Role of Resultant Dipole Moment in Mechanical Dissociation of Biological Complexes.

Protein-peptide interactions play essential roles in many cellular processes and their structural characterization is the major focus of current experimental and theoretical research. Two decades ago, it was proposed to employ the steered molecular dynamics (SMD) to assess the strength of protein-peptide interactions. The idea behind using SMD simulations is that the mechanical stability can be used as a promising and an efficient alternative to computationally highly demanding estimation of binding affinity. However, mechanical stability defined as a peak in force-extension profile depends on the choice of the pulling direction. Here we propose an uncommon choice of the pulling direction along resultant dipole moment (RDM) vector, which has not been explored in SMD simulations so far. Using explicit solvent all-atom MD simulations, we apply SMD technique to probe mechanical resistance of ligand-receptor system pulled along two different vectors. A novel pulling direction-when ligand unbinds along the RDM vector-results in stronger forces compared to commonly used ligand unbinding along center of masses vector. Our observation that RDM is one of the factors influencing the mechanical stability of protein-peptide complex can be used to improve the ranking of binding affinities by using mechanical stability as an effective scoring function.

Fractal nature of protein surface roughness: a note on quantification of change of surface roughness in active sites, before and after binding.

Year 2010 marked the 25th year since we came to know that roughness of a protein surface has fractal symmetry. Ever since the publication of Lewis and Rees' paper, hundreds of works from a spectrum of perspectives have established that fractal dimension (FD) can be considered as a reliable marker that describes roughness of protein surface objectively. In this article, we introduce readers to the fundamentals of fractals and present categorical biophysical and geometrical reasons as to why FD-based constructs can describe protein surface roughness more accurately. We then review the commonality (and the lack of it) between numerous approaches that have attempted to investigate protein surface with fractal measures, before exploring the patterns in the results that they have produced. Apart from presenting the genealogy of approaches and results, we present an analysis that quantifies the difference in surface roughness in stretches of protein surface containing the active site, before and after binding to ligands, to underline the utility of FD-based measures further. It has been found that surface stretches containing the active site, in general, undergo a significant increment in its roughness after binding. After presenting the entire repertoire of FD-based surface roughness studies, we talk about two yet-unexplored problems where application of FD-based techniques can help in deciphering underlying patterns of surface interactions. Finally, we list the limitations of FD-based constructs and put down several precautions that one must take while working with them.

Fractal symmetry of protein interior: what have we learned?

The application of fractal dimension-based constructs to probe the protein interior dates back to the development of the concept of fractal dimension itself. Numerous approaches have been tried and tested over a course of (almost) 30 years with the aim of elucidating the various facets of symmetry of self-similarity prevalent in the protein interior. In the last 5 years especially, there has been a startling upsurge of research that innovatively stretches the limits of fractal-based studies to present an array of unexpected results on the biophysical properties of protein interior. In this article, we introduce readers to the fundamentals of fractals, reviewing the commonality (and the lack of it) between these approaches before exploring the patterns in the results that they produced. Clustering the approaches in major schools of protein self-similarity studies, we describe the evolution of fractal dimension-based methodologies. The genealogy of approaches (and results) presented here portrays a clear picture of the contemporary state of fractal-based studies in the context of the protein interior. To underline the utility of fractal dimension-based measures further, we have performed a correlation dimension analysis on all of the available non-redundant protein structures, both at the level of an individual protein and at the level of structural domains. In this investigation, we were able to separately quantify the self-similar symmetries in spatial correlation patterns amongst peptide-dipole units, charged amino acids, residues with the π-electron cloud and hydrophobic amino acids. The results revealed that electrostatic environments in the interiors of proteins belonging to 'α/α toroid' (all-α class) and 'PLP-dependent transferase-like' domains (α/ß class) are highly conducive. In contrast, the interiors of 'zinc finger design' ('designed proteins') and 'knottins' ('small proteins') were identified as folds with the least conducive electrostatic environments. The fold 'conotoxins' (peptides) could be unambiguously identified as one type with the least stability. The same analyses revealed that peptide-dipoles in the α/ß class of proteins, in general, are more correlated to each other than are the peptide-dipoles in proteins belonging to the all-α class. Highly favorable electrostatic milieu in the interiors of TIM-barrel, α/ß-hydrolase structures could explain their remarkably conserved (evolutionary) stability from a new light. Finally, we point out certain inherent limitations of fractal constructs before attempting to identify the areas and problems where the implementation of fractal dimension-based constructs can be of paramount help to unearth latent information on protein structural properties.

