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Phase transition theory, implemented quantitatively by thermodynamic scaling, has explained the evolution of Coronavirus extremely high contagiousness caused by a few key mutations from CoV2003 to CoV2019 identified among hundreds, as well as the later 2021 evolution to Omicron caused by 30 mutations. It also showed that the 2022 strain BA.5 with five mutations began a new path. Here we show that the early 2023 strains BKK with one stiffening mutation confirm that path, and the single flexing mutation of a later 2023 variant EG.5 strengthens it further. The few mutations of the new path have greatly reduced pandemic deaths, for mechanical reasons proposed here., Comment: 5 pages, 1 figure

Rhodopsin is a G-protein coupled receptor found in retinal rod cells, where it mediates monocrhromatic vision in dim light. It is one of the most studied proteins with thousands of reviewed entries in Uniprot. It has seven transmembrane segments, here examined for their hydrophobic character, and how that has evolved from chickens to humans. Elastic features associated with Proline are also discussed. Finally, differences between rhodopsin and cone opsins are also discussed., Comment: 11 pages, 5 figures, 1 table

TRPC(3,6) are two ~ 930 amino acid membrane proteins that form calcium permeant cation channels. Here we examine the differences between mammals and oviparous species. Our method is based on the concept of evolution towards criticality, a general concept we have previously applied to many proteins, especially in describing the evolution of pandemic sequences through natural selection., Comment: 7 pages, two figures

The major intrinsic protein (MIP) of the lens fiber cell membrane plays a role in lens biogenesis and maintenance. Its polypeptide chains span the membrane six times, and the protein is naturally divided into two halves. We use modern sequence analysis to identify differences between halves for humans (common to animals) and chickens (common to birds)., Comment: 6 pages, 1 Figure

Because of their large size and widespread mechanosensitive interactions the only recently discovered titled transmembrane proteins have attracted much attention. Here we present and discuss their hydropathic profiles using a new method of sequence analysis. We find large-scale similarities and differences not obtainable by conventional sequence or structural studies. These differences support the evolution-towards-criticality conjecture popular among physicists., Comment: 10 page, two figures

Structural Maintenance of Chromosomes, SMCs, proteins have long rod like structures immersed in water. Here we use our hydroanalytic methods based on amino acid sequences to discuss their dynamics at multiple length scales identified by evolution. The length scales are 10 to 100 times longer than used in normal studies of sequence evolution. Their hydropathic profiles exhibit many features unique to their structure and function., Comment: 1 pages, 12 figures, 1 table

In 2022 new subvariants of Coronavirus appeared in South Africa, and spread rapidly to other parts of the world. The effects of selective evolution on increasing the already high contagiousness of CoV19 up to Omicron were previously discussed with high accuracy using concepts new to molecular biology (from mathematics and physics) that have been developed over the last few decades. Here we discuss the new subvariants, and find novel features successfully combining both improved flexibility and improved stability., Comment: 9 pages, 2 figures, 1 table

Here we examine the evolution of beta-2 microglobulin in terms of its hydropathic shapes, a theoretical construct that has revealed important trends. The dynamics of many proteins are largely driven by interactions between the protein itself and the thin water film that covers it. \b{eta}2m constitutes the basic building unit of the immunoglobulin superfamily; the evolution of its amino acid sequences from chickens to mice to humans provides new information about its multiple functions. Our hydrodynamic method involves concepts of topological shape evolution towards a critical point for optimized functions. The results are in excellent agreement with experiment for the details of the mouse-human evolution, as well as both the dangerous natural amyloid aggregation mutation D76N, and six other DN test mutations., Comment: 10 pages, 4 figures

Evolution of the amino acid sequences of transthyretin (TTR) can provide additional information about its dynamics that both complements and extends the already extensive static structural data. Protein dynamics is largely driven by interactions between the protein itself and the thin water film that covers it. Here those interactions are connected to profiles of water waves connecting domain pivots (hydrophobic extrema), as well as a broad hydrophilic central hinge region that has evolved to provide human TTR with greater flexibility and stability. This central region has a density of single mutations related to amyloid polyneuropathy that is three times higher than other regions., Comment: 9 pages 3 figures 1 table

