached. For biomolecular allostery, the algorithm uses the correlation coefficients as a metrics to identify the closest nodes (i.e., $w_{ij}=-logGC$), maximizing the correlation between starting and destination nodes. (b) Allosteric pathway within the HNH domain of CRISPR-Cas9 connecting the DNA recognition region (REC2) to the RuvC cleavage site. The signaling route identified through the Dijkstra algorithm (pink line) overlaps with slow dynamical residues found through solution NMR (purple spheres).[23]

Figure 7.. Enhanced network models.

(a) The conformational landscape obtained through enhanced sampling molecular dynamics (top) is used as a basis to construct the allosteric network (bottom). Enhanced network models are constructed by applying graph theory on the reweighted conformational landscape, which reports the canonical ensemble. Inspired by Wereszczynski & McCammon (2012) Proc. Natl. Acad. Sci. USA 109, 7759–7764. [94] (b) Gaussian accelerated MD (GaMD) method.[86] Quadratic functions are used to modify the original potential energy of the system to overcome energetic barriers. The extent of acceleration is controlled by the harmonic constant ${\mathrm{k}}_0$, varying from 0 to 1. The greater the value of ${\mathrm{k}}_0$, the greater the acceleration and the easier the system overcomes the barrier between states, enhancing the conformational ensemble.

Figure 8.. Ab-initio network models.

(a) Catalytic mechanism of DNA cleavage in the RuvC active site of CRISPR-Cas9, investigated through QM/MM ab-initio simulations.[95,96] The reaction evolves from the Reactants (R) to the Transition State (TS^‡) and Product though an associative S_N2 mechanism activated by H983, and with an activation barrier of ~16.5 kcal mol⁻¹ (free energy profile at the bottom left). Analysis of the generalized correlations (GC, bottom right) reveals highly coupled motions in the R state, which are progressively reduced in the TS^‡ and in the P states. This reveals a tense-to-relaxed model for the allosteric regulation of the chemical step (details in the main text). (b) Allosteric pathways connecting the DNA recognition region (REC) to the RuvC catalytic core in the R (green) and P (magenta) states. Adapted with permission from Casalino et al. (2020).[95] Copyright 2020 American Chemical Society. https://pubs.acs.org/doi/10.1021/acscatal.0c03566. Further permissions related to the material excerpted should be directed to the American Chemical Society.