An evolutionary theory on virus mutation in COVID-19.

With the rapid evolution of SARS-CoV-2, the emergence of new strains is an intriguing question. This paper presents an evolutionary theory to analyze the mutations of the virus and identify the conditions that lead to the generation of new strains. We represent the virus variants using a 4-letter sequence based on amino acid mutations on the spike protein and employ an n-distance algorithm to derive a variant phylogenetic tree. We show that the theoretically-derived tree aligns with experimental data on virus evolution. Additionally, we propose an A-X model, utilizing the set of existing mutation sites (A) and a set of randomly generated sites (X), to calculate the emergence of new strains. Our findings demonstrate that a sufficient number of random iterations can predict the generation of new macro-lineages when the number of sites in X is large enough. These results provide a crucial theoretical basis for understanding the evolution of SARS-CoV-2.

Competitive Chemical Reaction Kinetic Model of Nucleosome Assembly Using the Histone Variant H2A.Z and H2A In Vitro.

Nucleosomes not only serve as the basic building blocks for eukaryotic chromatin but also regulate many biological processes, such as DNA replication, repair, and recombination. To modulate gene expression in vivo, the histone variant H2A.Z can be dynamically incorporated into the nucleosome. However, the assembly dynamics of H2A.Z-containing nucleosomes remain elusive. Here, we demonstrate that our previous chemical kinetic model for nucleosome assembly can be extended to H2A.Z-containing nucleosome assembly processes. The efficiency of H2A.Z-containing nucleosome assembly, like that of canonical nucleosome assembly, was also positively correlated with the total histone octamer concentration, reaction rate constant, and reaction time. We expanded the kinetic model to represent the competitive dynamics of H2A and H2A.Z in nucleosome assembly, thus providing a novel method through which to assess the competitive ability of histones to assemble nucleosomes. Based on this model, we confirmed that histone H2A has a higher competitive ability to assemble nucleosomes in vitro than histone H2A.Z. Our competitive kinetic model and experimental results also confirmed that in vitro H2A.Z-containing nucleosome assembly is governed by chemical kinetic principles.

Mathematical Modelling of Virus Spreading in COVID-19.

A mathematical model is proposed to analyze the spreading dynamics of COVID-19. By using the parameters of the model, namely the basic reproduction number (R0) and the attenuation constant (k), the daily number of infections (DNI) and the cumulative number of infections (CNI) over time (m) are deduced and shown to be in good agreement with experimental data. This model effectively addresses three key issues: (1) inferring the conditions under which virus infections die out for a specific strain given R0; (2) explaining the occurrence of second waves of infection and developing preventive measures; and (3) understanding the competitive spread of two viruses within a region and devising control strategies. The findings highlight the potential of this simple mathematical framework in comprehensively addressing these challenges. The theoretical insights derived from this model can guide the evaluation of infection wave severity and the formulation of effective strategies for controlling and mitigating epidemic outbreaks.

Characterizing Cellular Differentiation Potency and Waddington Landscape via Energy Indicator.

The precise characterization of cellular differentiation potency remains an open question, which is fundamentally important for deciphering the dynamics mechanism related to cell fate transition. We quantitatively evaluated the differentiation potency of different stem cells based on the Hopfield neural network (HNN). The results emphasized that cellular differentiation potency can be approximated by Hopfield energy values. We then profiled the Waddington energy landscape of embryogenesis and cell reprogramming processes. The energy landscape at single-cell resolution further confirmed that cell fate decision is progressively specified in a continuous process. Moreover, the transition of cells from one steady state to another in embryogenesis and cell reprogramming processes was dynamically simulated on the energy ladder. These two processes can be metaphorized as the motion of descending and ascending ladders, respectively. We further deciphered the dynamics of the gene regulatory network (GRN) for driving cell fate transition. Our study proposes a new energy indicator to quantitatively characterize cellular differentiation potency without prior knowledge, facilitating the further exploration of the potential mechanism of cellular plasticity.

Nucleosome Assembly and Disassembly in vitro Are Governed by Chemical Kinetic Principles.