Improvement of protein function by evolution (natural selection) is expected on general grounds, but even with the modern database positive proof has remained a difficult problem for theory. Here we extend our recent analysis of the evolution of CoV-1 to much more contagious CoV-2, to Omicron, which appears to be qualitatively different from other recent strains like Delta. Overall the synchronized dynamics of Omicron is more elaborate than CoV-2 or its variants like Delta. The surprising result is that while Omicron could be more contagious than even Delta, it is probably much less dangerous, Comment: 10 pages, 5 figures

Spike proteins, 1200 amino acids, are divided into two nearly equal parts, S1 and S2. We review here phase transition theory, implemented quantitatively by thermodynamic scaling. The theory explains the evolution of Coronavirus extremely high contagiousness caused by a few mutations from CoV2003 to CoV2019 identified among hundreds in S1. The theory previously predicted the unprecedented success of spike-based vaccines. Here we analyze impressive successes by McClellan et al., 2020, in stabilizing their original S2P vaccine to Hexapro. Hexapro has expanded the two proline mutations of S2P, 2017, to six combined proline mutations in S2. Their four new mutations are the result of surveying 100 possibilities in their detailed structure-based context Our analysis, based on only sparse publicly available data, suggests new proline mutations could improve the Hexapro combination to Octapro or beyond., Comment: 8 pages

The titled subject has attracted much interest. Here we summarize the substantial results obtained by a physical model of protein evolution based on hydropathic domain dynamics. In a recent Letter eighteen biologists suggested that the titled subject should be studied in a way inclusive of broad expertise (1). There is an even broader view that has been developed over several decades by physicists (2,3). This view is based on analyzing amino acid sequences of proteins. These sequences are now available on-line at Uniprot, and represent a treasure-trove of data (4)., Comment: 2 pages, no figures or tables

We review the development of thermodynamic protein hydropathic scaling theory, starting from backgrounds in mathematics and statistical mechanics, and leading to biomedical applications. Darwinian evolution has organized each protein family in different ways, but dynamical hydropathic scaling theory is both simple and effective in providing readily transferable dynamical insights for many proteins represented in the uncounted amino acid sequences, as well as the 90 thousand static structures contained in the online Protein Data Base. Critical point theory is general, and recently it has proved to be the most effective way of describing protein networks that have evolved towards nearly perfect functionality in given environments, self-organized criticality. Darwinian evolutionary patterns are governed by common dynamical hydropathic scaling principles, which can be quantified using scales that have been developed bioinformatically by studying thousands of static PDB structures. The most effective dynamical scales involve hydropathic globular sculpting interactions averaged over length scales centered on domain dimensions. A central feature of dynamical hydropathic scaling theory is the characteristic domain length associated with a given protein functionality. Evolution has functioned in such a way that the minimal critical length scale established so far is about nine amino acids, but in some cases it is much larger. Some ingenuity is needed to find this primary length scale, as shown by the examples discussed here. Often a survey of the Darwinian evolution of a protein sequence suggests a means of determining the critical length scale. The evolution of Coronavirus is an interesting application; it identifies critical mutations., Comment: 93 pages, 37 figures. This is a review article that highlights the main ideas from arXiv:1610.04116

CoV2019 has evolved to be much more dangerous than CoV2003. Experiments suggest that structural rearrangements dramatically enhance CoV2019 activity. We identify a new first stage of infection that precedes structural rearrangements by using biomolecular evolutionary theory to identify sequence differences enhancing viral attachment rates. We find a small cluster of four single mutations which show that CoV-2 has a new feature that promotes much stronger viral attachment and enhances contagiousness. The extremely dangerous dynamics of human coronavirus infection is a dramatic example of evolutionary approach of self-organized networks to criticality. It may favor a very successful vaccine. The identified mutations can be used to test the present theory experimentally. The theory also works well for the newer strains and explains their increased contagiousness., Comment: 15 pages, 4 figures, 1 table

Intelligence is often discussed in terms of neural networks in the cerebral cortex, whose evolution has presumably been influenced by Darwinian selection. Here we present molecular evidence that one of the many kinesin motors, Kif14, has evolved to exhibit special features in its amino acid sequence that could have evolved to improve neural networks. The improvement is quantified by comparison of Kif14 sequences for 12 species. The special feature is level sets of hydrophobic extrema in water wave profiles based on several hydropathic scales. The most effective scale is a new one based on fractals, indicative of approach of globular curvatures to self-organized criticality., Comment: 7 pages, 1 figure, 1 table

