Homeostasis in networks with multiple inputs.

Homeostasis, also known as adaptation, refers to the ability of a system to counteract persistent external disturbances and tightly control the output of a key observable. Existing studies on homeostasis in network dynamics have mainly focused on 'perfect adaptation' in deterministic single-input single-output networks where the disturbances are scalar and affect the network dynamics via a pre-specified input node. In this paper we provide a full classification of all possible network topologies capable of generating infinitesimal homeostasis in arbitrarily large and complex multiple inputs networks. Working in the framework of 'infinitesimal homeostasis' allows us to make no assumption about how the components are interconnected and the functional form of the associated differential equations, apart from being compatible with the network architecture. Remarkably, we show that there are just three distinct 'mechanisms' that generate infinitesimal homeostasis. Each of these three mechanisms generates a rich class of well-defined network topologies-called homeostasis subnetworks. More importantly, we show that these classes of homeostasis subnetworks provides a topological basis for the classification of 'homeostasis types': the full set of all possible multiple inputs networks can be uniquely decomposed into these special homeostasis subnetworks. We illustrate our results with some simple abstract examples and a biologically realistic model for the co-regulation of calcium ( Ca ) and phosphate ( PO 4 ) in the rat. Furthermore, we identify a new phenomenon that occurs in the multiple input setting, that we call homeostasis mode interaction, in analogy with the well-known characteristic of multiparameter bifurcation theory.

Whole-genome analysis of monozygotic Brazilian twins discordant for type 1 narcolepsy: a case report.

BACKGROUND: Narcolepsy type 1 (NT1) is a rare and chronic neurological disease characterized by sudden sleep attacks, overwhelming daytime drowsiness, and cataplexy. When associated with a sudden loss of muscle tone (cataplexy) narcolepsy is classified as type 1, while the absence of cataplexy indicates type 2. Genetic, degenerative, and immunological hypotheses to explain the pathophysiology of NT1 are still a matter of debate. To contribute to the understanding of NT1 genetic basis, here we describe, for the first time, a whole genome analysis of a monozygotic twin pair discordant for NT1. CASE PRESENTATION: We present the case of a pair of 17-year-old male, monozygotic twins discordant for NT1. The affected twin had Epworth Sleepiness Scale (ESS) of 20 (can range from 0 to 24), cataplexy, hypnagogic hallucinations, polysomnography without abnormalities, multiple sleep latency tests (MSLT) positive for narcolepsy, a mean sleep latency of 3 min, sleep-onset REM periods SOREMPs of 5, presence of allele HLA-DQB1*06:02, and Hypocretin-1 level of zero pg/mL (normal values are > 200 pg/mL). The other twin had no narcolepsy symptoms (ESS of 4), normal polysomnography, MSLT without abnormalities, presence of allele HLA-DQB1*06:02, and Hypocretin-1 level of 396,74 pg/mL. To describe the genetic background for the NT1 discordant manifestations in this case, we present the whole-genome analysis of this monozygotic twin pair. The whole-genome comparison revealed that both twins have identical NT1 pathogenic mutations in known genes, such as HLA-DQB1*06:02:01, HLA-DRB1*11:01:02/*15:03:01. The affected twin has the expected clinical manifestation while the unaffected twin has an unexpected phenotype. The unaffected twin has significantly more frameshift mutations as compared to the affected twin (108 versus 75) and mutations that affect stop codons (61 versus 5 in stop gain, 26 versus 2 in start lost). CONCLUSIONS: The differences observed in frameshift and stop codon mutations in the unaffected twin are consistent with loss-of-function effects and protective alleles, that are almost always associated with loss-of-function rare alleles. Also, overrepresentation analysis of genes containing variants with potential clinical relevance in the unaffected twin shows that most mutations are in genes related to immune regulation function, Golgi apparatus, MHC, and olfactory receptor. These observations support the hypothesis that NT1 has an immunological basis although protective mutations in non-HLA alleles might interfere with the expression of the NT1 phenotype and consequently, with the clinical manifestation of the disease.

The structure of infinitesimal homeostasis in input-output networks.

