Using Chaos-Game-Representation for Analysing the SARS-CoV-2 Lineages, Newly Emerging Strains and Recombinants.

Background: Viruses have high mutation rates, facilitating rapid evolution and the emergence of new species, subspecies, strains and recombinant forms. Accurate classification of these forms is crucial for understanding viral evolution and developing therapeutic applications. Phylogenetic classification is typically performed by analyzing molecular differences at the genomic and sub-genomic levels. This involves aligning homologous proteins or genes. However, there is growing interest in developing alignment-free methods for whole-genome comparisons that are computationally efficient. Methods: Here we elaborate on the Chaos Game Representation (CGR) method, based on concepts of statistical physics and free of sequence alignment assumptions. We adopt the CGR method for classification of the closely related clades/lineages A and B of the SARS-Corona virus 2019 (SARS-CoV-2), which is one of the fastest evolving viruses. Results: Our study shows that the CGR approach can easily yield the SARS-CoV-2 phylogeny from the available whole genomes of lineage A and lineage B sequences. It also shows an accurate classification of eight different strains and the newly evolved XBB variant from its parental strains. Compared to alignment-based methods (Neighbour-Joining and Maximum Likelihood), the CGR method requires low computational resources, is fast and accurate for long sequences, and, being a K-mer based approach, allows simultaneous comparison of a large number of closely-related sequences of different sizes. Further, we developed an R pipeline CGRphylo, available on GitHub, which integrates the CGR module with various other R packages to create phylogenetic trees and visualize them. Conclusion: Our findings demonstrate the efficacy of the CGR method for accurate classification and tracking of rapidly evolving viruses, offering valuable insights into the evolution and emergence of new SARS-CoV-2 strains and recombinants.

A systems level approach to study metabolic networks in prokaryotes with the aromatic amino acid biosynthesis pathway.

Metabolism of an organism underlies its phenotype, which depends on many factors, such as the genetic makeup, habitat, and stresses to which it is exposed. This is particularly important for the prokaryotes, which undergo significant vertical and horizontal gene transfers. In this study we have used the energy-intensive Aromatic Amino Acid (Tryptophan, Tyrosine and Phenylalanine, TTP) biosynthesis pathway, in a large number of prokaryotes, as a model system to query the different levels of organization of metabolism in the whole intracellular biochemical network, and to understand how perturbations, such as mutations, affects the metabolic flux through the pathway - in isolation and in the context of other pathways connected to it. Using an agglomerative approach involving complex network analysis and Flux Balance Analyses (FBA), of the Tryptophan, Tyrosine and Phenylalanine and other pathways connected to it, we identify several novel results. Using the reaction network analysis and Flux Balance Analyses of the Tryptophan, Tyrosine and Phenylalanine and the genome-scale reconstructed metabolic pathways, many common hubs between the connected networks and the whole genome network are identified. The results show that the connected pathway network can act as a proxy for the whole genome network in Prokaryotes. This systems level analysis also points towards designing functional smaller synthetic pathways based on the reaction network and Flux Balance Analyses analysis.

Small Conformational Changes Underlie Evolution of Resistance to NNRTI in HIV Reverse Transcriptase.

Despite achieving considerable success in reducing the number of fatalities due to acquired immunodeficiency syndrome, emergence of resistance against the reverse transcriptase (RT) inhibitor drugs remains one of the biggest challenges of the human immunodeficiency virus antiretroviral therapy (ART). Non-nucleoside reverse transcriptase inhibitors (NNRTIs) form a large class of drugs and a crucial component of ART. In NNRTIs, even a single resistance mutation is known to make the drugs completely ineffective. Additionally, several inhibitor-bound RTs with single resistance mutations do not exhibit any significant variations in their three-dimensional structures compared with the inhibitor-bound RT but completely nullify their inhibitory functions. This makes understanding the structural mechanism of these resistance mutations crucial for drug development. Here, we study several single resistance mutations in the allosteric inhibitor (nevirapine)-bound RT to analyze the mechanism of small structural changes leading to these large functional effects. In this study, we have shown that in absence of significant conformational variations in the inhibitor-bound wild-type RT and RT with single resistance mutations, the protein contact network analysis of their static structures, along with molecular dynamics simulations, can be a useful approach to understand the functional effect of small local conformational variations. The simple network analysis exposes the localized contact changes that lead to global rearrangement in the communication pattern within RT. Furthermore, these conformational changes have implications on the overall dynamics of RT. Using various measures, we show that a single resistance mutation can change the network structure and dynamics of RT to behave more like unbound RT, even in the presence of the inhibitor. This combined coarse-grained contact network and molecular dynamics approach promises to be a useful tool to analyze structure-function studies of proteins that show large functional changes with negligible variations in their overall conformation.