Cytoskeletons are self-organized networks based on polymerized proteins: actin, tubulin, and driven by motor proteins, such as myosin, kinesin and dynein. Their positive Darwinian evolution enables them to approach optimized functionality (self-organized criticality). The principal features of the eukaryotic evolution of the cytoskeleton motor protein myosin-1 parallel those of actin and tubulin, but also show striking differences connected to its dynamical function. Optimized (long) hydropathic waves characterize the molecular level Darwinian evolution towards optimized functionality (self-organized criticality). The N-terminal and central domains of myosin-1 have evolved in eukaryotes at different rates, with the central domain hydropathic extrema being optimally active in humans. A test shows that hydropathic scaling can yield accuracies of better than 1% near optimized functionality. Evolution towards synchronized level extrema is connected to a special function of Mys-1 in humans involving Golgi complexes., Comment: 20 pages, 9 figures

What is life. Schrodingers question is discussed here for a specific protein, villin, which builds cells in tissues that detect taste and sound. Villin is represented by a sequence of 827 amino acids bound to a peptide backbone chain. We focus attention on a limited problem, the Darwinian evolution of villin sequences from chickens to humans. This biophysical problem is analyzed using a new physicical method based on thermodynamic domain scaling, a technique that bridges the gap between physical concepts, self-organized criticality, and conventional biostructural practice. It turns out that the evolutionary changes can be explained by Darwinian selection, which is not generally accepted by biologists at the protein level. The presentation is self-contained, and requires no prior experience with proteins at the molecular level., Comment: 7 pages, 3 figures

CoV2019 has evolved to be much more dangerous than CoV2003. Experiments suggest that structural rearrangements dramatically enhance CoV2019 activity. We identify a new first stage of infection which precedes structural rearrangements by using biomolecular evolutionary theory to identify sequence differences enhancing viral attachment rates. We find a small cluster of mutations which show that CoV-2 has a new feature that promotes much stronger viral attachment and enhances contagiousness. The extremely dangerous dynamics of human coronavirus infection is a dramatic example of evolutionary approach of self-organized networks to criticality. It may favor a very successful vaccine. The identified mutations can be used to test the present theory experimentally., Comment: 11 pages, 4 figures

Cytoskeletons are self-organized networks based on polymerized proteins: actin, tubulin, and driven by motor proteins, such as myosin, kinesin and dynein. Their positive Darwinian evolution enables them to approach optimized functionality (self-organized criticality). Our theoretical analysis uses hydropathic waves to identify and contrast the functional differences between the polymerizing $\alpha$ and $\beta$ tubulin monomers, which are similar in length and secondary structures, as well as having indistinguishable phylogenetic trees. We show how evolution has improved water-driven flexibility especially for $\alpha$ tubulin, and thus facilitated heterodimer microtubule assembly, in agreement with recent atomistic simulations and topological models. We conclude that the failure of phylogenetic analysis to identify functionally specific positive Darwinian evolution has been caused by 20th century technical limitations. These are overcome using 21st century quantitative mathematical methods based on thermodynamic scaling and hydropathic modular averaging. Our most surprising result is the identification of large level sets, especially in hydrophobic extrema, with both thermodynamically first- and second-order scaled water waves. Our calculations include explicitly long-range water-protein interactions described by fractals. We also suggest a much-needed corrective for large protein drug development costs., Comment: 17 pages, 5 figures

Thermodynamic profiles, based on bioinformatic hydropathicity scales and membrane-fitted sliding windows, exhibit accurately level sets of hydrophobic peaks or valleys in the constant fragment Fc of monoclonal antibodies. These sets provide a roadmap for selected short regions where a few directed amino acid mutations could produce either accelerated antibody kinetics or increased stability. These profiles may reveal dramatic differences in antibody activity, Comment: 15 pages, 5 figures

Cytoskeletons are self organized networks based on polymerized proteins, actin, tubulin, and driven by motor proteins, such as myosin, kinesin and dynein. Their positive Darwinian evolution enables them to approach optimized functionality self organized criticality. Dynein has three distinct titled subunits, but how these units connect to function as a molecular motor is mysterious. Dynein binds to tubulin through two coiled coil stalks and a stalk head. The energy used to alter the head binding and propel cargo along tubulin is supplied by ATP at a ring 1500 amino acids away., Comment: 17 pages,6 figures