As the elementary unit of eukaryotic chromatin, nucleosomes in vivo are highly dynamic in many biological processes, such as DNA replication, repair, recombination, or transcription, to allow the necessary factors to gain access to their substrate. The dynamic mechanism of nucleosome assembly and disassembly has not been well described thus far. We proposed a chemical kinetic model of nucleosome assembly and disassembly in vitro. In the model, the efficiency of nucleosome assembly was positively correlated with the total concentration of histone octamer, reaction rate constant and reaction time. All the corollaries of the model were well verified for the Widom 601 sequence and the six artificially synthesized DNA sequences, named CS1-CS6, by using the salt dialysis method in vitro. The reaction rate constant in the model may be used as a new parameter to evaluate the nucleosome reconstitution ability with DNAs. Nucleosome disassembly experiments for the Widom 601 sequence detected by Förster resonance energy transfer (FRET) and fluorescence thermal shift (FTS) assays demonstrated that nucleosome disassembly is the inverse process of assembly and can be described as three distinct stages: opening phase of the (H2A-H2B) dimer/(H3-H4)2 tetramer interface, release phase of the H2A-H2B dimers from (H3-H4)2 tetramer/DNA and removal phase of the (H3-H4)2 tetramer from DNA. Our kinetic model of nucleosome assembly and disassembly allows to confirm that nucleosome assembly and disassembly in vitro are governed by chemical kinetic principles.

Intrinsic laws of k-mer spectra of genome sequences and evolution mechanism of genomes.

BACKGROUND: K-mer spectra of DNA sequences contain important information about sequence composition and sequence evolution. We want to reveal the evolution rules of genome sequences by studying the k-mer spectra of genome sequences. RESULTS: The intrinsic laws of k-mer spectra of 920 genome sequences from primate to prokaryote were analyzed. We found that there are two types of evolution selection modes in genome sequences, named as CG Independent Selection and TA Independent Selection. There is a mutual inhibition relationship between CG and TA independent selections. We found that the intensity of CG and TA independent selections correlates closely with genome evolution and G + C content of genome sequences. The living habits of species are related closely to the independent selection modes adopted by species genomes. Consequently, we proposed an evolution mechanism of genomes in which the genome evolution is determined by the intensities of the CG and TA independent selections and the mutual inhibition relationship. Besides, by the evolution mechanism of genomes, we speculated the evolution modes of prokaryotes in mild and extreme environments in the anaerobic age and the evolving process of prokaryotes from anaerobic to aerobic environment on earth as well as the originations of different eukaryotes. CONCLUSION: We found that there are two independent selection modes in genome sequences. The evolution of genome sequence is determined by the two independent selection modes and the mutual inhibition relationship between them.

Statistical analyses of protein folding rates from the view of quantum transition.

Understanding protein folding rate is the primary key to unlock the fundamental physics underlying protein structure and its folding mechanism. Especially, the temperature dependence of the folding rate remains unsolved in the literature. Starting from the assumption that protein folding is an event of quantum transition between molecular conformations, we calculated the folding rate for all two-state proteins in a database and studied their temperature dependencies. The non-Arrhenius temperature relation for 16 proteins, whose experimental data had previously been available, was successfully interpreted by comparing the Arrhenius plot with the first-principle calculation. A statistical formula for the prediction of two-state protein folding rate was proposed based on quantum folding theory. The statistical comparisons of the folding rates for 65 two-state proteins were carried out, and the theoretical vs. experimental correlation coefficient was 0.73. Moreover, the maximum and the minimum folding rates given by the theory were consistent with the experimental results.

Prediction of protein secondary structure using feature selection and analysis approach.

The prediction of the secondary structure of a protein from its amino acid sequence is an important step towards the prediction of its three-dimensional structure. However, the accuracy of ab initio secondary structure prediction from sequence is about 80% currently, which is still far from satisfactory. In this study, we proposed a novel method that uses binomial distribution to optimize tetrapeptide structural words and increment of diversity with quadratic discriminant to perform prediction for protein three-state secondary structure. A benchmark dataset including 2,640 proteins with sequence identity of less than 25% was used to train and test the proposed method. The results indicate that overall accuracy of 87.8% was achieved in secondary structure prediction by using ten-fold cross-validation. Moreover, the accuracy of predicted secondary structures ranges from 84 to 89% at the level of residue. These results suggest that the feature selection technique can detect the optimized tetrapeptide structural words which affect the accuracy of predicted secondary structures.

Measurement of entropy production in living cells under an alternating electric field.

Entropy is a thermodynamic property toward equilibrium based on the dissipation of energy. Cells constitute such a thermodynamic system, in which entropy production is both inevitable and highly significant. Although the experimental measurement of entropy production in a cell is very difficult, a new method to accomplish this in living cells is reported herein. Through heating the sample by alternating electric fields and recording the heat flow from cells, the entropy production in two normal cell lines, MCF10A and HL-7702, and two cancerous cell lines, MDA-MB-231 and SMMC-7721, was measured and compared. The scaled electroinduced entropy production rate (SEEP) of cancer cells monotonically increases with electric field strength at 5-40 V/cm, while that of normal cells changes nonmonotonically with electric field strength, reaching a peak at 5-30 V/cm. For all cell lines, the cancerous-to-normal ratio of field-induced entropy production is clearly <1 in a large range of field strength from 5 to 25 V/cm. Therefore, this work presents an easy and effective strategy for experimentally investigating the thermodynamic properties of the cell, and gives deeper insight into the physical differences between normal and cancerous cells exposed to electric fields.

