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A novel approach to protein folding dynamics is presented. We suggest that folding of protein may be mediated via interaction with solitons which propagate along the molecular chain. A simple toy model is presented in which a Sine-Gordon field interact with another field corresponding to the conformation angles of the protein. We demonstrate how a soliton carries this field over energy barriers and consequently enhances the rate of the folding process. The soliton compensate for its energy loss by pumping the energy gained by the folded field. This scenario does not change significantly even in the presence of dissipation and imposed disorder.
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The intricate three-dimensional geometries of protein tertiary structures underlie protein function and emerge through a folding process from one-dimensional chains of amino acids. The exact spatial sequence and configuration of amino acids, the biochemical environment and the temporal sequence of distinct interactions yield a complex folding process that cannot yet be easily tracked for all proteins. To gain qualitative insights into the fundamental mechanisms behind the folding dynamics and generic features of the folded structure, we propose a simple model of structure formation that takes into account only fundamental geometric constraints and otherwise assumes randomly paired connections. We find that despite its simplicity, the model results in a network ensemble consistent with key overall features of the ensemble of Protein Residue Networks we obtained from more than 1000 biological protein geometries as available through the Protein Data Base. Specifically, the distribution of the number of interaction neighbors a unit (amino acid) has, the scaling of the structures spatial extent with chain length, the eigenvalue spectrum and the scaling of the smallest relaxation time with chain length are all consistent between model and real proteins. These results indicate that geometric constraints alone may already account for a number of generic features of protein tertiary structures.
The protein folding problem is stated and a list of properties that do not depend upon specific molecules is compiled and analyzed. The relationship of this analysis to future simulations is emphasized. The choice of power and time as variables as opposed to energy and time is discussed. A wave motion model is reviewed and related to the action in classical mechanics. It is argued that the properties of the action support the idea that folding takes place in small steps. It is explained how catastrophe theory has been employed in wave motion models and how it can be used in examination of successful simulations
A geometric analysis of protein folding, which complements many of the models in the literature, is presented. We examine the process from unfolded strand to the point where the strand becomes self-interacting. A central question is how it is possible that so many initial configurations proceed to fold to a unique final configuration. We put energy and dynamical considerations temporarily aside and focus upon the geometry alone. We parameterize the structure of an idealized protein using the concept of a ribbon from differential geometry. The deformation of the ribbon is described by introducing a generic twisting Ansatz. The folding process in this picture entails a change in shape guided by the local amino acid geometry. The theory is reparamaterization invariant from the start, so the final shape is independent of folding time. We develop differential equations for the changing shape. For some parameter ranges, a sine-Gordon torsion soliton is found. This purely geometric waveform has properties similar to dynamical solitons. Namely: A threshold distortion of the molecule is required to initiate the soliton, after which, small additional distortions do not change the waveform. In this analysis, the soliton twists the molecule until bonds form. The analysis reveals a quantitative relationship between the geometry of the amino acids and the folded form.
In spite of decades of research, much remains to be discovered about folding: the detailed structure of the initial (unfolded) state, vestigial folding instructions remaining only in the unfolded state, the interaction of the molecule with the solvent, instantaneous power at each point within the molecule during folding, the fact that the process is stable in spite of myriad possible disturbances, potential stabilization of trajectory by chaos, and, of course, the exact physical mechanism (code or instructions) by which the folding process is specified in the amino acid sequence. Simulations based upon microscopic physics have had some spectacular successes and continue to improve, particularly as super-computer capabilities increase. The simulations, exciting as they are, are still too slow and expensive to deal with the enormous number of molecules of interest. In this paper, we introduce an approximate model based upon physics, empirics, and information science which is proposed for use in machine learning applications in which very large numbers of sub-simulations must be made. In particular, we focus upon machine learning applications in the learning phase and argue that our model is sufficiently close to the physics that, in spite of its approximate nature, can facilitate stepping through machine learning solutions to explore the mechanics of folding mentioned above. We particularly emphasize the exploration of energy flow (power) within the molecule during folding, the possibility of energy scale invariance (above a threshold), vestigial information in the unfolded state as attractive targets for such machine language analysis, and statistical analysis of an ensemble of folding micro-steps.
A model to describe the mechanism of conformational dynamics in secondary protein based on matter interactions is proposed. The approach deploys the lagrangian method by imposing certain symmetry breaking. The protein backbone is initially assumed to be nonlinear and represented by the Sine-Gordon equation, while the nonlinear external bosonic sources is represented by $phi^4$ interaction. It is argued that the nonlinear source induces the folding pathway in a different way than the previous work with initially linear backbone. Also, the nonlinearity of protein backbone decreases the folding speed.
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