Amyloid precursor with 770 amino acids dimerizes and aggregates, as do its c terminal 99 amino acids and amyloid 40,42 amino acids fragments. The titled question has been discussed extensively, and here it is addressed further using thermodynamic scaling theory to analyze mutational trends in structural factors and kinetics. Special attention is given to Family Alzheimer's Disease mutations outside amyloid 42. The scaling analysis is connected to extensive docking simulations which included membranes, thereby confirming their results and extending them to Amyloid precursor., Comment: 11 pages, 3 figures, 1 table

Ubiquitin tags diseased proteins and initiates an enzyme conjugation cascade, which has three stages. The first-stage enzyme Uba1 (E1) has evolved only modestly from slime mold to humans, and is > 14 times larger than Ub. Here we use critical point thermodynamic scaling theory to connect Uba1 (E1) evolution from yeast and slime mold to fruit flies and humans to subtle changes in its amino acid sequences., Comment: 12 pages, 6 figures

Ubiquitin, discovered less than 50 years ago, tags thousands of diseased proteins for destruction. It is small (only 76 amino acids), and is found unchanged in mammals, birds, fish and even worms. Key features of its functionality are identified here using critical point thermodynamic scaling theory. These include Fano interference between first- and second-order elements of globular surface shape transitions. Comparison with its closest relative, 76 amino acid Nedd8, shows that the latter lacks these features. A cracked elastic network model is proposed for the common target shared by many diseased proteins., Comment: 11pages, 4 figures

Thermodynamic scaling theory, previously applied mainly to small proteins, here analyzes quantitative evolution of the titled functional network giant hub enzymes. The broad domain structure identified homologically is confirmed hydropathically using amino acid sequences only. The most surprising results concern the evolution of the tyrosine kinase globular surface roughness from avian to mammals, which is first order, compared to the evolution within mammals from rodents to humans, which is second order. The mystery of the unique amide terminal region of proto oncogene tyrosine protein kinase is resolved by the discovery there of a septad targeting cluster, which is paralleled by an octad catalytic cluster in tyrosine kinase in humans and a few other species. These results, which go far towards explaining why these proteins are among the largest giant hubs in protein interaction networks, use no adjustable parameters., Comment: 18 pages, 8 figures

Here we review the development of protein scaling theory, starting from backgrounds in mathematics and statistical mechanics, and leading to biomedical applications. Evolution has organized each protein family in different ways, but scaling theory is both simple and effective in providing readily transferable dynamical insights complementary for many proteins represented in the 90 thousand static structures contained in the online Protein Data Base (PDB). Scaling theory is a simplifying magic wand that enables one to search the hundreds of millions of protein articles in the Web of Science, and identify those proteins that present new cost-effective methods for early detection and/or treatment of disease through individual protein sequences (personalized medicine). Critical point theory is general, and recently it has proved to be the most effective way of describing protein networks that have evolved towards nearly perfect functionality in given environments (self-organized criticality). Evolutionary patterns are governed by common scaling principles, which can be quantified using scales that have been developed bioinformatically by studying thousands of PDB structures. The most effective scales involve either hydropathic globular sculpting interactions averaged over length scales centered on membrane dimensions, or exposed beta strand propensities associated with aggregative (strong) protein-protein interactions., Comment: 53 pages, 16 figures

Thermodynamic scaling explains the dramatic successes of CTP fused human growth proteins as regards lifetime in vivo and enhanced functionality compared to their wild-type analogues, like Biogen. The theory is semi-quantitative and contains no adjustable parameters. It shows how hydrophilic terminal spheres orient fused proteins in the neighborhood of a membrane surface, extending lifetimes and improving functionality., Comment: 9 pages, 5 figures

To be cost-effective, biomedical proteins must be optimized with regard to many factors. Road maps are customary for large-scale projects, and here descriptive methods based on bioinformatic fractal thermodynamic scales are tested against an important example, HPV vaccine. Older scales from before 2000 are found to yield inconclusive results, but modern bioinformatic scales are amazingly accurate, with a high level of internal consistency, and little ambiguity., Comment: 7 pages, 2 figures

The most cost-effective blood-based, noninvasive molecular cancer biomarkers are based on p53 epitopes and MUC1 tandem repeats. Here we use dimensionally compressed bioinformatic fractal scaling analysis to compare the two distinct and comparable probes, which examine different sections of the autoantibody population, achieving combined sensitivities of order 50%. We discover a promising MUC1 epitope in the SEA region outside the tandem repeats., Comment: 13 pages, 7 figures