Complex network analysis of thermostable mutants of Bacillus subtilis Lipase A.

Three-dimensional structures of proteins that regulate their functions can be modelled using complex network based approaches for understanding the structure-function relationship. The six mutants of the protein Lipase A from Bacillus subtilis, harbouring 2 to 12 mutations, retain their function at higher temperatures with negligible variation in their overall three-dimensional crystallographic structures. This enhanced thermostability of the mutants questions the structure-function paradigm. In this paper, a coarse-grained complex network approach is used to elucidate the structural basis of enhanced thermostability in the mutant proteins, by uncovering small but significant local changes distributed throughout the structure, rendering stability to the mutants at higher temperatures. Community structure analysis of the six mutant protein networks uncovers the specific reorganisations among the nodes/residues that occur, in absence of overall structural variations, which induce enhanced rigidity underlying the increased thermostability. This study offers a novel and significant application of complex network analysis that proposes to be useful in the understanding and designing of thermostable proteins.

Uncoupling of an ammonia channel as a mechanism of allosteric inhibition in anthranilate synthase of Serratia marcescens: dynamic and graph theoretical analysis.

Anthranilate synthase (AS) is the first branch node enzyme that catalyzes the conversion of chorismate to anthranilate in the high energy-consuming tryptophan biosynthetic pathway in Serratia marcescens. AS, with an allosterically-bound inhibitor (tryptophan), shows complete inhibition in its catalytic function, but the inhibitor-bound structure is very similar to that of the substrate-bound AS. Even though the reaction mechanisms of several chorismate-utilizing enzymes are known, the unusual structure-function relationship in catalysis and allosteric inhibition of AS by tryptophan, with an insignificant change in structure, remains elusive. In the absence of structural variation, we use an integrated computational approach of coarse-grained protein contact networks, Gaussian network model, and atomistic Molecular Dynamics simulations of the substrate-bound and inhibitor-bound AS structures, and show the role of small but critical allosteric changes that induce complete inhibition of AS activity. We predict, through dynamic correlation studies, perturbation in crucial inter-subunit interactions between the two substrate-binding sites ("ammonia channel") and the allosteric inhibitor-binding site, and identify, through shortest path analysis, the non-active site residues participating in the communication pathways. We argue that such a regulatory mechanism (change in function without a significant change in the structure) for catalysis is useful for a branch point enzyme that has to undergo fast redistribution of fluxes according to different metabolic states of the organism. Being essential to the survival of microorganisms, including pathogenic ones, and absent in mammals, AS is a highly attractive drug target. Thus, the allosteric AS residues participating in catalysis identified in this study could be important for drugability.

Thermostability of in vitro evolved Bacillus subtilis lipase A: a network and dynamics perspective.