Homeostasis refers to a phenomenon whereby the output [Formula: see text] of a system is approximately constant on variation of an input [Formula: see text]. Homeostasis occurs frequently in biochemical networks and in other networks of interacting elements where mathematical models are based on differential equations associated to the network. These networks can be abstracted as digraphs [Formula: see text] with a distinguished input node [Formula: see text], a different distinguished output node o, and a number of regulatory nodes [Formula: see text]. In these models the input-output map [Formula: see text] is defined by a stable equilibrium [Formula: see text] at [Formula: see text]. Stability implies that there is a stable equilibrium [Formula: see text] for each [Formula: see text] near [Formula: see text] and infinitesimal homeostasis occurs at [Formula: see text] when [Formula: see text]. We show that there is an [Formula: see text] homeostasis matrix [Formula: see text] for which [Formula: see text] if and only if [Formula: see text]. We note that the entries in H are linearized couplings and [Formula: see text] is a homogeneous polynomial of degree [Formula: see text] in these entries. We use combinatorial matrix theory to factor the polynomial [Formula: see text] and thereby determine a menu of different types of possible homeostasis associated with each digraph [Formula: see text]. Specifically, we prove that each factor corresponds to a subnetwork of [Formula: see text]. The factors divide into two combinatorially defined classes: structural and appendage. Structural factors correspond to feedforward motifs and appendage factors correspond to feedback motifs. Finally, we discover an algorithm for determining the homeostasis subnetwork motif corresponding to each factor of [Formula: see text] without performing numerical simulations on model equations. The algorithm allows us to classify low degree factors of [Formula: see text]. There are two types of degree 1 homeostasis (negative feedback loops and kinetic or Haldane motifs) and there are two types of degree 2 homeostasis (feedforward loops and a degree two appendage motif).

Stochastic Modeling and Simulation of Viral Evolution.

RNA viruses comprise vast populations of closely related, but highly genetically diverse, entities known as quasispecies. Understanding the mechanisms by which this extreme diversity is generated and maintained is fundamental when approaching viral persistence and pathobiology in infected hosts. In this paper, we access quasispecies theory through a mathematical model based on the theory of multitype branching processes, to better understand the roles of mechanisms resulting in viral diversity, persistence and extinction. We accomplish this understanding by a combination of computational simulations and the theoretical analysis of the model. In order to perform the simulations, we have implemented the mathematical model into a computational platform capable of running simulations and presenting the results in a graphical format in real time. Among other things, we show that the establishment of virus populations may display four distinct regimes from its introduction into new hosts until achieving equilibrium or undergoing extinction. Also, we were able to simulate different fitness distributions representing distinct environments within a host which could either be favorable or hostile to the viral success. We addressed the most used mechanisms for explaining the extinction of RNA virus populations called lethal mutagenesis and mutational meltdown. We were able to demonstrate a correspondence between these two mechanisms implying the existence of a unifying principle leading to the extinction of RNA viruses.

Homeostasis in a feed forward loop gene regulatory motif.

The internal state of a cell is affected by inputs from the extra-cellular environment such as external temperature. If some output, such as the concentration of a target protein, remains approximately constant as inputs vary, the system exhibits homeostasis. Special sub-networks called motifs are unusually common in gene regulatory networks (GRNs), suggesting that they may have a significant biological function. Potentially, one such function is homeostasis. In support of this hypothesis, we show that the feed-forward loop GRN produces homeostasis. Here the inputs are subsumed into a single parameter that affects only the first node in the motif, and the output is the concentration of a target protein. The analysis uses the notion of infinitesimal homeostasis, which occurs when the input-output map has a critical point (zero derivative). In model equations such points can be located using implicit differentiation. If the second derivative of the input-output map also vanishes, the critical point is a chair: the output rises roughly linearly, then flattens out (the homeostasis region or plateau), and then starts to rise again. Chair points are a common cause of homeostasis. In more complicated equations or networks, numerical exploration would have to augment analysis. Thus, in terms of finding chairs, this paper presents a proof of concept. We apply this method to a standard family of differential equations modeling the feed-forward loop GRN, and deduce that chair points occur. This function determines the production of a particular mRNA and the resulting chair points are found analytically. The same method can potentially be used to find homeostasis regions in other GRNs. In the discussion and conclusion section, we also discuss why homeostasis in the motif may persist even when the rest of the network is taken into account.

