Protein representation and potential function are essential ingredients for studying proteins folding and protein prediction. We introduce a novel geometric representation of contact interactions using the edge simplices from alpha shape of protein structure. This representation can eliminate implausible neighbors not in physical contact, and can avoid spurious contact between two residues when a third residue is between them. We develop statistical alpha contact potential. A studentized bootstrap method is then introduced for assessing the 95% confidence intervals for each of the 210 parameters. We found with confidence that there is significant long range propensity (>30 residues apart) for hydrophobic interactions. We test alpha contact potential for native structure discrimination using several decoy sets, and found it often has comparable performance with atom-based potentials requiring more parameters. We also show that alpha contact potential has better performance than potential defined by cut-off distance between geometric centers of side chains. Clustering of alpha contact potentials reveals natural grouping of residues. To explore the relationship between shape representation and physicochemical representation, we test the minimum alphabet size for structure discrimination. We found that there is no significant difference in discrimination when alphabet size varies from 7 to 20, if geometry is represented accurately by alpha simplicial edges. This result suggests that the geometry of packing plays an important role, but the specific residue types are often interchangeable.
We propose the conformon as a quantum of conformational change for energy transfer in alpha-helical proteins. The underlying mechanism of interaction between the quantum of excitation and the conformational degrees of freedom is nonlinear and leads to solitary wave packets of conformational energy. The phenomenon is specific to alpha-helices and not to beta-sheets in proteins due to the three strands of hydrogen bonds constituting the alpha-helical backbone.
Two proteins, one belonging to the mainly alpha class and the other belonging to the alpha/beta class, are selected to test a kinetic mechanism for protein folding. Targeted molecular dynamics is applied to generate folding pathways for those two proteins, starting from two well defined initial conformations: a fully extended and a alpha-helical conformation. The results show that for both proteins the alpha-helical initial conformation provides overall lower energy pathways to the native state. For the alpha/beta protein, 30 % (40%) of the pathways from an initial alpha-helix (fully extended)…
The computer artificial intelligence system AlphaFold has recently predicted previously unknown three-dimensional structures of thousands of proteins. Focusing on the subset with high-confidence scores, we algorithmically analyze these predictions for cases where the protein backbone exhibits rare topological complexity, i.e. knotting. Amongst others, we discovered a $7_1$-knot, the most topologically complex knot ever found in a protein, as well several 6-crossing composite knots comprised of two methyltransferase or carbonic anhydrase domains, each containing a simple trefoil knot. These dee…
We propose that protein loops can be interpreted as topological domain-wall solitons. They interpolate between ground states that are the secondary structures like alpha-helices and beta-strands. Entire proteins can then be folded simply by assembling the solitons together, one after another. We present a simple theoretical model that realizes our proposal and apply it to a number of biologically active proteins including 1VII, 2RB8, 3EBX (Protein Data Bank codes). In all the examples that we have considered we are able to construct solitons that reproduce secondary structural motifs such as a…
The proposal of this paper is to provide a simple angular random walk model to build up polypeptide structures, which encompass properties of dihedral angles of folded proteins. From this model, structures will be built with lengths ranging from 125 up to 400 amino acids for the different fractions of secondary structure motifs, which dihedral angles were randomly chosen according to narrow Gaussian probability distributions. In order to measure the fractal dimension of proteins three different cases were analyzed. The first contained alpha-helix structures only, the second beta-strands struct…
Integrins are transmembrane proteins involved in hemostasis, wound healing, immunity and cancer. In response to intracellular signals and ligand binding, integrins adopt different conformations: the bent (resting) form; the intermediate extended form; and the ligand-occupied active form. An integrin undergoing such conformational dynamics is the heterodimeric platelet receptor alphaIIbbeta3. Although the dramatic rearrangement of the overall structure of alphaIIbbeta3 during the activation process is potentially related to changes in the protein secondary structure, this has not been investiga…
We inquire to what extent protein peptide plane and side chain dynamics can be reconstructed from knowledge of C-alpha dynamics. Due to lack of experimental data we analyze all atom molecular dynamics trajectories from Anton supercomputer, and for clarity we limit our attention to the peptide plane O atoms and side chain C-beta atoms. We try and reconstruct their dynamics using four different approaches. Three of these are the publicly available reconstruction programs Pulchra, Remo Scwrl4. The fourth, Statistical Method, builds entirely on statistical analysis of Protein Data Bank (PDB) struc…
Unsupervisedly Prompting AlphaFold2 for Few-Shot Learning of Accurate Folding Landscape and Protein Structure Prediction
