Xubiao Peng

Soliton concepts and protein structure

Structural classification shows that the number of different protein folds is surprisingly small. It also appears that proteins are built in a modular fashion from a relatively small number of components. Here we propose that the modular building blocks are made of the dark soliton solution of a generalized discrete nonlinear Schrödinger equation. We find that practically all protein loops can be obtained simply by scaling the size and by joining together a number of copies of the soliton, one after another. The soliton has only two loop-specific parameters, and we compute their statistical distribution in the Protein Data Bank (PDB). We explicitly construct a collection of 200 sets of parameters, each determining a soliton profile that describes a different short loop. The ensuing profiles cover practically all those proteins in PDB that have a resolution which is better than 2.0 Å, with a precision such that the average root-mean-square distance between the loop and its soliton is less than the experimental B-factor fluctuation distance. We also present two examples that describe how the loop library can be employed both to model and to analyze folded proteins.

Towards quantitative classification of folded proteins in terms of elementary functions.

A comparative classification scheme provides a good basis for several approaches to understand proteins, including prediction of relations between their structure and biological function. But it remains a challenge to combine a classification scheme that describes a protein starting from its well-organized secondary structures and often involves direct human involvement, with an atomary-level physics-based approach where a protein is fundamentally nothing more than an ensemble of mutually interacting carbon, hydrogen, oxygen, and nitrogen atoms. In order to bridge these two complementary approaches to proteins, conceptually novel tools need to be introduced. Here we explain how an approach toward geometric characterization of entire folded proteins can be based on a single explicit elementary function that is familiar from nonlinear physical systems where it is known as the kink soliton. Our approach enables the conversion of hierarchical structural information into a quantitative form that allows for a folded protein to be characterized in terms of a small number of global parameters that are in principle computable from atomary-level considerations. As an example we describe in detail how the native fold of the myoglobin 1M6C emerges from a combination of kink solitons with a very high atomary-level accuracy. We also verify that our approach describes longer loops and loops connecting α helices with β strands, with the same overall accuracy.

A three dimensional visualisation approach to protein heavy-atom structure reconstruction

BackgroundA commonly recurring problem in structural protein studies, is the determination of all heavy atom positions from the knowledge of the central α-carbon coordinates.ResultsWe employ advances in virtual reality to address the problem. The outcome is a 3D visualisation based technique where all the heavy backbone and side chain atoms are treated on equal footing, in terms of the Cα coordinates. Each heavy atom is visualised on the surfaces of a different two-sphere, that is centered at another heavy backbone and side chain atoms. In particular, the rotamers are visible as clusters, that display a clear and strong dependence on the underlying backbone secondary structure.ConclusionsWe demonstrate that there is a clear interdependence between rotameric states and secondary structure. Our method easily detects those atoms in a crystallographic protein structure which are either outliers or have been likely misplaced, possibly due to radiation damage. Our approach forms a basis for the development of a new generation, visualization based side chain construction, validation and refinement tools. The heavy atom positions are identified in a manner which accounts for the secondary structure environment, leading to improved accuracy.

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

We construct an energy function that describes the crystallographic structure of sperm whale myoglobin backbone. As a model in our construction, we use the Protein Data Bank entry 1ABS that has been measured at liquid helium temperature. Consequently, the thermal B-factor fluctuations are very small, which is an advantage in our construction. The energy function that we utilize resembles that of the discrete nonlinear Schrödinger equation. Likewise, ours supports topological solitons as local minimum energy configurations. We describe the 1ABS backbone in terms of topological solitons with a precision that deviates from 1ABS by an average root-mean-square distance, which is less than the experimentally observed Debye-Waller B-factor fluctuation distance. We then subject the topological multi-soliton solution to extensive numerical heating and cooling experiments, over a very wide range of temperatures. We concentrate in particular to temperatures above 300 K and below the Θ-point unfolding temperature, which is around 348 K. We confirm that the behavior of the topological multi-soliton is fully consistent with Anfinsens thermodynamic principle, up to very high temperatures. We observe that the structure responds to an increase of temperature consistently in a very similar manner. This enables us to characterize the onset of thermally induced conformational changes in terms of three distinct backbone ligand gates. One of the gates is made of the helix F and the helix E. The two other gates are chosen similarly, when open they provide a direct access route for a ligand to reach the heme. We find that out of the three gates we investigate, the one which is formed by helices B and G is the most sensitive to thermally induced conformational changes. Our approach provides a novel perspective to the important problem of ligand entry and exit.

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.

Clustering and percolation in protein loop structures

BackgroundHigh precision protein loop modelling remains a challenge, both in template based and template independent approaches to protein structure prediction.MethodWe introduce the concepts of protein loop clustering and percolation, to develop a quantitative approach to systematically classify the modular building blocks of loops in crystallographic folded proteins. These fragments are all different parameterisations of a unique kink solution to a generalised discrete nonlinear Schrödinger (DNLS) equation. Accordingly, the fragments are also local energy minima of the ensuing energy function.ResultsWe show how the loop fragments cover practically all ultrahigh resolution crystallographic protein structures in Protein Data Bank (PDB), with a 0.2 Ångström root-mean-square (RMS) precision. We find that no more than 12 different loop fragments are needed, to describe around 38 % of ultrahigh resolution loops in PDB. But there is also a large number of loop fragments that are either unique, or very rare, and examples of unique fragments are found even in the structure of a myoglobin.ConclusionsProtein loops are built in a modular fashion. The loops are composed of fragments that can be modelled by the kink of the DNLS equation. The majority of loop fragments are also common, which are shared by many proteins. These common fragments are probably important for supporting the overall protein conformation. But there are also several fragments that are either unique to a given protein, or very rare. Such fragments are probably related to the function of the protein. Furthermore, we have found that the amino acid sequence does not determine the structure in a unique fashion. There are many examples of loop fragments with an identical amino acid sequence, but with a very different structure.

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.

Kink Formation Dynamics in a Single α-helical Protein

Protein folding remains an open problem despite the progress in understanding the process rate and the success in folding prediction for some small proteins. The reason is the absence of a constructive theoretical framework, both general and specific enough.In earlier papers, we have argued that protein-folding dynamics can be described in terms of solitons of a generalized discrete non-linear Schrodinger equation (GDNLSE) obtained from the energy function in terms of bond and torsion angles [1]. The soliton manifestation is the pattern helix--loop--helix in the secondary structure of the protein, which explains the importance of understanding loop formation in helical proteins and the kink assignment to it [2]. We propose a new mechanism for this process based on the energy transmission along the chain---a disturbance in the latter leads to energy accumulation sufficient to form a kink. We present first insights into the process dynamics by all-atom molecular-dynamics analysis of unfolding of a single alpha-helical protein–--one chain of the core structure of gp41 from the HIV envelope glycoprotein (PDB ID: 1AIK). We suggest an adequate quantification of the side-chain orientation dynamics and also identify some force-field related artefacts.