Protein Synthesis Driven by Dynamical Stochastic Transcription.

In this manuscript, we propose a mathematical framework to couple transcription and translation in which mRNA production is described by a set of master equations, while the dynamics of protein density is governed by a random differential equation. The coupling between the two processes is given by a stochastic perturbation whose statistics satisfies the master equations. In this approach, from the knowledge of the analytical time-dependent distribution of mRNA number, we are able to calculate the dynamics of the probability density of the protein population.

MIA: Mutual Information Analyzer, a graphic user interface program that calculates entropy, vertical and horizontal mutual information of molecular sequence sets.

BACKGROUND: Short and long range correlations in biological sequences are central in genomic studies of covariation. These correlations can be studied using mutual information because it measures the amount of information one random variable contains about the other. Here we present MIA (Mutual Information Analyzer) a user friendly graphic interface pipeline that calculates spectra of vertical entropy (VH), vertical mutual information (VMI) and horizontal mutual information (HMI), since currently there is no user friendly integrated platform that in a single package perform all these calculations. MIA also calculates Jensen-Shannon Divergence (JSD) between pair of different species spectra, herein called informational distances. Thus, the resulting distance matrices can be presented by distance histograms and informational dendrograms, giving support to discrimination of closely related species. RESULTS: In order to test MIA we analyzed sequences from Drosophila Adh locus, because the taxonomy and evolutionary patterns of different Drosophila species are well established and the gene Adh is extensively studied. The search retrieved 959 sequences of 291 species. From the total, 450 sequences of 17 species were selected. With this dataset MIA performed all tasks in less than three hours: gathering, storing and aligning fasta files; calculating VH, VMI and HMI spectra; and calculating JSD between pair of different species spectra. For each task MIA saved tables and graphics in the local disk, easily accessible for future analysis. CONCLUSIONS: Our tests revealed that the "informational model free" spectra may represent species signatures. Since JSD applied to Horizontal Mutual Information spectra resulted in statistically significant distances between species, we could calculate respective hierarchical clusters, herein called Informational Dendrograms (ID). When compared to phylogenetic trees all Informational Dendrograms presented similar taxonomy and species clusterization.

Reconstructing Prehistoric Viral Genomes from Neanderthal Sequencing Data.

DNA viruses that produce persistent infections have been proposed as potential causes for the extinction of Neanderthals, and, therefore, the identification of viral genome remnants in Neanderthal sequence reads is an initial step to address this hypothesis. Here, as proof of concept, we searched for viral remnants in sequence reads of Neanderthal genome data by mapping to adenovirus, herpesvirus and papillomavirus, which are double-stranded DNA viruses that may establish lifelong latency and can produce persistent infections. The reconstructed ancient viral genomes of adenovirus, herpesvirus and papillomavirus revealed conserved segments, with nucleotide identity to extant viral genomes and variable regions in coding regions with substantial divergence to extant close relatives. Sequence reads mapped to extant viral genomes showed deamination patterns of ancient DNA, and these ancient viral genomes showed divergence consistent with the age of these samples (≈50,000 years) and viral evolutionary rates (10-5 to 10-8 substitutions/site/year). Analysis of random effects showed that the Neanderthal mapping to genomes of extant persistent viruses is above what is expected by random similarities of short reads. Also, negative control with a nonpersistent DNA virus does not yield statistically significant assemblies. This work demonstrates the feasibility of identifying viral genome remnants in archaeological samples with signal-to-noise assessment.

Virus replication as a phenotypic version of polynucleotide evolution.

