Developmental graphs comparison strategy for analysis of pattern formation and phylogeny.

In most taxa of plant and animal kingdoms the initial steps of embryogenesis and the final morphology of an organism are strongly determined. However, these two phenomena do not correlate from phylogenetic point of view, namely, different unrelated taxa can have the same type of early embryogenesis, while there can be different types of cleavage inside one taxon. Here we discuss an approach enabling giving an insight into the understanding of this phenomenon. First, we propose a strategy for constructing developmental graphs (trees) that provide mathematical formalization of a process of embryogenesis. Second, we suggested an algorithm of trees comparison, developed specifically for this type of labeled graphs, which allows calculating a distance between two developmental trees, and thus clustering them into groups. Next we performed the analysis of correspondence between the obtained clusters and the inception of morphological characters in given clustered groups of organisms, which allows describing several particular cases of interrelation between developmental trends and formation of morphological structures. Here we present some illustrations of the suggested methodology on the analysis of plant angiosperm species belonging to different taxa of various ranks.

Determinism and variability of the morphogenesis pathways.

Along with a strict determinism of early embryogenesis in most living organisms, some of them exhibit variability of cell fates and developmental pathways. Here we discuss the phenomena of determinism and variability of developmental pathways, defining its dependence upon cell potency, cell sensitivity to the external signals and cell signaling. We propose a set of conjectures on the phenomenon of variability of developmental pathways, and denote a difference between a normal (local) variability, leading to an invariant final structure (e.g., embryo shape), and fundamental one, which is a switching between different developmental pathways, leading to different possible structures. For illustrating our conjectures, we analyzed early developmental stages of plant embryos with different levels of variability of morphogenesis pathways, and provide a set of computational experiments by Morphogenesis Software.

Inference on tissue transplantation experiments.

We review studies on tissue transplantation experiments for various species: one piece of the donor tissue is excised and transplanted into a slit in the host tissue, then observe the behavior of this grafted tissue. Although we have known the results of some transplantation experiments, there are many more possible experiments with unknown results. We develop a penalty function-based method that uses the known experimental results to infer the unknown experimental results. Similar experiments without similar results get penalized and correspond to smaller probability. This method can provide the most probable results of a group of experiments or the probability of a specific result for each experiment. This method is also generalized to other situations. Besides, we solve a problem: how to design experiments so that such a method can be applied most efficiently.

Biological notion of positional information/value in morphogenesis theory.

The notions of positional information and positional value describe the role of cell position in cell development and pattern formation. Despite their frequent usage in literature, their definitions are blurry, and are interpreted differently by different researchers. Through reflection on previous definitions and usage, and analysis of related experiments, we propose three clear and verifiable criteria for positional information/value. Then we reviewed literature on molecular mechanisms of cell development and pattern formation, to search for a possible molecular basis of positional information/value, including those used in theoretical models. We conclude that although morphogen gradients and cell-to-cell contacts are involved in the pattern formation process, complete molecular explanations of positional information/value are still far from reality.

MasterPATH: network analysis of functional genomics screening data.

BACKGROUND: Functional genomics employs several experimental approaches to investigate gene functions. High-throughput techniques, such as loss-of-function screening and transcriptome profiling, allow to identify lists of genes potentially involved in biological processes of interest (so called hit list). Several computational methods exist to analyze and interpret such lists, the most widespread of which aim either at investigating of significantly enriched biological processes, or at extracting significantly represented subnetworks. RESULTS: Here we propose a novel network analysis method and corresponding computational software that employs the shortest path approach and centrality measure to discover members of molecular pathways leading to the studied phenotype, based on functional genomics screening data. The method works on integrated interactomes that consist of both directed and undirected networks - HIPPIE, SIGNOR, SignaLink, TFactS, KEGG, TransmiR, miRTarBase. The method finds nodes and short simple paths with significant high centrality in subnetworks induced by the hit genes and by so-called final implementers - the genes that are involved in molecular events responsible for final phenotypic realization of the biological processes of interest. We present the application of the method to the data from miRNA loss-of-function screen and transcriptome profiling of terminal human muscle differentiation process and to the gene loss-of-function screen exploring the genes that regulates human oxidative DNA damage recognition. The analysis highlighted the possible role of several known myogenesis regulatory miRNAs (miR-1, miR-125b, miR-216a) and their targets (AR, NR3C1, ARRB1, ITSN1, VAV3, TDGF1), as well as linked two major regulatory molecules of skeletal myogenesis, MYOD and SMAD3, to their previously known muscle-related targets (TGFB1, CDC42, CTCF) and also to a number of proteins such as C-KIT that have not been previously studied in the context of muscle differentiation. The analysis also showed the role of the interaction between H3 and SETDB1 proteins for oxidative DNA damage recognition. CONCLUSION: The current work provides a systematic methodology to discover members of molecular pathways in integrated networks using functional genomics screening data. It also offers a valuable instrument to explain the appearance of a set of genes, previously not associated with the process of interest, in the hit list of each particular functional genomics screening.

