BurstDECONV: a signal deconvolution method to uncover mechanisms of transcriptional bursting in live cells.

Monitoring transcription in living cells gives access to the dynamics of this complex fundamental process. It reveals that transcription is discontinuous, whereby active periods (bursts) are separated by one or several types of inactive periods of distinct lifetimes. However, decoding temporal fluctuations arising from live imaging and inferring the distinct transcriptional steps eliciting them is a challenge. We present BurstDECONV, a novel statistical inference method that deconvolves signal traces into individual transcription initiation events. We use the distribution of waiting times between successive polymerase initiation events to identify mechanistic features of transcription such as the number of rate-limiting steps and their kinetics. Comparison of our method to alternative methods emphasizes its advantages in terms of precision and flexibility. Unique features such as the direct determination of the number of promoter states and the simultaneous analysis of several potential transcription models make BurstDECONV an ideal analytic framework for live cell transcription imaging experiments. Using simulated realistic data, we found that our method is robust with regards to noise or suboptimal experimental designs. To show its generality, we applied it to different biological contexts such as Drosophila embryos or human cells.

An in silico analysis of robust but fragile gene regulation links enhancer length to robustness.

Organisms must ensure that expression of genes is directed to the appropriate tissues at the correct times, while simultaneously ensuring that these gene regulatory systems are robust to perturbation. This idea is captured by a mathematical concept called r-robustness, which says that a system is robust to a perturbation in up to r - 1 randomly chosen parameters. r-robustness implies that the biological system has a small number of sensitive parameters and that this number can be used as a robustness measure. In this work we use this idea to investigate the robustness of gene regulation using a sequence level model of the Drosophila melanogaster gene even-skipped. We consider robustness with respect to mutations of the enhancer sequence and with respect to changes of the transcription factor concentrations. We find that gene regulation is r-robust with respect to mutations in the enhancer sequence and identify a number of sensitive nucleotides. In both natural and in silico predicted enhancers, the number of nucleotides that are sensitive to mutation correlates negatively with the length of the sequence, meaning that longer sequences are more robust. The exact degree of robustness obtained is dependent not only on DNA sequence, but also on the local concentration of regulatory factors. We find that gene regulation can be remarkably sensitive to changes in transcription factor concentrations at the boundaries of expression features, while it is robust to perturbation elsewhere.

Network Reconstruction and Significant Pathway Extraction Using Phosphoproteomic Data from Cancer Cells.

Protein phosphorylation acts as an efficient switch controlling deregulated key signaling pathway in cancer. Computational biology aims to address the complexity of reconstructed networks but overrepresents well-known proteins and lacks information on less-studied proteins. A bioinformatic tool to reconstruct and select relatively small networks that connect signaling proteins to their targets in specific contexts is developed. It enables to propose and validate new signaling axes of the Syk kinase. To validate the potency of the tool, it is applied to two phosphoproteomic studies on oncogenic mutants of the well-known phosphatidyl-inositol 3-kinase (PIK3CA) and the unfamiliar Src-related tyrosine kinase lacking C-terminal regulatory tyrosine and N-terminal myristoylation sites (SRMS) kinase. By combining network reconstruction and signal propagation, comprehensive signaling networks from large-scale experimental data are built and multiple molecular paths from these kinases to their targets are extracted. Specific paths from two distinct PIK3CA mutants are retrieved, and their differential impact on the HER3 receptor kinase is explained. In addition, to address the missing connectivities of the SRMS kinase to its targets in interaction pathway databases, phospho-tyrosine and phospho-serine/threonine proteomic data are integrated. The resulting SRMS-signaling network comprises casein kinase 2, thereby validating its currently suggested role downstream of SRMS. The computational pipeline is publicly available, and contains a user-friendly graphical interface (http://doi.org/10.5281/zenodo.3333687).

Spatio-Genetic and phenotypic modelling elucidates resistance and re-sensitisation to treatment in heterogeneous melanoma.