In this paper, we revisit and adapt to viral evolution an approach based on the theory of branching process advanced by Demetrius et al. (Bull. Math. Biol. 46:239-262, 1985), in their study of polynucleotide evolution. By taking into account beneficial effects, we obtain a non-trivial multivariate generalization of their single-type branching process model. Perturbative techniques allows us to obtain analytical asymptotic expressions for the main global parameters of the model, which lead to the following rigorous results: (i) a new criterion for "no sure extinction", (ii) a generalization and proof, for this particular class of models, of the lethal mutagenesis criterion proposed by Bull et al. (J. Virol. 18:2930-2939, 2007), (iii) a new proposal for the notion of relaxation time with a quantitative prescription for its evaluation, (iv) the quantitative description of the evolution of the expected values in four distinct "stages": extinction threshold, lethal mutagenesis, stationary "equilibrium", and transient. Finally, based on these quantitative results, we are able to draw some qualitative conclusions.

The epitranscriptome of Vero cells infected with SARS-CoV-2 assessed by direct RNA sequencing reveals m6A pattern changes and DRACH motif biases in viral and cellular RNAs.

The epitranscriptomics of the SARS-CoV-2 infected cell reveals its response to viral replication. Among various types of RNA nucleotide modifications, the m6A is the most common and is involved in several crucial processes of RNA intracellular location, maturation, half-life and translatability. This epitranscriptome contains a mixture of viral RNAs and cellular transcripts. In a previous study we presented the analysis of the SARS-CoV-2 RNA m6A methylation based on direct RNA sequencing and characterized DRACH motif mutations in different viral lineages. Here we present the analysis of the m6A transcript methylation of Vero cells (derived from African Green Monkeys) and Calu-3 cells (human) upon infection by SARS-CoV-2 using direct RNA sequencing data. Analysis of these data by nonparametric statistics and two computational methods (m6anet and EpiNano) show that m6A levels are higher in RNAs of infected cells. Functional enrichment analysis reveals increased m6A methylation of transcripts involved in translation, peptide and amine metabolism. This analysis allowed the identification of differentially methylated transcripts and m6A unique sites in the infected cell transcripts. Results here presented indicate that the cell response to viral infection not only changes the levels of mRNAs, as previously shown, but also its epitranscriptional pattern. Also, transcriptome-wide analysis shows strong nucleotide biases in DRACH motifs of cellular transcripts, both in Vero and Calu-3 cells, which use the signature GGACU whereas in viral RNAs the signature is GAACU. We hypothesize that the differences of DRACH motif biases, might force the convergent evolution of the viral genome resulting in better adaptation to target sequence preferences of writer, reader and eraser enzymes. To our knowledge, this is the first report on m6A epitranscriptome of the SARS-CoV-2 infected Vero cells by direct RNA sequencing, which is the sensu stricto RNA-seq.

Direct RNA Sequencing Reveals SARS-CoV-2 m6A Sites and Possible Differential DRACH Motif Methylation among Variants.

The causative agent of COVID-19 pandemic, SARS-CoV-2, has a 29,903 bases positive-sense single-stranded RNA genome. RNAs exhibit about 150 modified bases that are essential for proper function. Among internal modified bases, the N6-methyladenosine, or m6A, is the most frequent, and is implicated in SARS-CoV-2 immune response evasion. Although the SARS-CoV-2 genome is RNA, almost all genomes sequenced thus far are, in fact, reverse transcribed complementary DNAs. This process reduces the true complexity of these viral genomes because the incorporation of dNTPs hides RNA base modifications. Here, we present an initial exploration of Nanopore direct RNA sequencing to assess the m6A residues in the SARS-CoV-2 sequences of ORF3a, E, M, ORF6, ORF7a, ORF7b, ORF8, N, ORF10 and the 3'-untranslated region. We identified fifteen m6A methylated positions, of which, six are in ORF N. Additionally, because m6A is associated with the DRACH motif, we compared its distribution in major SARS-CoV-2 variants. Although DRACH is highly conserved among variants, we show that variants Beta and Eta have a fourth position C > U change in DRACH at 28,884b that could affect methylation. This is the first report of direct RNA sequencing of a Brazilian SARS-CoV-2 sample coupled with the identification of modified bases.

Comparative Analysis of the Secretome and Interactome of Trypanosoma cruzi and Trypanosoma rangeli Reveals Species Specific Immune Response Modulating Proteins.