Model of Morphogenesis.

We build a theoretical model of morphogenesis. This model describes cell fate in the developing organism using the notion of epigenetic code of each cell. Namely, given the epigenetic spectra of a cell and its neighboring cells, we can determine the corresponding cell event it will perform. This means that the properties of a group of cells (comprising an embryo or its part) at any time point are also known, and thus, the evolution of an embryo can be described. By this strategy, it is possible to establish the tissue, organ, or embryo shapes at any time, starting from a zygote. As an essential part of the model, the formalization of the notion of cell potency is introduced, and the related properties are discussed.

Mathematical modeling reveals the factors involved in the phenomena of cancer stem cells stabilization.

Cancer Stem Cells (CSC), a subset of cancer cells resembling normal stem cells with self-renewal and asymmetric division capabilities, are present at various but low proportions in many tumors and are thought to be responsible for tumor relapses following conventional cancer therapies. In vitro, most intriguingly, isolated CSCs rapidly regenerate the original population of stem and non-stem cells (non-CSCs) as shown by various investigators. This phenomenon still remains to be explained. We propose a mathematical model of cancer cell population dynamics, based on the main parameters of cell population growth, including the proliferation rates, the rates of cell death and the frequency of symmetric and asymmetric cell divisions both in CSCs and non-CSCs sub-populations, and taking into account the stabilization phenomenon. The analysis of the model allows determination of time-varying corridors of probabilities for different cell fates, given the particular dynamics of cancer cells populations; and determination of a cell-cell communication factors influencing these time-varying probabilities of cell behavior (division, transition) scenarios. Though the results of the model have to be experimentally confirmed, we can anticipate the development of several fundamental and practical applications based on the theoretical results of the model.

Basic, simple and extendable kinetic model of protein synthesis.

Protein synthesis is one of the most fundamental biological processes. Despite existence of multiple mathematical models of translation, surprisingly, there is no basic and simple chemical kinetic model of this process, derived directly from the detailed kinetic scheme. One of the reasons for this is that the translation process is characterized by indefinite number of states, because of the structure of the polysome. We bypass this difficulty by applying lumping of multiple states of translated mRNA into few dynamical variables and by introducing a variable describing the pool of translating ribosomes. The simplest model can be solved analytically. The simplest model can be extended, if necessary, to take into account various phenomena such as the limited amount of ribosomal units or regulation of translation by microRNA. The introduced model is more suitable to describe the protein synthesis in eukaryotes but it can be extended to prokaryotes. The model can be used as a building block for more complex models of cellular processes. We demonstrate the utility of the model in two examples. First, we determine the critical parameters of the synthesis of a single protein for the case when the ribosomal units are abundant. Second, we demonstrate intrinsic bi-stability in the dynamics of the ribosomal protein turnover and predict that a minimal number of ribosomes should pre-exists in a living cell to sustain its protein synthesis machinery, even in the absence of proliferation.

Morphogenesis software based on epigenetic code concept.

