[Paper Review] Allosteric interactions in a birod model of DNA

Jaspreet Singh, Prashant K. Purohit|arXiv (Cornell University)|Mar 12, 2018

Bacteriophages and microbial interactions27 references3 citations

TL;DR

This paper proposes a birod model of DNA as an elastic double-helix with inextensible backbones and an elastic web representing base-pair interactions to quantify allosteric protein-protein interactions. By modeling protein binding as localized defects, it derives an interaction energy that decays exponentially with distance while oscillating with a 10–11 bp periodicity, matching experimental data and linking the decay length to DNA mechanical properties and GC content.

ABSTRACT

Allosteric interactions between molecules bound to DNA at distant locations have been known for a long time. The phenomenon has been studied via experiments and numerical simulations, but a comprehensive understanding grounded in a theory of DNA elasticity remains a challenge. Here we quantify allosteric interactions between two entities bound to DNA by using the theory of birods. We recognize that molecules bound to DNA cause local deformations that can be captured in a birod model which consists of two elastic strands interacting via an elastic web representing the base-pairs. We show that the displacement field caused by bound entities decays exponentially with distance from the binding site. We compute the interaction energy between two proteins on DNA as a function of distance between them and find that it decays exponentially while oscillating with the periodicity of the double-helix, in excellent agreement with experiments. The decay length of the interaction energy can be determined in terms of the mechanical properties of the strands and the webbing in our birod model, and it varies with the GC content of the DNA. Our model provides a framework for viewing allosteric interactions in DNA within the ambit of configurational forces of continuum elasticity.

Motivation & Objective

• To provide a theoretical framework for allosteric interactions between proteins bound to distant sites on DNA using continuum elasticity.
• To quantify how the interaction energy between two bound proteins depends on their separation distance and DNA mechanical properties.
• To explain the experimentally observed oscillatory decay of interaction energy with distance, independent of electrostatics or DNA looping.
• To investigate the sequence dependence of allosteric interactions, particularly the role of GC content in modulating interaction range.
• To establish a connection between configurational forces in elastic solids and protein-DNA interactions via a birod model of DNA.

Proposed method

• Model DNA as a birod with two inextensible, unshearable backbones connected by an elastic web representing base-pair interactions.
• Use a displacement field ansatz (Eq. 19) to describe micro-displacements and micro-rotations of the strands and base-pairs.
• Solve the governing equations for the birod system under boundary conditions specifying curvature and radius of the helix.
• Compute the interaction energy between two bound proteins as a function of separation distance by analyzing the overlap of their induced elastic deformation fields.
• Relate the decay length of the interaction energy to the elastic constants of the backbones and the web, including a parameter χ to account for AT vs. GC base-pair stiffness differences.
• Use numerical solutions and eigenvalue analysis to extract the decay length and validate the model against experimental data from Kim et al. [4].

Experimental results

Research questions

• RQ1 How does the interaction energy between two proteins bound to distant sites on DNA depend on their separation distance?
• RQ2 What is the physical origin of the 10–11 bp periodic oscillation in the interaction energy observed experimentally?
• RQ3 How does the GC content of DNA influence the range and strength of allosteric interactions?
• RQ4 Can the exponential decay of interaction energy be derived from a continuum elastic model of DNA with localized deformations?
• RQ5 To what extent can configurational forces in elastic solids explain protein-DNA allosteric effects without invoking DNA looping or electrostatics?

Key findings

• The interaction energy between two proteins on DNA decays exponentially with distance, with a decay length of approximately 9 base pairs for χ = 1 (representing GC-rich DNA).
• The interaction energy oscillates with a period of 10–11 base pairs, matching experimental observations and arising from the helical periodicity of DNA.
• The decay length increases with decreasing elastic constants of the base-pair web, implying that AT-rich DNA sequences exhibit longer-ranged allosteric interactions than GC-rich sequences.
• The model predicts a power-law dependence of decay length on the stiffness parameter χ as $ l_d ightarrow ext{const} imes ho^{-2/3} $, consistent with experimental and simulation trends.
• The interaction energy is independent of ionic strength, supporting the conclusion that mechanical deformation—not electrostatics—drives the observed allosteric effects.
• The model successfully reproduces the experimentally measured off-rate dependence on separation distance, validating its predictive power for protein-DNA interaction energetics.