Case for an RNA-prion world: a hypothesis based on conformational diversity.

Prions and other misfolded proteins can impart their structure and functions to normal molecules. Based upon a thorough structural assessment of RNA, prions and misfolded proteins, especially from the perspective of conformational diversity, we propose a case for co-existence of these in the pre-biotic world. Analyzing the evolution of physical aspects of biochemical structures, we put forward a case for an RNA-prion pre-biotic world, instead of, merely, the "RNA World".

A new computational model to study mass inhomogeneity and hydrophobicity inhomogeneity in proteins.

We propose a simple yet reliable computational framework that characterizes the differential mass and hydrophobicity distribution within structural classes of proteins. Radial partitioning of protein interior that could successfully distinguish the mass and hydrophobicity distribution patterns in extremophilic proteins from that in their structurally aligned mesophilic counterparts. Distance-dependent mass and hydrophobicity magnitudes could retrieve vital structural insights; needed to probe the hidden connections between packing, folding and stability within different structural classes of proteins, with causality. New computational markers; one, to represent the total mass content; other, related to hydrophobic centrality of proteins, are proposed as well. Results reveal that mass and hydrophobicity packing within extremophilic proteins is indeed more compact than that in their mesophilic counterparts. Analysis of structural constraints within them vindicate it. Total mass (and hydrophobicity) content is found to be maximum in alpha/beta thermophilic proteins and minimum for the all-alpha mesophilic proteins.

An attempt to construct a (general) mathematical framework to model biological "context-dependence".

Context-dependent nature of biological phenomena is well documented in every branch of biology. While there have been few previous attempts to (implicitly) model various (particular) facets of biological context-dependence, a formal and general mathematical construct to model the wide spectrum of context-dependence, eludes the students of biology. Such an objective model, from both 'bottom-up' as well as 'top-down' perspective, is proposed here to serve as the template to describe the various kinds of context-dependence that we encounter in different branches of biology. Interactions between biological contexts was found to be transitive but non-commutative. It is found that a hierarchical nature of dependence among the biological contexts models the emergent biological properties efficiently. Reasons for these findings are provided in a general model to describe biological reality. Scheme to algorithmically implement the hierarchic structure of organization of biological contexts was proposed with a construct named 'Context tree'. A 'Context tree' based analysis of context interactions among biophysical factors influencing protein structure was performed.

Revisiting the myths of protein interior: studying proteins with mass-fractal hydrophobicity-fractal and polarizability-fractal dimensions.

A robust marker to describe mass, hydrophobicity and polarizability distribution holds the key to deciphering structural and folding constraints within proteins. Since each of these distributions is inhomogeneous in nature, the construct should be sensitive in describing the patterns therein. We show, for the first time, that the hydrophobicity and polarizability distributions in protein interior follow fractal scaling. It is found that (barring 'all-alpha') all the major structural classes of proteins have an amount of unused hydrophobicity left in them. This amount of untapped hydrophobicity is observed to be greater in thermophilic proteins, than that in their (structurally aligned) mesophilic counterparts. 'All-beta'(thermophilic, mesophilic alike) proteins are found to have maximum amount of unused hydrophobicity, while 'all-alpha' proteins have been found to have minimum polarizability. A non-trivial dependency is observed between dielectric constant and hydrophobicity distributions within (alpha+beta) and 'all-alpha' proteins, whereas absolutely no dependency is found between them in the 'all-beta' class. This study proves that proteins are not as optimally packed as they are supposed to be. It is also proved that origin of alpha-helices are possibly not hydrophobic but electrostatic; whereas beta-sheets are predominantly hydrophobic in nature. Significance of this study lies in protein engineering studies; because it quantifies the extent of packing that ensures protein functionality. It shows that myths regarding protein interior organization might obfuscate our knowledge of actual reality. However, if the later is studied with a robust marker of strong mathematical basis, unknown correlations can still be unearthed; which help us to understand the nature of hydrophobicity, causality behind protein folding, and the importance of anisotropic electrostatics in stabilizing a highly complex structure named 'proteins'.