The process of morphogenesis is an evolution of shape of an organism together with the differentiation of its parts. This process encompasses numerous biological processes ranging from embryogenesis to regeneration following crisis such as amputation or transplantation. A fundamental theoretical question is where exactly do these instructions for (re-)construction reside and how are they implemented? We have recently proposed a set of concepts, aiming to respond to these questions and to provide an appropriate mathematical formalization of the geometry of morphogenesis [1]. First, we consider a possibility that the evolution of shape is determined by epigenetic information, responsible for realization of different types of cell events. Second, we suggest a set of rules for converting this epigenetic information into instructive signals for cell event for each cell, as well as for transforming it after each cell event. Next we give notions of cell state, determined by its epigenetic array, and cell event, which is a change of cell state, and formalize development as a graph (tree) of cell states connected by 5 types of cell events, corresponding to the processes of cell division, cell growth, cell death, cell movement and cell differentiation. Here we present a Morphogenesis software capable to simulate an evolution of a 3D embryo starting from zygote, following a set of rules, based on our theoretical assumptions, and thus to provide a proof-of-concept of the hypothesis of epigenetic code regulation. The software creates a developing embryo and a corresponding graph of cell events according to the zygotic epigenetic spectrum and chosen parameters of the developmental rules. Variation of rules influencing the resulting shape of an embryo may help elucidating the principal laws underlying pattern formation.

Centrality and the shortest path approach in the human interactome.

Many notions and concepts for network analysis, including the shortest path approach, came to systems biology from the theory of graphs - the field of mathematics that studies graphs. We studied the relationship between the shortest paths and a biologically meaningful molecular path between vertices in human molecular interaction networks. We analyzed the sets of the shortest paths in the human interactome derived from HPRD and HIPPIE databases between all possible combinations of start and end proteins in eight signaling pathways in the KEGG database - NF-kappa B, MAPK, Jak-STAT, mTOR, ErbB, Wnt, TGF-beta, and the signaling part of the apoptotic process. We investigated whether the shortest paths match the canonical paths. We studied whether centrality of vertices and paths in the subnetworks induced by the shortest paths can highlight vertices and paths that are part of meaningful molecular paths. We found that the shortest paths match canonical counterparts only for canonical paths of length 2 or 3 interactions. The shortest paths match longer canonical counterparts with shortcuts or substitutions by protein complex members. We found that high centrality vertices are part of the canonical paths for up to 80% of the canonical paths depending on the database and the length.

Theory of Morphogenesis.

A model of morphogenesis is proposed based on seven explicit postulates. The mathematical import and biological significance of the postulates are explored and discussed.

Post-transcriptional modulation of interleukin 8 by CNOT6L regulates skeletal muscle differentiation.

CNOT6L is a deadenylase subunit belonging to the CCR4-NOT complex, a major deadenylase complex in eukaryotes involved at multiple levels in regulation of gene expression. While CNOT6L is expressed in skeletal muscle cells, its specific functions in this tissue are still largely unknown. Our previous work highlighted the functional of CNOT6L in skeletal muscle cell differentiation. To further explore how CNOT6L regulates myogenesis, we used here gene expression analysis to identify CNOT6L mRNA targets in human myoblasts. Among these novel targets, IL-8 (interleukin 8) mRNA was the most upregulated in CNOT6L knock-down (KD) cells. Biochemical approaches and poly (A) tail length assays showed that IL-8 mRNA is a direct target of CNOT6L, and further investigations by loss- and gain-of-function assays pointed out that IL-8 is an important effector of myogenesis. Therefore, we have characterized CNOT6L-IL-8 as a new signaling axis that regulates myogenesis.

On a model of pattern regeneration based on cell memory.

We present here a new model of the cellular dynamics that enable regeneration of complex biological morphologies. Biological cell structures are considered as an ensemble of mathematical points on the plane. Each cell produces a signal which propagates in space and is received by other cells. The total signal received by each cell forms a signal distribution defined on the cell structure. This distribution characterizes the geometry of the cell structure. If a part of this structure is removed, the remaining cells have two signals. They keep the value of the signal which they had before the amputation (memory), and they receive a new signal produced after the amputation. Regeneration of the cell structure is stimulated by the difference between the old and the new signals. It is stopped when the two signals coincide. The algorithm of regeneration contains certain rules which are essential for its functioning, being the first quantitative model of cellular memory that implements regeneration of complex patterns to a specific target morphology. Correct regeneration depends on the form and the size of the cell structure, as well as on some parameters of regeneration.

Target morphology and cell memory: a model of regenerative pattern formation.