Hemoglobin (Hgb) forms tetramers (dimerized dimers), which enhance its globular stability and may also facilitate small gas molecule transport, as shown by recent all-atom Newtonian solvated simulations. Hydropathic bioinformatic scaling reveals many wave-like features of strained Hgb structures at the coarse-grained amino acid level, while distinguishing between these features thermodynamically. Strain fields localized near hemes interfere with extended strain fields associated with dimer interfacial misfit, resulting in wave-length dependent dimer correlation function antiresonances., Comment: 10 pages, 4 figures

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 the modern 2007 hydropathicity scale MZ, and compare the results. The 20-parameter KD and MZ hydropathicity scales have different thermodynamic character, corresponding to first and second order transitions. The KD and MZ comparisons show that the mutation rates reflect quantitative iteration of qualitative amino acid phobic and philic binary 2x10 properties that define quaternary 4x5 subgroups (but not quinary 5x4 subgroups), with the modern MZ bioinformatic scale giving much better results. The quaternary 5 mer MZ 4x5 subgroups are called mutons (Mu5)., Comment: 14 pages, 4 figures, 4 tables

Minimizing time delays in manufacturing vaccines appropriate to rapidly mutating viruses is the key step for improving vaccine effectiveness. The vaccine for the H3N2 flu type has failed for the last two years (~ 15% effective). Here we summarize the state of the predictive art and report the most current results for H3N2 flu vaccine design. Using a 2006 model of dimensional reduction of viral mutational complexity, we show that this model can reduce vaccine time delays by a year or more in some cases., Comment: 9 pages, 2 fgures

Allosteric (long-range) interactions can be surprisingly strong in proteins of biomedical interest. Here we use bioinformatic scaling to connect prior results on nonsteroidal anti-inflammatory drugs to promising new drugs that inhibit cancer cell metabolism. Many parallel features are apparent, which explain how even one amino acid mutation, remote from active sites, can alter medical results. The enzyme twins involved are cyclooxygenase (aspirin) and isocitrate dehydrogenase (IDH). The IDH results are accurate to 1% and are overdetermined by adjusting a single bioinformatic scaling parameter. It appears that the final stage in optimizing protein functionality may involve leveling of the hydrophobic cutoffs of the arms of conformational hydrophilic hinges., Comment: 12 pages, 5 figures

There is an urgent need for economical blood based, noninvasive molecular biomarkers to assist in the detection and diagnosis of cancers in a cost effective manner at an early stage, when curative interventions are still possible. Serum autoantibodies are attractive biomarkers for early cancer detection, but their development has been hindered by the punctuated genetic nature of the ten million known cancer mutations. A recent study of 50,000 patients (Pedersen et al., 2013) showed p53 15mer epitopes are much more sensitive colon cancer biomarkers than p53, which in turn is a more sensitive cancer biomarker than any other protein. The function of p53 as a nearly universal tumor suppressor is well established, because of its strong immunogenicity in terms of not only antibody recruitment, but also stimulation of autoantibodies. Here we examine bioinformatic fractal scaling analysis for identifying sensitive epitopes from the p53 amino acid sequence, and show how it could be used for early cancer detection (ECD). We trim 15mers to 7mers, and identify specific 7mers from other species that could be more sensitive to aggressive human cancers, such as liver cancer., Comment: 20 pages, 12 figures

More virulent strains of influenza virus subtypes H1N1 appeared widely in 2007 and H3N2 in 2011, and especially 2013-4, when the effectiveness of the H3N2 vaccine decreased nearly to zero. The amino acid differences of neuraminidase from prior less virulent strains appear to be small (<1%) when tabulated through sequence alignments and counting site identities and similarities. Here we show how analyzing fractal hydropathic forces responsible for neuraminidase globular compaction and modularity quantifies the mutational origins of increased virulence. It also predicts vaccine escape and specifies optimized targets for the 2015 H3N2 vaccine different from the WHO target. Unlike some earlier methods based on measuring hemagglutinin antigenic drift and ferret sera, which take several years, cover only a few candidate strains, and are ambiguous, the new methods are timely and can be completed, using NCBI and GISAID amino acid sequences only, in a few days., Comment: 12 pages, 3 figures

