Molecular Dynamics Simulations of Flexible Biomolecules: Development of Enhanced Sampling Methods and Integration of Experimental Data

Molecular dynamics (MD) simulations act as molecular microscopes, giving access to the position of every atom at every instant of time. This access comes at a price: the reliability of the result is limited by the accuracy of the underlying force field, and by the amount of conformational space that the simulation is actually able to explore. This thesis addresses both sides of this problem, by developing techniques that make the exploration of conformational space more efficient and by integrating experimental data into simulations, across chemically very different systems that share the property of being flexible. We first characterise the association of RNA with a fluid zwitterionic phospholipid bilayer using all-atom MD and well-tempered metadynamics, obtaining binding free energies and partition coefficients for systems ranging from single nucleosides to a 19-mer. In the absence of divalent cations, binding is driven by hydrogen bonding between nucleobases and lipid headgroups, with guanine emerging as the principal actor and the only nucleobase whose affinity increases systematically with sequence length. Base pairing competes with membrane binding, so that unstructured strands bind more strongly than folded ones of the same sequence, suggesting that disordered G-rich segments may be a hallmark of membrane-binding RNA molecules. We then address the cost of converging RNA ensembles. We introduce a protocol that optimises the Hamiltonian parametrisation of a replica-exchange ladder directly against a kinetic objective: from an existing set of HREX simulations, a Markov State Model of the generalised ensemble is built, reweighted to candidate parameters, and the round-trip times between the states whose populations one wants to converge are minimised. We show that the implied timescales of that model, which would appear to be the natural quantity to minimise, are the wrong objective, since they can be reduced by suppressing metastable states altogether. On adenosine, two rounds of optimisation yield a ladder sampling almost four times as many transitions as standard REST$2$; on tetranucleotides and hexamers the gains are modest but measurable, and transfer to sequences absent from the training set. Finally, we use EMMIVox to integrate experimental cryo-EM data into simulations of the E7--AP2 complex, in which a disordered viral oncoprotein binds a folded adaptor complex. Ensemble refinement reproduces the density substantially better than the original single structure, with the improvement concentrated in the voxels occupied by the disordered chains, and shows that Yxx$\Phi$ binding is preserved while the surrounding contacts are fuzzy and were likely over-counted by a single model. Taken together, these results illustrate a recurring point: for flexible systems, staying close to a single structure can be misleading, and it becomes necessary to study the ensemble, be it for small tetranucleotides or for fitting a cryo-EM density map of a large complex. Obtaining such ensembles is expensive, which is why part of this thesis is devoted to reducing that cost.