Scaling and self-organized criticality in proteins I

Abstract

The complexity of proteins is substantially simplified by regarding them as archetypical examples of self-organized criticality (SOC). To test this idea and elaborate on it, this article applies the Moret-Zebende SOC hydrophobicity scale to the large-scale scaffold repeat protein of the HEAT superfamily, PR65/A. Hydrophobic plasticity is defined and used to identify docking platforms and hinges from repeat sequences alone. The difference between the MZ scale and conventional hydrophobicity scales reflects longrange conformational forces that are central to protein functionality.hydrophobicity ͉ repeat ͉ scaling T here are many scales (hydrophobicity, charge, helix-forming propensity, etc.) that bioinformatically describe various aspects of amino acid interactions in proteins and their relations to sequence, structure, stability, and functionality, all justified by combining plausible constructs with parameters adjusted through statistical searches. Are all such scales equally useful, and are the substantial differences among them attributable to their inevitably heuristic character? Here, I discuss differences in methodology, with special emphasis on holistic vs. reductionist approaches. I suggest that a better understanding of the limitations and potential of scaling analysis of proteins will result from systematic studies of simple cases first, such as repeat proteins and their associates. Scaling analysis may prove to be a valuable tool in designing proteins with desired functions.Many physical systems exhibit power-law distributions over limited ranges (hence the popularity of log-log graph paper), and power-law distributions are the characteristic feature of the modern theory of phase transitions near a critical point. Self-organized criticality (SOC) is a methodology that attempts to explain why so many complex systems exhibit power-law distributions and appear to be ''accidentally'' located near critical points. It is argued that the critical points are dynamical fixed points (''tipping points'') toward which the system evolves without tuning external parameters (1). The critical points are extrema in some property (or properties) with respect to which the system has been optimized, especially with respect to long-range, highly-cooperative interactions, such as conformational changes.Given the widespread occurrence of power laws, SOC has great intuitive appeal: it has achieved an enduring popularity among theorists (Ͼ2,500 papers discussing SOC, Ͼ25 current books from a single publisher), notably in modeling the critical stability of sand piles against avalanches, but its concrete applications have been limited largely to seismic phenomena. A cautionary remark: power laws, especially in the context of dissipative reactions, have often been interpreted in terms of SOC, but a simpler interpretation involves only slow sweeping of a control parameter toward a global extremal, as could occur in the context of commercial product optimization (2). However, more recently Boolchand and coworkers (3) discovered a r...

Scaling and self-organized criticality in proteins II

“…The basic features of the L19 structure, including the deepest hydrophilic minima, are charge neutral, suggesting that its zipping functionality relies primarily on hydrophobic collapse, which in turn is limited by L8, leaving space within the horseshoe for Ran and cargoes. As in earlier cases (2,16), all of these long-range L8 and L19 symmetries disappear when hydroprofiles (Fig. S3 and Fig.…”

“…In PR65/A hydroflexibility peaks in ⌽ B (S) correlate exactly with binding sites in a heterotrimeric complex (2).…”

“…Hydrophobic profiles constructed from such scales are noisy for several reasons (2); this is always true, but it is especially apparent for repeat proteins. Profiles constructed by using the MZ scale based on SOC are different.…”

“…Indeed two independent alignments of transportin yielded results that shared many common features, but also exhibited significant differences (9,15). These differences can be analyzed by using the exact MZ hydrophobicity scale, constructing profiles of the proposed units, and comparing them for consecutive consistency, the idea being that maximum stability is associated with minimum repeat hydroplasticity (2).…”

Anti-Icing Superhydrophobic Surfaces: Controlling Entropic Molecular Interactions to Design Novel Icephobic Concrete

“…According to the authors of [45,46], protein folding governed by the hydrophobic forces is controlled by SOC, which is a universal feature of hydrophobic interactions present during both wetting of hydrophobic surfaces and protein folding. Furthermore, folding of proteins is thought to be the main driving force of the evolution on the gene level [47], which also demonstrates power law and fractal quantitative behavior [48].…”