Escherichia coli mutants induced by multi-ion irradiation.

Wild-type Escherichia coli K12 strain W3110 was irradiated by 10 keV nitrogen ions. Specifically, irradiation was performed six times by N(+) ions, followed by the selection of lac constitutive mutants, and each time a stable S55 mutant was produced. By sequencing the whole genome, the fine map of S55 was completed. Compared with reference sequences, a total of eighteen single nucleotide polymorphisms (SNPs), two insertions and deletions (Indels), and nine structural variations (SVs) were found in the S55 genome. Among the 18 SNPs, 11 are transversional from A, T or C to G, accounting for 55.6% of point mutations. GCCA insertion occurs in the target gene lacI. Four SNPs, including three in rlpB and one in ygbN, are connected with cell envelope and transport. All nine structural variations of S55 are deletions and contain insertion sequence (IS) elements. Six deleted SVs contain disrupted ISs, nonfunctional pseudogenes, and one more 23 252 bp SV in the Rac prophage region. Overall, our results show that deletion bias observed in E. coli K12 genome evolution is generally related to the deletion of some nonfunctional regions. Furthermore, since ISs are unstable factors in a genome, the multi-ion irradiations that caused these deleted fragments in S55 turn out to be beneficial to genome stability, generating a wider mutational spectrum. Thus, it is possible that the mutation of these genes increases the ability of the E. coli genome to resist etch and damage caused by ion irradiation.

Protein photo-folding and quantum folding theory.

The rates of protein folding with photon absorption or emission and the cross section of photon -protein inelastic scattering are calculated from quantum folding theory by use of a field-theoretical method. All protein photo-folding processes are compared with common protein folding without the interaction of photons (non-radiative folding). It is demonstrated that there exists a common factor (thermo-averaged overlap integral of the vibration wave function, TAOI) for protein folding and protein photo-folding. Based on this finding it is predicted that (i) the stimulated photo-folding rates and the photon-protein resonance Raman scattering sections show the same temperature dependence as protein folding; (ii) the spectral line of the electronic transition is broadened to a band that includes an abundant vibration spectrum without and with conformational transitions, and the width of each vibration spectral line is largely reduced. The particular form of the folding rate-temperature relation and the abundant spectral structure imply the existence of quantum tunneling between protein conformations in folding and photo-folding that demonstrates the quantum nature of the motion of the conformational-electronic system.

Genome-based phylogeny of dsDNA viruses by a novel alignment-free method.

Sequence alignment is not directly applicable to whole genome phylogeny since several events such as rearrangements make full length alignments impossible. Here, a novel alignment-free method derived from the standpoint of information theory is proposed and used to construct the whole-genome phylogeny for a population of viruses from 13 viral families comprising 218 dsDNA viruses. The method is based on information correlation (IC) and partial information correlation (PIC). We observe that (i) the IC-PIC tree segregates the population into clades, the membership of each is remarkably consistent with biologist's systematics only with little exceptions; (ii) the IC-PIC tree reveals potential evolutionary relationships among some viral families; and (iii) the IC-PIC tree predicts the taxonomic positions of certain "unclassified" viruses. Our approach provides a new way for recovering the phylogeny of viruses, and has practical applications in developing alignment-free methods for sequence classification.

The dynamical contact order: protein folding rate parameters based on quantum conformational transitions.

Protein folding is regarded as a quantum transition between the torsion states of a polypeptide chain. According to the quantum theory of conformational dynamics, we propose the dynamical contact order (DCO) defined as a characteristic of the contact described by the moment of inertia and the torsion potential energy of the polypeptide chain between contact residues. Consequently, the protein folding rate can be quantitatively studied from the point of view of dynamics. By comparing theoretical calculations and experimental data on the folding rate of 80 proteins, we successfully validate the view that protein folding is a quantum conformational transition. We conclude that (i) a correlation between the protein folding rate and the contact inertial moment exists; (ii) multi-state protein folding can be regarded as a quantum conformational transition similar to that of two-state proteins but with an intermediate delay. We have estimated the order of magnitude of the time delay; (iii) folding can be classified into two types, exergonic and endergonic. Most of the two-state proteins with higher folding rate are exergonic and most of the multi-state proteins with low folding rate are endergonic. The folding speed limit is determined by exergonic folding.

The organization of nucleosomes around splice sites.

