Fractals and self-organized criticality in proteins

Phillips, J. C.

doi:10.1016/j.physa.2014.08.034

Cited by 43 publications

(67 citation statements)

References 43 publications

(72 reference statements)

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“…+ 16], including condensed matter theory [WWAM06], economics [BPR15,SW94], epidemiology [SMM14], evolutionary biology [Phi14], high-energy astrophysics [Asc11,MTN94], materials science [RAM09], neuroscience [BdACA + 16, LHG07], statistical physics [Dha06,Man91], seismology [SS89], and sociology [KG09]. A stochastic process is a selforganized critical system if it naturally evolves to highly imbalanced critical states where slight local disturbances can completely alter the current state.…”

Section: Introductionmentioning

confidence: 99%

Nearly Tight Bounds for Sandpile Transience on the Grid

Durfee

Fahrbach

Gao

et al. 2018

Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms

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We use techniques from the theory of electrical networks to give nearly tight bounds for the transience class of the Abelian sandpile model on the two-dimensional grid up to polylogarithmic factors. The Abelian sandpile model is a discrete process on graphs that is intimately related to the phenomenon of self-organized criticality. In this process, vertices receive grains of sand, and once the number of grains exceeds their degree, they topple by sending grains to their neighbors. The transience class of a model is the maximum number of grains that can be added to the system before it necessarily reaches its steady-state behavior or, equivalently, a recurrent state. Through a more refined and global analysis of electrical potentials and random walks, we give an O(n 4 log 4 n) upper bound and an Ω(n 4 ) lower bound for the transience class of the n × n grid. Our methods naturally extend to n d -sized d-dimensional grids to give O(n 3d−2 log d+2 n) upper bounds and Ω(n 3d−2 ) lower bounds.

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Section: Introductionmentioning

confidence: 99%

Nearly Tight Bounds for Sandpile Transience on the Grid

Durfee

Fahrbach

Gao

et al. 2018

Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms

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“…There are secondary effects associated with longitudinal hydrogen bonding (α helices) and transverse hydrogen bonding (β strands), and even weaker charge effects, but in most proteins the dominant physico-chemical factor in a kinetic property such as aggregation [3] is hydropathic interactions.…”

Section: Introductionmentioning

confidence: 99%

“…Since 2007, the classical 1982 KD Ψ scale has been cited > 3300 times, while the modern MZ Ψ scale has been cited only 1% as often. The differences between the two Ψ scales, although small, lead not only to the large universal muton effects discussed here, but even larger differences for specific proteins [3]. In specific applications, modern bioinformatic scaling methods can advance the development of biomedically important subjects, such as a simple blood test for early cancer detection (arXiv 1509.01577).…”

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confidence: 95%

“…The present results show that all hydropathicity scales are not equal. The modern 2007 MZ fractal scale is much more accurate than the standard classic KD scale in describing the evolution of lysozyme c [3]. Similarly epitope analysis and dimensional compression are more accurate than phylogenetic trees in identifying clusters of rapidly drifting viral strains, the critical factor in engineering effective H3N2 vaccines [7][8][9] and arXiv 1510.00488.…”

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confidence: 99%

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Hidden thermodynamic information in protein amino acid mutation tables

Phillips

2017

Physica A: Statistical Mechanics and its Applications

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We combine the standard 1992 20x20 substitution matrix based on block alignment, BLOSUM62, with the standard 1982 amino acid hydropathicity scale KD as well as Protein amino acid sequences (aas) are rich in information, especially when combined with structural data. There are many Web-based tools for analyzing aas, but by far the most utilized is BLAST (Basic Local Alignment Search Tool), which compares two given sequences, or searches for sequences similar to a given sequence. The original BLAST paper[1] was the most highly cited paper published in the 1990s. A key BLAST element is the "substitution matrix", which assigns a score for aligning any possible pair of residues, and identifies "positive" mutations between similar aas. The BLOSUM62 matrix (available online) is the default for most BLAST programs [2]. It obtains mutation rates Γ of aa pairs from protein blocks (distantly related but conserved regions), which leads to accurate homological lists of functionally similar protein blocks.Competing effects of hydrophobic and hydrophilic segments of a given protein have long been known to be the primary driving force behind the folding of protein chains into protein globules. There are secondary effects associated with longitudinal hydrogen bonding (α helices) and transverse hydrogen bonding (β strands), and even weaker charge effects, but in most proteins the dominant physico-chemical factor in a kinetic property such as aggregation [3] is hydropathic interactions.

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“…14 Mutations in lysozyme c are associated with amyloidosis. 14 Recently bioinformatic scales of α helicity and β strand propensities, separated into different values for exposed and buried residues, have appeared, based again on surveys of thousands of PDB structures. 20 Can these propensity scales recognize the 13-mer sandwich structure ( Figure 1)?…”

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confidence: 99%

Thermodynamic Description of Beta Amyloid Formation Using Physicochemical Scales and Fractal Bioinformatic Scales

Phillips

2015

ACS Chem. Neurosci.

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Protein function depends on both protein structure and amino acid (aa) sequence. Here we show that modular features of both structure and function can be quantified economically from the aa sequences alone for the small (40,42 aa) plaque-forming (aggregative) amyloid beta fragments. Some edge and center features of the fragments are predicted. Bioinformatic scales based on β strand formation propensities and the thermodynamically second order fractal hydropathicity scale based on evolutionary optimization (self-organized criticality) are contrasted with the standard first order physicochemical scale based on complete protein (water-air) unfolding. The results are consistent with previous studies of these physicochemical factors that show that aggregative properties, even of beta fragments, are driven primarily by near-equilibrium hydropathic forces.

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Fractals and self-organized criticality in proteins

Cited by 43 publications

References 43 publications

Nearly Tight Bounds for Sandpile Transience on the Grid

Nearly Tight Bounds for Sandpile Transience on the Grid

Hidden thermodynamic information in protein amino acid mutation tables

Thermodynamic Description of Beta Amyloid Formation Using Physicochemical Scales and Fractal Bioinformatic Scales

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