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Local Softening as a Universal Feature of Conformational Transitions of Biological Macromolecules

  • Author(s): Qu, Hao
  • Advisor(s): ZOCCHI, GIOVANNI
  • et al.
Abstract

Conformational changes are essential to biological macromolecules because they are tightly coupled to function and dynamics of these macromolecules. In cells, under most occasions, the macromolecules are deformed rather than in free states as in solution, due to mechanical stresses exposed. It is therefore of great interest and importance to understand conformational changes associated with the macromolecules. More in details, the conformational changes of two types of macromolecules, DNA and protein, are studied in this dissertation.

In order to study bending elasticity of DNA, constructs of short (18 to 30 base pairs) double stranded (ds) DNA molecules which are self-constrained into a sharply bent conformation are built. We develop two thermodynamic methods to investigate the elastic energy of these stressed DNA molecules directly and at equilibrium, namely dimerization equilibrium and melting-curve analysis approaches.

Based on the dimerization equilibrium measurements on the elastic energy of stressed nicked DNA molecules by extracting the elastic energy from the equilibrium monomer and dimer concentrations and taking a small energy correction (electrostatic energy and entropic stretching energy) in the dimer formation, we identify a transition in the conformation ds DNA from smooth bending to sharp bending by developing a constant force kink at a finite critical torque τc ∼ 27 pN × nm. We derive an analytic function for the bending energy vs end-to-end distance, with only three effective materials parameters, bending modulus B, contour length 2L and the critical torque τc, valid in both smoothly bent and sharply bent regimes. The bending energy of a more generalized case, non-nicked DNA is measured through melting-curve analysis, by fitting the melting curves of DNA molecules in three different configurations (linear, circular nicked and circular non-nicked) with a modified zipper model. The bending behavior of the non-nicked ds DNA turns out very much similar to that of the nicked one, i.e. forming a constant force kink under sharp bending, but at a slightly larger cortical torque τc ∼ 31 pN × nm. The bending energy of the non-nicked DNA can also be described by the analytic expression. The effect of the nick on the bending of ds DNA is evaluated to be small, ∼ 2 kBT in terms of energy. The critical torque τc introduces a characteristic energy scale (π/2) τc ∼ 12 kBT relevant for molecular biology processes associated with DNA bending.

The conformational dynamics of an enzyme (Guanylate Kinase) is measured through a set of nano-mechanical measurements with extraordinary resolution ∼ 0.2 Å. The enzyme undergoes a sharp transition from linear elasticity to softer ("viscoelastic") dynamics as a function of force and frequency. We observed frequency dependence of the force response of the enzyme, namely the stress - strain curve changes with frequency. A non-equilibrium thermodynamic cycle is proposed based on the (frequency dependent) viscoelastic transition, as one universal feature of enzyme action. In this framework, several general properties of enzymes are understood or predicted. The force dependence of the frequency response is also observed and characterized. We experimentally define a line in the frequency - force plane separating elastic from viscoelastic response, presenting a "phase diagram" for the dynamics of the enzyme. We also give a simple argument (based on a heuristic Maxwell model) for the shape of this phase line, and show that in the closed state (with substrate bound) it shifts to lower frequencies compared to the open state (no substrate bound). The open state is "softer" than the closed state, not in the linear elastic regime (i.e. no soft mode), but because it is easier to access the soft (viscoelastic) state. And the hinge motion of Guanylate Kinase which is the conformational motion connecting the open and closed states therefore has nothing to do with soft modes but everything to do with the viscoelastic transition.

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