Mechanisms of DNA-Mediated Allostery

Midas Segers, Aderik Voorspoels, Takahiro Sakaue, and Enrico Carlon

Phys. Rev. Lett. 131, 238402 – Published 7 December 2023

Abstract

Proteins often regulate their activities via allostery—or action at a distance—in which the binding of a ligand at one binding site influences the affinity for another ligand at a distal site. Although less studied than in proteins, allosteric effects have been observed in experiments with DNA as well. In these experiments two or more proteins bind at distinct DNA sites and interact indirectly with each other, via a mechanism mediated by the linker DNA molecule. We develop a mechanical model of DNA/protein interactions which predicts three distinct mechanisms of allostery. Two of these involve an enthalpy-mediated allostery, while a third mechanism is entropy driven. We analyze experiments of DNA allostery and highlight the distinctive signatures allowing one to identify which of the proposed mechanisms best fits the data.

Received 23 May 2023
Accepted 7 November 2023

DOI:https://doi.org/10.1103/PhysRevLett.131.238402

Physics Subject Headings (PhySH)

Classical statistical mechanics DNA-protein interactions

DNA

Statistical Physics & ThermodynamicsPhysics of Living SystemsPolymers & Soft Matter

Authors & Affiliations

Midas Segers ¹, Aderik Voorspoels ¹, Takahiro Sakaue ², and Enrico Carlon ¹

¹Soft Matter and Biophysics, KU Leuven, Celestijnenlaan 200D, 3001 Leuven, Belgium
²Department of Physical Sciences, Aoyama Gakuin University, 5-10-1 Fuchinobe, Chuo-ku, Sagamihara, Kanagawa 252-5258, Japan

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Vol. 131, Iss. 23 — 8 December 2023

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Images

Figure 1
(a) DNA-mediated interaction for two bound proteins separated by a linker molecule of $m$ base pairs. (b) Model of DNA allostery. The DNA substrate (yellow) is described as a set of variables $X_{n} \equiv u_{n} + \bar{l}$ defined at each base-pair site, with $⟨ X_{n} ⟩ = \bar{l}$ the equilibrium value. These variables are characterized by a local stiffness ( $K_{0}$ ) and distal couplings ( $K_{1}, K_{2}, \dots$ ), with energy given by (2). Upon binding, the protein (orange blob) modifies the local mechanical properties of the DNA substrate. The distal couplings carry the signal to distinct sites. The schematic plot in (b) shows a protein interacting with a single DNA site. The more realistic case of proteins binding to several DNA sites is also considered.
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Figure 2
Plots of $Δ Δ F_{int}$ vs linker DNA length $m$ for the three different mechanisms of DNA-mediated allostery proposed: (a) enthalpic, (b) entropic, and (c) mixed. An angular frequency $ϕ = 2 π / 10.5$ , corresponding to the periodicity of the DNA double helix and $ξ_{E} = 15 bp$ were used. These parameters match those observed in experiments [see Fig. 3]. In the case (a) the interaction is stabilizing/destabilizing depending on the values of $m$ and the asymptotic oscillating behavior is universal, i.e., also valid for interactions involving $n_{a}$ , $n_{b}$ sites for protein a and b, respectively. In the cases (b) and (c) the interaction is always stabilizing and destabilizing, respectively. In (b) and (c) the asymptotic decay is nonuniversal, being dependent on the number of interacting sites $n_{a, b}$ per protein.
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Figure 3
(a) Symbols: experimental data of interaction free energies for BamHI-GRDBD [3]. Oscillating sign in $Δ Δ F_{int}$ indicates an enthalpic type of allostery. Dashed line: fit to the asymtptotic expression (9) ( $ϕ = 2 π / 10.5$ , $ξ_{E} = 15 bp$ ). (b) Symbols: experimental data for $Δ Δ F_{int}$ for the ComK system [4]. The negative sign indicates an allosteric interaction which is of predominant entropic. Dashed line: full numerical solution of $Δ Δ F_{int} (m)$ ( $ϕ = 2 π / 10.5$ , $ξ_{E} = 22 bp$ ) for a global allostery model with extended perturbations [17]. As $Δ Δ F_{int}$ does not seem to converge to zero for large $m$ , we have added an asymptotic nonzero offset (dotted line).
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Figure 4
(a) Schematic representation of the major groove width of DNA, for which the $Curves +$ [35] definition is used. (b) Normalized correlation function of the major groove width as obtained from all-atom simulations obtained using the $Curves +$ software [35]. (c) Plot of the momentum-space stiffness for the major groove width obtained from all-atom data. The inset coplots ${\tilde{K}}_{q}$ for the minimal model [Eq. (17)] for two sets of parameters. The solid line is a direct fit of the stiffness data. The dashed line uses $ϕ$ and $ξ_{E}$ from a fit of the experimental $Δ Δ F_{int}$ data. The error bars in (b) and (c) indicate the standard deviation calculated over 21 time windows of 10 ns.
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