Although novel targeted therapies have significantly improved the overall survival of patients with advanced melanoma, understanding and combatting drug resistance remains a major clinical challenge. Using partial differential equations, we describe the evolution of a cellular population through time, space, and phenotype dimensions, in the presence of various drug species. We then use this framework to explore models in which resistance is attained by either mutations (irreversible) or plasticity (reversible). Numerical results suggest that punctuated evolutionary assumptions are more consistent with results obtained from murine melanoma models than gradual evolution. Furthermore, in the context of an evolving tumour cell population, sequencing the treatment, for instance applying immunotherapy before BRAF inhibitors, can increase treatment effectiveness. However, drug strategies which showed success within a spatially homogeneous tumour environment were unsuccessful under heterogeneous conditions, suggesting that spatio-environmental heterogeneity may be the greatest challenge to tumour therapies. Plastic metabolic models are additionally capable of reproducing the characteristic resistant tumour volume curves and predicting re-sensitisation to secondary waves of treatment observed in patient derived xenograft (PDX) melanomas treated with MEK and BRAF inhibitors. Nevertheless, secondary relapse due to a pre-adapted subpopulation, remaining after the first wave of treatment, results in a more rapid development of resistance. Our model provides a framework through which tumour resistance can be understood and would suggest that carefully phased treatments may be able to overcome the development of long-term resistance in melanoma.

Linking metabolic network features to phenotypes using sparse group lasso.

MOTIVATION: Integration of metabolic networks with '-omics' data has been a subject of recent research in order to better understand the behaviour of such networks with respect to differences between biological and clinical phenotypes. Under the conditions of steady state of the reaction network and the non-negativity of fluxes, metabolic networks can be algebraically decomposed into a set of sub-pathways often referred to as extreme currents (ECs). Our objective is to find the statistical association of such sub-pathways with given clinical outcomes, resulting in a particular instance of a self-contained gene set analysis method. In this direction, we propose a method based on sparse group lasso (SGL) to identify phenotype associated ECs based on gene expression data. SGL selects a sparse set of feature groups and also introduces sparsity within each group. Features in our model are clusters of ECs, and feature groups are defined based on correlations among these features. RESULTS: We apply our method to metabolic networks from KEGG database and study the association of network features to prostate cancer (where the outcome is tumor and normal, respectively) as well as glioblastoma multiforme (where the outcome is survival time). In addition, simulations show the superior performance of our method compared to global test, which is an existing self-contained gene set analysis method. AVAILABILITY AND IMPLEMENTATION: R code (compatible with version 3.2.5) is available from http://www.abi.bit.uni-bonn.de/index.php?id=17. CONTACT: samal@combine.rwth-aachen.de or frohlich@bit.uni-bonn.de. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Reconstruction and signal propagation analysis of the Syk signaling network in breast cancer cells.

The ability to build in-depth cell signaling networks from vast experimental data is a key objective of computational biology. The spleen tyrosine kinase (Syk) protein, a well-characterized key player in immune cell signaling, was surprisingly first shown by our group to exhibit an onco-suppressive function in mammary epithelial cells and corroborated by many other studies, but the molecular mechanisms of this function remain largely unsolved. Based on existing proteomic data, we report here the generation of an interaction-based network of signaling pathways controlled by Syk in breast cancer cells. Pathway enrichment of the Syk targets previously identified by quantitative phospho-proteomics indicated that Syk is engaged in cell adhesion, motility, growth and death. Using the components and interactions of these pathways, we bootstrapped the reconstruction of a comprehensive network covering Syk signaling in breast cancer cells. To generate in silico hypotheses on Syk signaling propagation, we developed a method allowing to rank paths between Syk and its targets. We first annotated the network according to experimental datasets. We then combined shortest path computation with random walk processes to estimate the importance of individual interactions and selected biologically relevant pathways in the network. Molecular and cell biology experiments allowed to distinguish candidate mechanisms that underlie the impact of Syk on the regulation of cortactin and ezrin, both involved in actin-mediated cell adhesion and motility. The Syk network was further completed with the results of our biological validation experiments. The resulting Syk signaling sub-networks can be explored via an online visualization platform.

Signal Propagation in Sensing and Reciprocating Cellular Systems with Spatial and Structural Heterogeneity.