Chagas disease, a zoonosis caused by the flagellate protozoan Trypanosoma cruzi, is a chronic and systemic parasitic infection that affects ~5-7 million people worldwide, mainly in Latin America. Chagas disease is an emerging public health problem due to the lack of vaccines and effective treatments. According to recent studies, several T. cruzi secreted proteins interact with the human host during cell invasion. Moreover, some comparative studies with T. rangeli, which is non-pathogenic in humans, have been performed to identify proteins directly involved in the pathogenesis of the disease. In this study, we present an integrated analysis of canonical putative secreted proteins (PSPs) from both species. Additionally, we propose an interactome with human host and gene family clusters, and a phylogenetic inference of a selected protein. In total, we identified 322 exclusively PSPs in T. cruzi and 202 in T. rangeli. Among the PSPs identified in T. cruzi, we found several trans-sialidases, mucins, MASPs, proteins with phospholipase 2 domains (PLA2-like), and proteins with Hsp70 domains (Hsp70-like) which have been previously characterized and demonstrated to be related to T. cruzi virulence. PSPs found in T. rangeli were related to protozoan metabolism, specifically carboxylases and phosphatases. Furthermore, we also identified PSPs that may interact with the human immune system, including heat shock and MASP proteins, but in a lower number compared to T. cruzi. Interestingly, we describe a hypothetical hybrid interactome of PSPs which reveals that T. cruzi secreted molecules may be down-regulating IL-17 whilst T. rangeli may enhance the production of IL-15. These results will pave the way for a better understanding of the pathophysiology of Chagas disease and may ultimately lead to the identification of molecular targets, such as key PSPs, that could be used to minimize the health outcomes of Chagas disease by modulating the immune response triggered by T. cruzi infection.

A Kolmogorov-Smirnov test for the molecular clock based on Bayesian ensembles of phylogenies.

Divergence date estimates are central to understand evolutionary processes and depend, in the case of molecular phylogenies, on tests of molecular clocks. Here we propose two non-parametric tests of strict and relaxed molecular clocks built upon a framework that uses the empirical cumulative distribution (ECD) of branch lengths obtained from an ensemble of Bayesian trees and well known non-parametric (one-sample and two-sample) Kolmogorov-Smirnov (KS) goodness-of-fit test. In the strict clock case, the method consists in using the one-sample Kolmogorov-Smirnov (KS) test to directly test if the phylogeny is clock-like, in other words, if it follows a Poisson law. The ECD is computed from the discretized branch lengths and the parameter λ of the expected Poisson distribution is calculated as the average branch length over the ensemble of trees. To compensate for the auto-correlation in the ensemble of trees and pseudo-replication we take advantage of thinning and effective sample size, two features provided by Bayesian inference MCMC samplers. Finally, it is observed that tree topologies with very long or very short branches lead to Poisson mixtures and in this case we propose the use of the two-sample KS test with samples from two continuous branch length distributions, one obtained from an ensemble of clock-constrained trees and the other from an ensemble of unconstrained trees. Moreover, in this second form the test can also be applied to test for relaxed clock models. The use of a statistically equivalent ensemble of phylogenies to obtain the branch lengths ECD, instead of one consensus tree, yields considerable reduction of the effects of small sample size and provides a gain of power.

A model of gene expression based on random dynamical systems reveals modularity properties of gene regulatory networks.

Here we propose a new approach to modeling gene expression based on the theory of random dynamical systems (RDS) that provides a general coupling prescription between the nodes of any given regulatory network given the dynamics of each node is modeled by a RDS. The main virtues of this approach are the following: (i) it provides a natural way to obtain arbitrarily large networks by coupling together simple basic pieces, thus revealing the modularity of regulatory networks; (ii) the assumptions about the stochastic processes used in the modeling are fairly general, in the sense that the only requirement is stationarity; (iii) there is a well developed mathematical theory, which is a blend of smooth dynamical systems theory, ergodic theory and stochastic analysis that allows one to extract relevant dynamical and statistical information without solving the system; (iv) one may obtain the classical rate equations form the corresponding stochastic version by averaging the dynamic random variables (small noise limit). It is important to emphasize that unlike the deterministic case, where coupling two equations is a trivial matter, coupling two RDS is non-trivial, specially in our case, where the coupling is performed between a state variable of one gene and the switching stochastic process of another gene and, hence, it is not a priori true that the resulting coupled system will satisfy the definition of a random dynamical system. We shall provide the necessary arguments that ensure that our coupling prescription does indeed furnish a coupled regulatory network of random dynamical systems. Finally, the fact that classical rate equations are the small noise limit of our stochastic model ensures that any validation or prediction made on the basis of the classical theory is also a validation or prediction of our model. We illustrate our framework with some simple examples of single-gene system and network motifs.