When a granular mixture involving grains of different sizes is shaken, sheared, mixed, or left to flow, grains tend to separate by sizes in a process known as size segregation. In this study, we explore the size segregation mechanism in granular chute flows in terms of pressure distribution and granular micro-structure. Therefore, 2D discrete numerical simulations of bi-disperse granular chute flows are systematically analysed. Based on the theoretical models by Gray and Thornton 2005 and Hill and Tan 2014, we explore the stress partition in the phases of small and large grains, discriminating between contact stresses and kinetic stresses. Our results support both gravity-induced and shear-gradient-induced segregation mechanisms. However, we show that the contact stress partition is extremely sensitive to the definition of the partial stress tensors, and more specifically, to the way mixed contacts (i.e. involving a small grain and a large grain) are handled, making conclusions on gravity-induced segregation uncertain. By contrast, the computation of the partial kinetic stress tensors is robust. Kinetic pressure partition exhibits a deviation from continuum mixture theory of a significantly larger amplitude than contact pressure, and display a clear dependence on the flow dynamics. Finally, using a simple approximation for the contact partial stress tensors, we investigate how contact stress partition relates with the flow micro-structure, and suggest that the latter may provide an interesting proxy for studying gravity-induced segregation., Comment: 8 pages, 6 figures, regular article

In early 2014 an outbreak of a slightly mutated Zaire Ebola subtype appeared in West Africa which is less virulent than 1976 and 1994 strains. The numbers of cases per year appear to be ~ 1000 times larger than the earlier strains, suggesting a greatly enhanced transmissibility. Although the fraction of the 2014 spike glycoprotein mutations is very small (~3%), the mortality is significantly reduced, while the transmission appears to have increased strongly. Bioinformatic scaling had previously shown similar inversely correlated trends in virulence and transmission in N1 (H1N1) and N2 (H3N2) influenza spike glycoprotein mutations. These trends appear to be related to various external factors (migration, availability of pure water, and vaccination programs). The molecular mechanisms for Ebola's mutational response involve mainly changes in the disordered mucin-like domain (MLD) of its spike glycoprotein amino acids. The MLD has been observed to form the tip of an oligomeric amphiphilic wedge that selectively pries apart cell-cell interfaces via an oxidative mechanism., Comment: arXiv admin note: text overlap with arXiv:1410.1417

Thermodynamic tools are well suited to connecting evolution of protein functionalities to mutations of amino acid sequences, especially for neuronal network structures. These tools enable one to quantify changes in modular structure and correlate them with corresponding changes in observable properties. Here we quantify modular rodent-primate changes in amyloid precursor protein A4 and \b{eta} amyloid fragments. These are related to changes in cortical connectivity and to the presence (absence) of plaque formation in primates (rodents). Two thermodynamic scales are used, descriptive of water/air protein unfolding (old), or fractal conformational restructuring (new). These describe complementary aspects of protein activity, at respectively higher and lower effective temperatures.

More virulent strains of influenza virus subtypes H1N1 appeared in 2007 and H3N2 in 2011. The amino acid differences from prior less virulent strains appear to be small when tabulated through sequence alignments and counting site identities and similarities. Here we show how analyzing fractal hydropathic forces responsible for globular compaction and modularity quantifies the mutational origins of increased virulence, and also analyzes receptor sites and N-linked glycan accretion.

Leading Ebola subtypes exhibit a wide mortality range, here explained at the molecular level by using fractal hydropathic scaling of amino acid sequences based on protein self-organized criticality. Specific hydrophobic features in the hydrophilic mucin-like domain suffice to account for the wide mortality range. Significance statement: Ebola virus is spreading rapidly in Africa. The connection between protein amino acid sequence and mortality is identified here.

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 from the aa sequences alone for the small (40,42 aa) plaque-forming amyloid beta fragments. Some edge and center features of the fragments are predicted. Contrasting results from the second order hydropathicity scale based on evolutionary optimization (self-organized criticality) and the first order scale based on complete protein (water-air) unfolding show that fragmentation has mixed first- and second-order character., Comment: 12 pages, 5 figures

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 from the aa sequence alone for the amyloid 770 aa precursor protein A4. Both the new second order hydropathicity scale, based on evolutionary optimization (self-organized criticality), and the standard first order scale, based on complete protein (water-air) unfolding, yield thermodynamically significant features of amyloid function related to spinodal decomposition into modules. Spinodal crossings are marked by breaks in slope of algebraic functions of aa sequences. The new scale is associated with a lower effective temperature than the standard scale., Comment: 8 pages, 2 figures, calculation improved

