On the role of thermal backbone fluctuations in myoglobin ligand gate dynamics

Protein tertiary structure and the myoglobin phase diagram

We develop an effective theory approach to investigate the phase properties of globular proteins. Instead of interactions between individual atoms or localized interaction centers, the approach builds directly on the tertiary structure of a protein. As an example we construct the phase diagram of (apo)myoglobin with temperature (T) and acidity (pH) as the thermodynamical variables. We describe how myoglobin unfolds from the native folded state to a random coil when temperature and acidity increase. We confirm the presence of two molten globule folding intermediates, and we predict an abrupt transition between the two when acidity changes. When temperature further increases we find that the abrupt transition line between the two molten globule states terminates at a tricritical point, where the helical structures fade away. Our results also suggest that the ligand entry and exit is driven by large scale collective motions that destabilize the myoglobin F-helix.

Solution x-ray scattering and structure formation in protein dynamics

We propose a computationally effective approach that builds on Landau mean-field theory in combination with modern nonequilibrium statistical mechanics to model and interpret protein dynamics and structure formation in small- to wide-angle x-ray scattering (S/WAXS) experiments. We develop the methodology by analyzing experimental data in the case of Engrailed homeodomain protein as an example. We demonstrate how to interpret S/WAXS data qualitatively with a good precision and over an extended temperature range. We explain experimental observations in terms of protein phase structure, and we make predictions for future experiments and for how to analyze data at different ambient temperature values. We conclude that the approach we propose has the potential to become a highly accurate, computationally effective, and predictive tool for analyzing S/WAXS data. For this, we compare our results with those obtained previously in an all-atom molecular dynamics simulation.

Aspects of structural landscape of human islet amyloid polypeptide

The human islet amyloid polypeptide (hIAPP) co-operates with insulin to maintain glycemic balance. It also constitutes the amyloid plaques that aggregate in the pancreas of type-II diabetic patients. We have performed extensive in silico investigations to analyse the structural landscape of monomeric hIAPP, which is presumed to be intrinsically disordered. For this, we construct from first principles a highly predictive energy function that describes a monomeric hIAPP observed in a nuclear magnetic resonance experiment, as a local energy minimum. We subject our theoretical model of hIAPP to repeated heating and cooling simulations, back and forth between a high temperature regime where the conformation resembles a random walker and a low temperature limit where no thermal motions prevail. We find that the final low temperature conformations display a high level of degeneracy, in a manner which is fully in line with the presumed intrinsically disordered character of hIAPP. In particular, we identify an isolated family of α-helical conformations that might cause the transition to amyloidosis, by nucleation.

Peierls-Nabarro barrier and protein loop propagation

When a self-localized quasiparticle excitation propagates along a discrete one-dimensional lattice, it becomes subject to a dissipation that converts the kinetic energy into lattice vibrations. Eventually the kinetic energy no longer enables the excitation to cross over the minimum energy barrier between neighboring sites, and the excitation becomes localized within a lattice cell. In the case of a protein, the lattice structure consists of the C(α) backbone. The self-localized quasiparticle excitation is the elemental building block of loops. It can be modeled by a kink that solves a variant of the discrete nonlinear Schrödinger equation. We study the propagation of such a kink in the case of the protein G related albumin-binding domain, using the united residue coarse-grained molecular-dynamics force field. We estimate the height of the energy barriers that the kink needs to cross over in order to propagate along the backbone lattice. We analyze how these barriers give rise to both stresses and reliefs, which control the kink movement. For this, we deform a natively folded protein structure by parallel translating the kink along the backbone away from its native position. We release the transposed kink, and we follow how it propagates along the backbone toward the native location. We observe that the dissipative forces that are exerted on the kink by the various energy barriers have a pivotal role in determining how a protein folds toward its native state.

Using THz time-scale infrared spectroscopy to examine the role of collective, thermal fluctuations in the formation of myoglobin allosteric communication pathways and ligand specificity

In this investigation we use THz time-scale spectroscopy to conduct an initial set of studies on myoglobin with the aim of providing further insight into the global, collective thermal fluctuations in the protein that have been hypothesized to play a prominent role in the dynamic formation of transient ligand channels as well as in shaping the molecular level basis for ligand discrimination. Using the two ligands O2 and CO, we have determined that the perturbation from the heme-ligand complex has a strong influence on the characteristics of the myoglobin collective dynamics that are excited upon binding. Further, the differences detected in the collective protein motions in Mb-O2 compared with those in Mb-CO appear to be intimately tied with the pathways of long-range allosteric communication in the protein, which ultimately determine the trajectories selected by the respective ligands on the path to and from the heme-binding cavity.

Gauge fields, strings, solitons, anomalies, and the speed of life

Joel Cohen proposed that “mathematics is biology’s next microscope, only better; biology is mathematics’ next physics, only better.” Here, we aim for something even better. We try to combine mathematical physics and biology into a picoscope of life. For this, we merge techniques that were introduced and developed in modern mathematical physics, largely by Ludvig Faddeev, to describe objects such as solitons and Higgs and to explain phenomena such as anomalies in gauge fields. We propose a synthesis that can help to resolve the protein folding problem, one of the most important conundrums in all of science. We apply the concept of gauge invariance to scrutinize the extrinsic geometry of strings in three-dimensional space. We evoke general principles of symmetry in combination with Wilsonian universality and derive an essentially unique Landau-Ginzburg energy that describes the dynamics of a generic stringlike configuration in the far infrared. We observe that the energy supports topological solitons that relate to an anomaly similarly to how a string is framed around its inflection points. We explain how the solitons operate as modular building blocks from which folded proteins are composed. We describe crystallographic protein structures by multisolitons with experimental precision and investigate the nonequilibrium dynamics of proteins under temperature variations. We simulate the folding process of a protein at in vivo speed and with close to picoscale accuracy using a standard laptop computer. With picobiology as next pursuit of mathematical physics, things can only get better.