Proteins in thermophilic organisms remain stable and function optimally at high temperatures. Owing to their important applicability in many industrial processes, such thermostable proteins have been studied extensively, and several structural factors attributed to their enhanced stability. How these factors render the emergent property of thermostability to proteins, even in situations where no significant changes occur in their three-dimensional structures in comparison to their mesophilic counter-parts, has remained an intriguing question. In this study we treat Lipase A from Bacillus subtilis and its six thermostable mutants in a unified manner and address the problem with a combined complex network-based analysis and molecular dynamic studies to find commonality in their properties. The Protein Contact Networks (PCN) of the wild-type and six mutant Lipase A structures developed at a mesoscopic scale were analyzed at global network and local node (residue) level using network parameters and community structure analysis. The comparative PCN analysis of all proteins pointed towards important role of specific residues in the enhanced thermostability. Network analysis results were corroborated with finer-scale molecular dynamics simulations at both room and high temperatures. Our results show that this combined approach at two scales can uncover small but important changes in the local conformations that add up to stabilize the protein structure in thermostable mutants, even when overall conformation differences among them are negligible. Our analysis not only supports the experimentally determined stabilizing factors, but also unveils the important role of contacts, distributed throughout the protein, that lead to thermostability. We propose that this combined mesoscopic-network and fine-grained molecular dynamics approach is a convenient and useful scheme not only to study allosteric changes leading to protein stability in the face of negligible over-all conformational changes due to mutations, but also in other molecular networks where change in function does not accompany significant change in the network structure.

Evolution of tryptophan biosynthetic pathway in microbial genomes: a comparative genetic study.

Biosynthetic pathway evolution needs to consider the evolution of a group of genes that code for enzymes catalysing the multiple chemical reaction steps leading to the final end product. Tryptophan biosynthetic pathway has five chemical reaction steps that are highly conserved in diverse microbial genomes, though the genes of the pathway enzymes show considerable variations in arrangements, operon structure (gene fusion and splitting) and regulation. We use a combined bioinformatic and statistical analyses approach to address the question if the pathway genes from different microbial genomes, belonging to a wide range of groups, show similar evolutionary relationships within and between them. Our analyses involved detailed study of gene organization (fusion/splitting events), base composition, relative synonymous codon usage pattern of the genes, gene expressivity, amino acid usage, etc. to assess inter- and intra-genic variations, between and within the pathway genes, in diverse group of microorganisms. We describe these genetic and genomic variations in the tryptophan pathway genes in different microorganisms to show the similarities across organisms, and compare the same genes across different organisms to find the possible variability arising possibly due to horizontal gene transfers. Such studies form the basis for moving from single gene evolution to pathway evolutionary studies that are important steps towards understanding the systems biology of intracellular pathways.

Analysis of dinucleotide signatures in HIV-1 subtype B genomes.

Dinucleotide usage is known to vary in the genomes of organisms. The dinucleotide usage profiles or genome signatures are similar for sequence samples taken from the same genome, but are different for taxonomically distant species. This concept of genome signatures has been used to study several organisms including viruses, to elucidate the signatures of evolutionary processes at the genome level. Genome signatures assume greater importance in the case of host-pathogen interactions, where molecular interactions between the two species take place continuously, and can influence their genomic composition. In this study, analyses of whole genome sequences of the HIV-1 subtype B, a retrovirus that caused global pandemic of AIDS, have been carried out to analyse the variation in genome signatures of the virus from 1983 to 2007. We show statistically significant temporal variations in some dinucleotide patterns highlighting the selective evolution of the dinucleotide profiles of HIV-1 subtype B, possibly a consequence of host specific selection.

A realistic host-vector transmission model for describing malaria prevalence pattern.

Malaria continues to be a major public health concern all over the world even after effective control policies have been employed, and considerable understanding of the disease biology have been attained, from both the experimental and modelling perspective. Interactions between different general and local processes, such as dependence on age and immunity of the human host, variations of temperature and rainfall in tropical and sub-tropical areas, and continued presence of asymptomatic infections, regulate the host-vector interactions, and are responsible for the continuing disease prevalence pattern.In this paper, a general mathematical model of malaria transmission is developed considering short and long-term age-dependent immunity of human host and its interaction with pathogen-infected mosquito vector. The model is studied analytically and numerically to understand the role of different parameters related to mosquitoes and humans. To validate the model with a disease prevalence pattern in a particular region, real epidemiological data from the north-eastern part of India was used, and the effect of seasonal variation in mosquito density was modelled based on local climactic data. The model developed based on general features of host-vector interactions, and modified simply incorporating local environmental factors with minimal changes, can successfully explain the disease transmission process in the region. This provides a general approach toward modelling malaria that can be adapted to control future outbreaks of malaria.

Multifractal analysis of HIV-1 genomes.