Despite the growing body of work on molecular components required for regenerative repair, we still lack a deep understanding of the ability of some animal species to regenerate their appropriate complex anatomical structure following damage. A key question is how regenerating systems know when to stop growth and remodeling - what mechanisms implement recognition of correct morphology that signals a stop condition? In this work, we review two conceptual models of pattern regeneration that implement a kind of pattern memory. In the first one, all cells communicate with each other and keep the value of the total signal received from the other cells. If a part of the pattern is amputated, the signal distribution changes. The difference fromthe original signal distribution stimulates cell proliferation and leads to pattern regeneration, in effect implementing an error minimization process that uses signaling memory to achieve pattern correction. In the second model, we consider a more complex pattern organization with different cell types. Each tissue contains a central (coordinator) cell that controls the tissue and communicates with the other central cells. Each of them keeps memory about the signals received from other central cells. The values of these signals depend on the mutual cell location, and the memory allows regeneration of the structure when it is modified. The purpose of these models is to suggest possible mechanisms of pattern regeneration operating on the basis of cell memory which are compatible with diverse molecular implementation mechanisms within specific organisms.

Genome-wide exploration of miRNA function in mammalian muscle cell differentiation.

MiRNAs impact on the control of cell fate by regulating gene expression at the post-transcriptional level. Here, using mammalian muscle differentiation as a model and a phenotypic loss-of-function screen, we explored the function of miRNAs at the genome-wide level. We found that the depletion of a high number of miRNAs (63) impacted on differentiation of human muscle precursors, underscoring the importance of this post-transcriptional mechanism of gene regulation. Interestingly, a comparison with miRNA expression profiles revealed that most of the hit miRNAs did not show any significant variations of expression during differentiation. These constitutively expressed miRNAs might be required for basic and/or essential cell function, or else might be regulated at the post-transcriptional level. MiRNA inhibition yielded a variety of phenotypes, reflecting the widespread miRNA involvement in differentiation. Using a functional screen (the STarS--Suppressor Target Screen--approach, i. e. concomitant knockdown of miRNAs and of candidate target proteins), we discovered miRNA protein targets that are previously uncharacterized controllers of muscle-cell terminal differentiation. Our results provide a strategy for functional annotation of the human miRnome.

Mathematical modeling of microRNA-mediated mechanisms of translation repression.

MicroRNAs can affect the protein translation using nine mechanistically different mechanisms, including repression of initiation and degradation of the transcript. There is a hot debate in the current literature about which mechanism and in which situations has a dominant role in living cells. The worst, same experimental systems dealing with the same pairs of mRNA and miRNA can provide ambiguous evidences about which is the actual mechanism of translation repression observed in the experiment. We start with reviewing the current knowledge of various mechanisms of miRNA action and suggest that mathematical modeling can help resolving some of the controversial interpretations. We describe three simple mathematical models of miRNA translation that can be used as tools in interpreting the experimental data on the dynamics of protein synthesis. The most complex model developed by us includes all known mechanisms of miRNA action. It allowed us to study possible dynamical patterns corresponding to different miRNA-mediated mechanisms of translation repression and to suggest concrete recipes on determining the dominant mechanism of miRNA action in the form of kinetic signatures. Using computational experiments and systematizing existing evidences from the literature, we justify a hypothesis about co-existence of distinct miRNA-mediated mechanisms of translation repression. The actually observed mechanism will be that acting on or changing the sensitive parameters of the translation process. The limiting place can vary from one experimental setting to another. This model explains the majority of existing controversies reported.

Argonaute proteins couple chromatin silencing to alternative splicing.

Argonaute proteins play a major part in transcriptional gene silencing in many organisms, but their role in the nucleus of somatic mammalian cells remains elusive. Here, we have immunopurified human Argonaute-1 and Argonaute-2 (AGO1 and AGO2) chromatin-embedded proteins and found them associated with chromatin modifiers and, notably, with splicing factors. Using the CD44 gene as a model, we show that AGO1 and AGO2 facilitate spliceosome recruitment and modulate RNA polymerase II elongation rate, thereby affecting alternative splicing. Proper AGO1 and AGO2 recruitment to CD44 transcribed regions required the endonuclease Dicer and the chromobox protein HP1γ, and resulted in increased histone H3 lysine 9 methylation on variant exons. Our data thus uncover a new model for the regulation of alternative splicing, in which Argonaute proteins couple RNA polymerase II elongation to chromatin modification.

