The effect of osmolytes on protein fold stability at the single-molecule level

By pulling and releasing the tension on protein homomers with the Atomic Force Miscroscope (AFM) at different pulling speeds, dwell times and dwell distances, the observed force-response of the protein can be fitted with suitable theoretical models. In this respect we developed mathematical procedures and open-source computer codes for driving such experiments and fitting Bell’s model to experimental protein unfolding forces and protein folding frequencies. We applied the above techniques to the study of proteins GB1 (the B1 IgG-binding domain of protein G from Streptococcus) and I27 (a module of human cardiac titin) in aqueous solutions of protecting osmolytes such as dimethyl sulfoxide (DMSO), glycerol and trimethylamine N-oxide (TMAO). In order to get a molecular understanding of the experimental results we developed an Ising-like model for proteins that incorporates the osmophobic nature of their backbone. The model benefits from analytical thermodynamics and kinetics amenable to Monte-Carlo simulation. The prevailing view used to be that small protecting osmolytes bridge the separating beta-strands of proteins with mechanical resistance, presumably shifting the transition state to significantly higher distances that correlate with the molecular size of the osmolyte molecules. Our experiments showed instead that protecting osmolytes slow down protein unfolding and speed-up protein folding at physiological pH without shifting the protein transition state on the mechanical reaction coordinate. Together with the theoretical results of the Ising-model, our results lend support to the osmophobic theory according to which osmolyte stabilisation is a result of the preferential exclusion of the osmolyte molecules from the protein backbone. The results obtained during this thesis work have markedly improved our understanding of the strategy selected by Nature to strengthen protein stability in hostile environments, shifting the focus from hypothetical protein-osmolyte interactions to the more general mechanism based on the osmophobicity of the protein backbone.

Correlations and Quantum Dynamics of 1D Fermionic Models: New Results for the Kitaev Chain with Long-Range Pairing

In the first part of the thesis, we propose an exactly-solvable one-dimensional model for fermions with long-range p-wave pairing decaying with distance as a power law. We studied the phase diagram by analyzing the critical lines, the decay of correlation functions and the scaling of the von Neumann entropy with the system size. We found two gapped regimes, where correlation functions decay (i) exponentially at short range and algebraically at long range, (ii) purely algebraically. In the latter the entanglement entropy is found to diverge logarithmically. Most interestingly, along the critical lines, long-range pairing breaks also the conformal symmetry. This can be detected via the dynamics of entanglement following a quench. In the second part of the thesis we studied the evolution in time of the entanglement entropy for the Ising model in a transverse field varying linearly in time with different velocities. We found different regimes: an adiabatic one (small velocities) when the system evolves according the instantaneous ground state; a sudden quench (large velocities) when the system is essentially frozen to its initial state; and an intermediate one, where the entropy starts growing linearly but then displays oscillations (also as a function of the velocity). Finally, we discussed the Kibble-Zurek mechanism for the transition between the paramagnetic and the ordered phase.