Hemagglutinin (HA) and neuraminidase (NA) are highly variable envelope glycoproteins. Here hydropathic analysis, previously applied to quantify common flu (H1N1) evolution (1934-), is applied to the evolution of less common but more virulent (avian derived) H3N2 (1968-), beginning with N2. Whereas N1 exhibited opposing migration and vaccination pressures, the dominant N2 trend is due to vaccination, with only secondary migration interactions. Separation and evaluation of these effects is made possible by the use of two distinct hydropathic scales representing first-order and second-order thermodynamic interactions. The evolutions of H1 and H3 are more complex, with larger competing migration and vaccination effects. The linkages of H3 and N2 evolutionary trends are examined on two modular length scales, medium (glycosidic) and large (corresponding to sialic acid interactions). The hierarchical hydropathic results complement and greatly extend advanced phylogenetic results obtained from similarity studies. They exhibit simple quantitative trends that can be transferred to engineer oncolytic properties of other viral proteins to treat recalcitrant cancers.

While the concepts involved in Self-Organized Criticality have stimulated thousands of theoretical models, only recently have these models addressed problems of biological and clinical importance. Here we outline how SOC can be used to engineer hybrid viral proteins whose properties, extrapolated from those of known strains, may be sufficiently effective to cure cancer.

Influenza virus contains two highly variable envelope glycoproteins, hemagglutinin (HA) and neuraminidase (NA). The structure and properties of HA, which is responsible for binding the virus to the cell that is being infected, change significantly when the virus is transmitted from avian or swine species to humans. Previously we identified much smaller human individual evolutionary amino acid mutational changes in NA, which cleaves sialic acid groups and is required for influenza virus replication. We showed that these smaller changes can be monitored very accurately across many Uniprot and NCBI strains using hydropathicity scales to quantify the roughness of water film packages, which increases gradually due to migration, but decreases abruptly under large-scale vaccination pressures. Here we show that, while HA evolution is much more complex, it still shows abrupt punctuation changes linked to those of NA. HA exhibits proteinquakes, which resemble earthquakes and are related to hydropathic shifting of sialic acid binding regions. HA proteinquakes based on sialic acid interactions are required for optimal balance between the receptor-binding and receptor-destroying activities of HA and NA for efficient virus replication. Our comprehensive results present an historical (1945-2011) panorama of HA evolution over thousands of strains, and are consistent with many studies of HA and NA interactions based on a few mutations of a few strains. While the common influenza virus discussed here has been rendered almost harmless by decades of vaccination programs, the sequential decoding lessons learned here are applicable to other viruses that are emerging as powerful weapons for controlling and even curing common organ cancers. Those engineered oncolytic drugs will be discussed in future papers.

Influenza virus contains two highly variable envelope glycoproteins, hemagglutinin (HA) and neuraminidase (NA). The structure and properties of HA, which is responsible for binding the virus to the cell that is being infected, change significantly when the virus is transmitted from avian or swine species to humans. Here we focus on much smaller human individual evolutionary amino acid mutational changes in NA, which cleaves sialic acid groups and is required for influenza virus replication. We show that very small amino acid changes can be monitored very accurately across many Uniprot and NCBI strains using hydropathicity scales to quantify the roughness of water film packages. Quantitative sequential analysis is most effective with the differential hydropathicity scale based on protein self-organized criticality (SOC). NA exhibits punctuated evolution at the molecular scale, millions of times smaller than the more familiar species scale, and thousands of times smaller than the genomic scale. Our analysis shows that large-scale vaccination programs have been responsible for a very large convergent reduction in influenza severity in the last century, a reduction which is hidden from short-term studies of vaccine effectiveness. Hydropathic analysis is capable of interpreting and even predicting trends of functional changes in mutation prolific viruses.

The behavior of disease-linked mutations of membrane proteins is especially simple in rhodopsin, where they are well-studied, as they are responsible for retinitis pigmentosa, RP (retinal degeneration). Here we show that the frequency of occurrence of single RP mutations is strongly influenced by their posttranslational survival rates, and that this survival correlates well (82%) with a long-range, non-local hydropathic measure of the roughness of the water interfaces of ex-membrane rhodopsin based on self-organized criticality (SOC). It is speculated that this concept may be generally useful in studying survival rates of many mutated proteins.