Pathogens like HIV-1, which evolve into many closely related variants displaying differential infectivity and evolutionary dynamics in a short time scale, require fast and accurate classification. Conventional whole genome sequence alignment-based methods are computationally expensive and involve complex analysis. Alignment-free methodologies are increasingly being used to effectively differentiate genomic variations between viral species. Multifractal analysis, which explores the self-similar nature of genomes, is an alignment-free methodology that has been applied to study such variations. However, whether multifractal analysis can quantify variations between closely related genomes, such as the HIV-1 subtypes, is an open question. Here we address the above by implementing the multifractal analysis on four retroviral genomes (HIV-1, HIV-2, SIVcpz, and HTLV-1), and demonstrate that individual multifractal properties can differentiate between different retrovirus types easily. However, the individual multifractal measures do not resolve within-group variations for different known subtypes of HIV-1 M group. We show here that these known subtypes can instead be classified correctly using a combination of the crucial multifractal measures. This method is simple and computationally fast in comparison to the conventional alignment-based methods for whole genome phylogenetic analysis.

Theoretical investigation of malaria prevalence in two Indian cities using the response surface method.

BACKGROUND: Elucidation of the relationships between malaria incidence and climatic and non-climatic factors in a region is of utmost importance in understanding the causative factors of disease spread and design of control strategies. Very often malaria prevalence data is restricted to short time scales (months to few years). This demands application of rigorous statistical modelling techniques for analysis and prediction. The monthly malaria prevalence data for three to five years from two cities in southern India, situated in two different climatic zones, are studied to capture their dependence on climatic factors. METHODS: The statistical technique of response surface method (RSM) is applied for the first time to study any epidemiological data. A new step-by-step model reduction technique is proposed to refine the initial model obtained from RSM. This provides a simpler structure and gives better fit. This combined approach is applied to two types of epidemiological data (Slide Positivity Rates values and Total Malaria cases), for two cities in India with varying strengths of disease prevalence and environmental conditions. RESULTS: The study on these data sets reveals that RSM can be used successfully to elucidate the important environmental factors influencing the transmission of the disease by analysing short epidemiological time series. The proposed approach has high predictive ability over relatively long time horizons. CONCLUSIONS: This method promises to provide reliable forecast of malaria incidence across varying environmental conditions, which may help in designing useful control programmes for malaria.

Mathematical models of malaria--a review.

Mathematical models have been used to provide an explicit framework for understanding malaria transmission dynamics in human population for over 100 years. With the disease still thriving and threatening to be a major source of death and disability due to changed environmental and socio-economic conditions, it is necessary to make a critical assessment of the existing models, and study their evolution and efficacy in describing the host-parasite biology. In this article, starting from the basic Ross model, the key mathematical models and their underlying features, based on their specific contributions in the understanding of spread and transmission of malaria have been discussed. The first aim of this article is to develop, starting from the basic models, a hierarchical structure of a range of deterministic models of different levels of complexity. The second objective is to elaborate, using some of the representative mathematical models, the evolution of modelling strategies to describe malaria incidence by including the critical features of host-vector-parasite interactions. Emphasis is more on the evolution of the deterministic differential equation based epidemiological compartment models with a brief discussion on data based statistical models. In this comprehensive survey, the approach has been to summarize the modelling activity in this area so that it helps reach a wider range of researchers working on epidemiology, transmission, and other aspects of malaria. This may facilitate the mathematicians to further develop suitable models in this direction relevant to the present scenario, and help the biologists and public health personnel to adopt better understanding of the modelling strategies to control the disease.

Design of regulation and dynamics in simple biochemical pathways.