Estimation of genetic diversity in viral populations from next generation sequencing data with extremely deep coverage.

BACKGROUND: In this paper we propose a method and discuss its computational implementation as an integrated tool for the analysis of viral genetic diversity on data generated by high-throughput sequencing. The main motivation for this work is to better understand the genetic diversity of viruses with high rates of nucleotide substitution, as HIV-1 and Influenza. Most methods for viral diversity estimation proposed so far are intended to take benefit of the longer reads produced by some next-generation sequencing platforms in order to estimate a population of haplotypes which represent the diversity of the original population. The method proposed here is custom-made to take advantage of the very low error rate and extremely deep coverage per site, which are the main features of some neglected technologies that have not received much attention due to the short length of its reads, which precludes haplotype estimation. This approach allowed us to avoid some hard problems related to haplotype reconstruction (need of long reads, preliminary error filtering and assembly). RESULTS: We propose to measure genetic diversity of a viral population through a family of multinomial probability distributions indexed by the sites of the virus genome, each one representing the distribution of nucleic bases per site. Moreover, the implementation of the method focuses on two main optimization strategies: a read mapping/alignment procedure that aims at the recovery of the maximum possible number of short-reads; the inference of the multinomial parameters in a Bayesian framework with smoothed Dirichlet estimation. The Bayesian approach provides conditional probability distributions for the multinomial parameters allowing one to take into account the prior information of the control experiment and providing a natural way to separate signal from noise, since it automatically furnishes Bayesian confidence intervals and thus avoids the drawbacks of preliminary error filtering. CONCLUSIONS: The methods described in this paper have been implemented as an integrated tool called Tanden (Tool for Analysis of Diversity in Viral Populations) and successfully tested on samples obtained from HIV-1 strain NL4-3 (group M, subtype B) cultivations on primary human cell cultures in many distinct viral propagation conditions. Tanden is written in C# (Microsoft), runs on the Windows operating system, and can be downloaded from: http://tanden.url.ph/.

HIV-1 Tropism Determines Different Mutation Profiles in Proviral DNA.

In order to establish new infections HIV-1 particles need to attach to receptors expressed on the cellular surface. HIV-1 particles interact with a cell membrane receptor known as CD4 and subsequently with another cell membrane molecule known as a co-receptor. Two major different co-receptors have been identified: C-C chemokine Receptor type 5 (CCR5) and C-X-C chemokine Receptor type 4 (CXCR4) Previous reports have demonstrated cellular modifications upon HIV-1 binding to its co-receptors including gene expression modulations. Here we investigated the effect of viral binding to either CCR5 or CXCR4 co-receptors on viral diversity after a single round of reverse transcription. CCR5 and CXCR4 pseudotyped viruses were used to infect non-stimulated and stimulated PBMCs and purified CD4 positive cells. We adopted the SOLiD methodology to sequence virtually the entire proviral DNA from all experimental infections. Infections with CCR5 and CXCR4 pseudotyped virus resulted in different patterns of genetic diversification. CCR5 virus infections produced extensive proviral diversity while in CXCR4 infections a more localized substitution process was observed. In addition, we present pioneering results of a recently developed method for the analysis of SOLiD generated sequencing data applicable to the study of viral quasi-species. Our findings demonstrate the feasibility of viral quasi-species evaluation by NGS methodologies. We presented for the first time strong evidence for a host cell driving mechanism acting on the HIV-1 genetic variability under the control of co-receptor stimulation. Additional investigations are needed to further clarify this question, which is relevant to viral diversification process and consequent disease progression.