The occupancy of nucleosomes along chromosome is a key factor for gene regulation. However, except promoter regions, genome-wide properties and functions of nucleosome organization remain unclear in mammalian genomes. Using the computational model of Increment of Diversity with Quadratic Discriminant (IDQD) trained from the microarray data, the nucleosome occupancy score (NOScore) was defined and applied to splice junction regions of constitutive, cassette exon, alternative 3' and 5' splicing events in the human genome. We found an interesting relation between NOScore and RNA splicing: exon regions have higher NOScores compared with their flanking intron sequences in both constitutive and alternative splicing events, indicating the stronger nucleosome occupation potential of exon regions. In addition, NOScore valleys present at approximately 25 bp upstream of the acceptor site in all splicing events. By defining folding diversity-to-energy ratio to describe RNA structural flexibility, we demonstrated that primary RNA transcripts from nucleosome occupancy regions are relatively rigid and those from nucleosome depleted regions are relatively flexible. The negative correlation between nucleosome occupation/depletion of DNA sequence and structural flexibility/rigidity of its primary transcript around splice junctions may provide clues to the deeper understanding of the unexpected role for nucleosome organization in the regulation of RNA splicing.

Recognition of DNase I hypersensitive sites in multiple cell lines.

DNase I hypersensitive sites (DHSs) associate with a wide variety of functional genomic elements. Successful prediction of DHSs in computational models would dramatically accelerate the annotation of the human genome. In this study, a method of Increment of Diversity with Quadratic Discriminant analysis (IDQD) is presented for DHSs prediction in K562, CD4+ T, Hela and GM06990 cell lines. The average accuracies of 10-fold cross-validation test are 98.52%, 96.50%, 99.25% and 97.58%, respectively, and the mean areas under ROC curves (auROC) are all greater than 0.90. The prediction results indicate that the IDQD method is an effective tool for DHSs recognition.

Classification of antimicrobial peptide using diversity measure with quadratic discriminant analysis.

Accurate classification of antimicrobial peptides according to their biological activities will facilitate the design of novel antimicrobial agents and the discovery of new therapeutic targets. In this work, an excellent algorithm of Increment of Diversity with Quadratic Discriminant analysis (IDQD) was proposed to classify antimicrobial peptides with diverse biological activities.

Prediction of cell wall lytic enzymes using Chou's amphiphilic pseudo amino acid composition.

Discriminating cell wall lytic enzymes from non lytic enzymes is a very important task for curing bacterial infections. In this paper, based on Chou's amphiphilic pseudo amino acid composition, we develop fisher-discriminant based classifier to predict cell wall lytic enzymes. Experiments show that 66.7% sensitivity with 88.6% specificity is obtained. The method is further able to predict endolysin and autolysin with an overall accuracy of 92.9%. Results demonstrated that our method can provide highly useful information for further bacterial control research.

Using estimative reaction free energy to predict splice sites and their flanking competitors.

A crucial part in the gene structure prediction is to identify the accurate splice sites, not only constitutive but also alternative ones. Here, we use the maximum information principle (MIP) to analyze the conservative segments around splice sites. According to the MIP, a reaction free energy (RFE) expression is deduced, which can be employed to estimate the free energy change during splicing reaction involving a donor or acceptor site. The expression contains not only the background probability factors, but also all kinds of dependencies among both adjacent and non-adjacent bases. We apply the RFE expression to recognize splice sites and their flanking competitors in human genes, the results show high sensitivity and specificity, so the RFE expression accords well with the splicing reaction process. Moreover, the RFE expression is better than previous methods for predicting competitors of splice sites, and it outperforms the reaction free energy subtraction (RFES), that implies RFE competition between a given splice site and its flanking competitor may not be an only primary factor for alternative splice site selection. The work is helpful to not only the understanding of splicing reaction from its relation to MIP, but also the research on computational recognition of splicing sites and alternative splice events.

Distance conservation of transcription regulatory motifs in human promoters.

To understanding the interaction network among transcription-regulation elements in human is an immediate challenge for modern molecular biology. Here a central problem is how to extract evolutionary information and search the evolutionary conservation from the comparison of promoters of closely related species. Through the comparative studies of k-mer distribution in human and mouse transcription factor binding site (TFBS) sequences we have discovered that the average distance between a pair of transcription regulatory 7-mer motifs is conservative in human-mouse promoters. The distance conservation is a new kind of evolutionary conservation, not based on the strict location of bases in genome sequence. By utilizing the conservation of k-mer distance it will be helpful to propose a non-alignment-based approach for fast genome-wide discovery of transcription regulatory motifs. We demonstrated the distance conservation by genome-wide searching of conservative regulatory 7-mer motifs with successful rate 90%. Then, after defining human-mouse pair-distance divergence parameter we studied the tissue-specific motif pairs and found that the parameter for motif pairs is 11-16 times smaller than for their controls for 28 tissues and these pairs can be clearly differentiated on two-dimensional parameter plane. Finally, the mechanism of distance conservation was discussed briefly which is supposed to be related to the module structure of TFBSs.