Complex regulation of biochemical pathways in a cell is brought about by the interaction of simpler regulatory structures. Among the basic regulatory designs, feedback inhibition of gene expression is the most common motif in gene regulation and a ubiquitous control structure found in nature. In this work, we have studied a common structural feature (delayed feedback) in gene organisation and shown, both theoretically and experimentally, its subtle but important functional role in gene expression kinetics in a negatively auto-regulated system. Using simple deterministic and stochastic models with varying levels of realism, we present detailed theoretical representations of negatively auto-regulated transcriptional circuits with increasing delays in the establishment of feedback of repression. The models of the circuits with and without delay are studied analytically as well as numerically for variation of parameters and delay lengths. The positive invariance, boundedness of the solutions, local and global asymptotic stability of both the systems around the unique positive steady state are studied analytically. Existence of transient temporal dynamics is shown mathematically. Comparison of the two types of model circuits shows that even though the long-term dynamics is stable and not affected by delays in repression, there is interesting variation in the transient dynamical features with increasing delays. Theoretical predictions are validated through experimentally constructed gene circuits of similar designs. This combined theoretical and experimental study helps delineate the opposing effects of delay-induced instability, and the stability-enhancing property of negative feedback in the pathway behaviour, and gives rationale for the abundance of similar designs in real biochemical pathways.

Differential trends in the codon usage patterns in HIV-1 genes.

Host-pathogen interactions underlie one of the most complex evolutionary phenomena resulting in continual adaptive genetic changes, where pathogens exploit the host's molecular resources for growth and survival, while hosts try to eliminate the pathogen. Deciphering the molecular basis of host-pathogen interactions is useful in understanding the factors governing pathogen evolution and disease propagation. In host-pathogen context, a balance between mutation, selection, and genetic drift is known to maintain codon bias in both organisms. Studies revealing determinants of the bias and its dynamics are central to the understanding of host-pathogen evolution. We considered the Human Immunodeficiency Virus (HIV) type 1 and its human host to search for evolutionary signatures in the viral genome. Positive selection is known to dominate intra-host evolution of HIV-1, whereas high genetic variability underlies the belief that neutral processes drive inter-host differences. In this study, we analyze the codon usage patterns of HIV-1 genomes across all subtypes and clades sequenced over a period of 23 years. We show presence of unique temporal correlations in the codon bias of three HIV-1 genes illustrating differential adaptation of the HIV-1 genes towards the host preferred codons. Our results point towards gene-specific translational selection to be an important force driving the evolution of HIV-1 at the population level.

Using genomic signatures for HIV-1 sub-typing.

BACKGROUND: Human Immunodeficiency Virus type 1 (HIV-1), the causative agent of Acquired Immune Deficiency Syndrome (AIDS), exhibits very high genetic diversity with different variants or subtypes prevalent in different parts of the world. Proper classification of the HIV-1 subtypes, displaying differential infectivity, plays a major role in monitoring the epidemic and is also a critical component for effective treatment strategy. The existing methods to classify HIV-1 sequence subtypes, based on phylogenetic analysis focusing only on specific genes/regions, have shown inconsistencies as they lack the capability to analyse whole genome variations. Several isolates are left unclassified due to unresolved sub-typing. It is apparent that classification of subtypes based on complete genome sequences, rather than sub-genomic regions, is a more robust and comprehensive approach to address genome-wide heterogeneity. However, no simple methodology exists that directly computes HIV-1 subtype from the complete genome sequence. RESULTS: We use Chaos Game Representation (CGR) as an approach to identify the distinctive genomic signature associated with the DNA sequence organisation in different HIV-1 subtypes. We first analysed the effect of nucleotide word lengths (k = 2 to 8) on whole genomes of the HIV-1 M group sequences, and found the optimum word length of k = 6, that could classify HIV-1 subtypes based on a Test sequence set. Using the optimised word length, we then showed accurate classification of the HIV-1 subtypes from both the Reference Set sequences and from all available sequences in the database. Finally, we applied the approach to cluster the five unclassified HIV-1 sequences from Africa and Europe, and predict their possible subtypes. CONCLUSION: We propose a genomic signature-based approach, using CGR with suitable word length optimisation, which can be applied to classify intra-species variations, and apply it to the complex problem of HIV-1 subtype classification. We demonstrate that CGR is a simple and computationally less intensive method that not only accurately segregates the HIV-1 subtype and sub-subtypes, but also aid in the classification of the unclassified sequences. We hope that it will be useful in subtype annotation of the newly sequenced HIV-1 genomes.

Delay-induced transient increase and heterogeneity in gene expression in negatively auto-regulated gene circuits.