Prognostic impact of vitamin B6 metabolism in lung cancer.

Patients with non-small cell lung cancer (NSCLC) are routinely treated with cytotoxic agents such as cisplatin. Through a genome-wide siRNA-based screen, we identified vitamin B6 metabolism as a central regulator of cisplatin responses in vitro and in vivo. By aggravating a bioenergetic catastrophe that involves the depletion of intracellular glutathione, vitamin B6 exacerbates cisplatin-mediated DNA damage, thus sensitizing a large panel of cancer cell lines to apoptosis. Moreover, vitamin B6 sensitizes cancer cells to apoptosis induction by distinct types of physical and chemical stress, including multiple chemotherapeutics. This effect requires pyridoxal kinase (PDXK), the enzyme that generates the bioactive form of vitamin B6. In line with a general role of vitamin B6 in stress responses, low PDXK expression levels were found to be associated with poor disease outcome in two independent cohorts of patients with NSCLC. These results indicate that PDXK expression levels constitute a biomarker for risk stratification among patients with NSCLC.

Kinetic signatures of microRNA modes of action.

MicroRNAs (miRNAs) are key regulators of all important biological processes, including development, differentiation, and cancer. Although remarkable progress has been made in deciphering the mechanisms used by miRNAs to regulate translation, many contradictory findings have been published that stimulate active debate in this field. Here we contribute to this discussion in three ways. First, based on a comprehensive analysis of the existing literature, we hypothesize a model in which all proposed mechanisms of microRNA action coexist, and where the apparent mechanism that is detected in a given experiment is determined by the relative values of the intrinsic characteristics of the target mRNAs and associated biological processes. Among several coexisting miRNA mechanisms, the one that will effectively be measurable is that which acts on or changes the sensitive parameters of the translation process. Second, we have created a mathematical model that combines nine known mechanisms of miRNA action and estimated the model parameters from the literature. Third, based on the mathematical modeling, we have developed a computational tool for discriminating among different possible individual mechanisms of miRNA action based on translation kinetics data that can be experimentally measured (kinetic signatures). To confirm the discriminatory power of these kinetic signatures and to test our hypothesis, we have performed several computational experiments with the model in which we simulated the coexistence of several miRNA action mechanisms in the context of variable parameter values of the translation.

Dynamical modeling of microRNA action on the protein translation process.

BACKGROUND: Protein translation is a multistep process which can be represented as a cascade of biochemical reactions (initiation, ribosome assembly, elongation, etc.), the rate of which can be regulated by small non-coding microRNAs through multiple mechanisms. It remains unclear what mechanisms of microRNA action are the most dominant: moreover, many experimental reports deliver controversial messages on what is the concrete mechanism actually observed in the experiment. Nissan and Parker have recently demonstrated that it might be impossible to distinguish alternative biological hypotheses using the steady state data on the rate of protein synthesis. For their analysis they used two simple kinetic models of protein translation. RESULTS: In contrary to the study by Nissan and Parker, we show that dynamical data allow discriminating some of the mechanisms of microRNA action. We demonstrate this using the same models as developed by Nissan and Parker for the sake of comparison but the methods developed (asymptotology of biochemical networks) can be used for other models. We formulate a hypothesis that the effect of microRNA action is measurable and observable only if it affects the dominant system (generalization of the limiting step notion for complex networks) of the protein translation machinery. The dominant system can vary in different experimental conditions that can partially explain the existing controversy of some of the experimental data. CONCLUSIONS: Our analysis of the transient protein translation dynamics shows that it gives enough information to verify or reject a hypothesis about a particular molecular mechanism of microRNA action on protein translation. For multiscale systems only that action of microRNA is distinguishable which affects the parameters of dominant system (critical parameters), or changes the dominant system itself. Dominant systems generalize and further develop the old and very popular idea of limiting step. Algorithms for identifying dominant systems in multiscale kinetic models are straightforward but not trivial and depend only on the ordering of the model parameters but not on their concrete values. Asymptotic approach to kinetic models allows putting in order diverse experimental observations in complex situations when many alternative hypotheses co-exist.