Changping Laboratory（昌平实验室）；Huawei Hangzhou Research Institute（华为杭州研究院）；Institute of Systems and Physical Biology（系统与物理生物学研究所）；Shenzhen Bay Laboratory（深圳湾实验室）；Beijing National Laboratory for Molecular Sciences（北京分子科学国家实验室）；College of Chemistry and Molecular Engineering, Peking University（北京大学化学与分子工程学院）；Biomedical Pioneering Innovation Center, Peking University（北京大学生物医学前沿创新中心）
Alpha helices are more evolutionarily robust to environmental perturbations than beta sheets: Bayesian learning and statistical mechanics for protein evolution
Intrinsically disordered proteins (IDPs) do not possess well-defined three-dimensional structures in solution under physiological conditions. We develop all-atom, united-atom, and coarse-grained Langevin dynamics simulations for the IDP alpha-synuclein that include geometric, attractive hydrophobic, and screened electrostatic interactions and are calibrated to the inter-residue separations measured in recent smFRET experiments. We find that alpha-synuclein is disordered with conformational statistics that are intermediate between random walk and collapsed globule behavior. An advantage of cali…
The influence of the intramolecular anharmonicity and the strong vibron-phonon coupling on the two-vibron dynamics in an $α$-helix protein is studied within a modified Davydov model. The intramolecular anharmonicity of each amide-I vibration is considered and the vibron dynamics is described according to the small polaron approach. A unitary transformation is performed to remove the intramolecular anharmonicity and a modified Lang-Firsov transformation is applied to renormalize the vibron-phonon interaction. Then, a mean field procedure is realized to obtain the dressed anharmonic vibron Hamil…
It was reported that buffalo is a low susceptibility species resisting to prion diseases, which are invariably fatal and highly infectious neurodegenerative diseases that affect a wide variety of species. In molecular structures, TSE neurodegenerative diseases are caused by the conversion from a soluble normal cellular prion protein, predominantly with alpha-helices, into insoluble abnormally folded infectious prions, rich in beta-sheets. This paper studies the molecular structure and structural dynamics of buffalo prion protein, in order to reveal the reason why buffalo are resistant to prion…
Natively unstructured proteins defy the classical "one sequence-one structure" paradigm of protein science. Monomers of these proteins in pathological conditions can aggregate in the cell, a process that underlies socially relevant neurodegenerative diseases such as Alzheimer and Parkinson. A full comprehension of the formation and structure of the so-called misfolded intermediates from which the aggregated states ensue is still lacking. We characterized the folding and the conformational diversity of alpha-synuclein (aSyn), a natively unstructured protein involved in Parkinson disease, by mec…
A commonly recurring problem in structural protein studies, is the determination of all heavy atom positions from the knowledge of the central alpha-carbon coordinates. We 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 C-alpha coordinates. Each heavy atom can be visualised on the surfaces of the different two-spheres, that are centered at the other heavy backbone and side chain atoms. In particular, the rotamers are visible as clusters wh…
We propose to combine a mean field approach with all atom molecular dynamics into a multistage algorithm that can model protein folding and dynamics over very long time periods yet with atomic level precision. As an example we investigate an isolated monomeric Myc oncoprotein that has been implicated in carcinomas including those in colon, breast and lungs. Under physiological conditions a monomeric Myc is presumed to be an example of intrinsically disordered proteins, that pose a serious challenge to existing modelling techniques. We argue that a room temperature monomeric Myc is in a dynamic…
Under dehydration conditions, amphipathic Late Embryogenesis Abundant (LEA) proteins fold spontaneously from a random conformation into alpha-helical structures and this transition is promoted by the presence of membranes. To gain insight into the thermodynamics of membrane association we model the resulting alpha-helical structures as infinite rigid cylinders patterned with hydrophobic and hydrophilic stripes oriented parallel to their axis. Statistical thermodynamic calculations using Single Chain Mean Field (SCMF) theory show that the relative thickness of the stripes controls the free ener…
The mechanisms by which a protein's 3D structure can be determined based on its amino acid sequence have long been one of the key mysteries of biophysics. Often simplistic models, such as those derived from geometric constraints, capture bulk real-world 3D protein-protein properties well. One approach is using protein contact maps to better understand proteins' properties. Here, we investigate the emergent behaviour of contact maps for different geometrically constrained models and real-world protein systems. We derive an analytical approximation for the distribution of model amino acid distan…
We present a new method to extract distance and orientation dependent potentials between amino acid side chains using a database of protein structures and the standard Boltzmann device. The importance of orientation dependent interactions is first established by computing orientational order parameters for proteins with alpha-helical and beta-sheet architecture. Extraction of the anisotropic interactions requires defining local reference frames for each amino acid that uniquely determine the coordinates of the neighboring residues. Using the local reference frames and histograms of the radial …