A generic feature in all intracellular biochemical processes is the time required to complete the whole sequence of reactions to yield any observable quantity--from gene expression to circadian rhythms. This widespread phenomenon points towards the importance of time delay in biological functions. Theoretically time delay is known to be the source of instability, and has been attributed to lead to oscillations or transient dynamics in several biological functions. Negative feedback loops, common in biochemical pathways, have been shown to provide stability and withstand considerable variations and random perturbations of biochemical parameters. The interaction of these two opposing factors--of instability and homeostasis--are features that are widespread in intracellular processes. To test the effect of these divergent forces in the dynamics of gene expression, we have designed and constructed simple negatively auto-regulated gene circuits consisting of a basic regulator and transcriptional repressor module, and compared it with one, which has delayed repression. We show, both theoretically and experimentally, that delayed repression induces transient increase and heterogeneity in gene expression before the gain of stability effected by the negative feedback. This design, therefore, seems to be suitable for conferring both stability and variability in cells required for adaptive response to a noisy environment.

Measuring collective behaviour of multicellular ensembles: role of space-time scales.

Living systems are spectacular examples of spatiotemporally organized structures. During the development of complex organization there is dynamic equilibrium between the local and global processes acting at the intra-and intercellular levels in multiple space and time scales. Although in modelling studies such spatiotemporal systems can be described by different space-time scales and at many organizational levels, the experimental quantities measured and predictions useful for practical applications are at a macroscopic (coarser or averaged) level/scale; these are limited by the resolution of the measuring method and experimental protocol. In this work, we address whether the spatiotemporal collective dynamics exhibited by a multiscale system can discriminate between,or be borne out by,the coarse-grained and averaged measurements done at different spatial and temporal scales. Using a simple model of a ring of cells, we show that measurements of both spatial and spatiotemporal average behaviour in this multicellular ensemble can mask the variety of collective dynamics observed at other space-time scales, and exhibit completely different behaviours. Such outcomes of measurements can lead to incomplete and incorrect understanding of physiological functions and pathogenesis in multicell ensembles.

Assortative mixing in Protein Contact Networks and protein folding kinetics.

MOTIVATION: Starting from linear chains of amino acids, the spontaneous folding of proteins into their elaborate 3D structures is one of the remarkable examples of biological self-organization. We investigated native state structures of 30 single-domain, two-state proteins, from complex networks perspective, to understand the role of topological parameters in proteins' folding kinetics, at two length scales--as 'Protein Contact Networks (PCNs)' and their corresponding 'Long-range Interaction Networks (LINs)' constructed by ignoring the short-range interactions. RESULTS: Our results show that, both PCNs and LINs exhibit the exceptional topological property of 'assortative mixing' that is absent in all other biological and technological networks studied so far. We show that the degree distribution of these contact networks is partly responsible for the observed assortativity. The coefficient of assortativity also shows a positive correlation with the rate of protein folding at both short- and long-contact scale, whereas, the clustering coefficients of only the LINs exhibit a negative correlation. The results indicate that the general topological parameters of these naturally evolved protein networks can effectively represent the structural and functional properties required for fast information transfer among the residues facilitating biochemical/kinetic functions, such as, allostery, stability and the rate of folding. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Propagation of extrinsic perturbation in a negatively auto-regulated pathway.

The apparent precision of the output in multi-step biochemical pathways in the face of external and intrinsic perturbations is non-obvious and conceptually difficult. Using a simple three-step negatively auto-regulated model pathway, we show that the effect of perturbation at different steps of the pathway and its transmission through the network is dependent on the context (i.e., the position) of the particular reaction step in relation to the topology of the regulatory network, stoichiometry of reactions, type of nonlinearity involved in the reactions and also on the intrinsic dynamical state of the pathway variables. We delineate the qualitative and quantitative changes in the pathway dynamics for constant ('bias') and random external perturbations acting on the pathway steps locally or globally to all steps. We show that constant perturbation induces qualitative change in dynamics, whereas random fluctuations cause significant quantitative variations in the concentrations of the different variables. Thus, the dynamic response of multi-step biochemical pathways to external perturbation depends on their biochemical, topological and dynamical features.