Sensing and reciprocating cellular systems (SARs) are important for the operation of many biological systems. Production in interferon (IFN) SARs is achieved through activation of the Jak-Stat pathway, and downstream upregulation of IFN regulatory factor (IRF)-7 and IFN transcription, but the role that high- and low-affinity IFNs play in this process remains unclear. We present a comparative between a minimal spatio-temporal partial differential equation model and a novel spatio-structural-temporal (SST) model for the consideration of receptor, binding, and metabolic aspects of SAR behaviour. Using the SST framework, we simulate single- and multi-cluster paradigms of IFN communication. Simulations reveal a cyclic process between the binding of IFN to the receptor, and the consequent increase in metabolism, decreasing the propensity for binding due to the internal feedback mechanism. One observes the effect of heterogeneity between cellular clusters, allowing them to individualise and increase local production, and within clusters, where we observe 'subpopular quiescence'; a process whereby intra-cluster subpopulations reduce their binding and metabolism such that other such subpopulations may augment their production. Finally, we observe the ability for low-affinity IFN to communicate a long range signal, where high affinity cannot, and the breakdown of this relationship through the introduction of cell motility. Biological systems may utilise cell motility where environments are unrestrictive and may use fixed system, with low-affinity communication, where a localised response is desirable.

Centralized Networks to Generate Human Body Motions.

We consider continuous-time recurrent neural networks as dynamical models for the simulation of human body motions. These networks consist of a few centers and many satellites connected to them. The centers evolve in time as periodical oscillators with different frequencies. The center states define the satellite neurons' states by a radial basis function (RBF) network. To simulate different motions, we adjust the parameters of the RBF networks. Our network includes a switching module that allows for turning from one motion to another. Simulations show that this model allows us to simulate complicated motions consisting of many different dynamical primitives. We also use the model for learning human body motion from markers' trajectories. We find that center frequencies can be learned from a small number of markers and can be transferred to other markers, such that our technique seems to be capable of correcting for missing information resulting from sparse control marker settings.

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.

A Geometric Method for Model Reduction of Biochemical Networks with Polynomial Rate Functions.

Model reduction of biochemical networks relies on the knowledge of slow and fast variables. We provide a geometric method, based on the Newton polytope, to identify slow variables of a biochemical network with polynomial rate functions. The gist of the method is the notion of tropical equilibration that provides approximate descriptions of slow invariant manifolds. Compared to extant numerical algorithms such as the intrinsic low-dimensional manifold method, our approach is symbolic and utilizes orders of magnitude instead of precise values of the model parameters. Application of this method to a large collection of biochemical network models supports the idea that the number of dynamical variables in minimal models of cell physiology can be small, in spite of the large number of molecular regulatory actors.

Reconciling molecular regulatory mechanisms with noise patterns of bacterial metabolic promoters in induced and repressed states.

Assessing gene expression noise in order to obtain mechanistic insights requires accurate quantification of gene expression on many individual cells over a large dynamic range. We used a unique method based on 2-photon fluorescence fluctuation microscopy to measure directly, at the single cell level and with single-molecule sensitivity, the absolute concentration of fluorescent proteins produced from the two Bacillus subtilis promoters that control the switch between glycolysis and gluconeogenesis. We quantified cell-to-cell variations in GFP concentrations in reporter strains grown on glucose or malate, including very weakly transcribed genes under strong catabolite repression. Results revealed strong transcriptional bursting, particularly for the glycolytic promoter. Noise pattern parameters of the two antagonistic promoters controlling the nutrient switch were differentially affected on glycolytic and gluconeogenic carbon sources, discriminating between the different mechanisms that control their activity. Our stochastic model for the transcription events reproduced the observed noise patterns and identified the critical parameters responsible for the differences in expression profiles of the promoters. The model also resolved apparent contradictions between in vitro operator affinity and in vivo repressor activity at these promoters. Finally, our results demonstrate that negative feedback is not noise-reducing in the case of strong transcriptional bursting.

Multimodality and flexibility of stochastic gene expression.

We consider a general class of mathematical models for stochastic gene expression where the transcription rate is allowed to depend on a promoter state variable that can take an arbitrary (finite) number of values. We provide the solution of the master equations in the stationary limit, based on a factorization of the stochastic transition matrix that separates timescales and relative interaction strengths, and we express its entries in terms of parameters that have a natural physical and/or biological interpretation. The solution illustrates the capacity of multiple states promoters to generate multimodal distributions of gene products, without the need for feedback. Furthermore, using the example of a three states promoter operating at low, high, and intermediate expression levels, we show that using multiple states operons will typically lead to a significant reduction of noise in the system. The underlying mechanism is that a three-states promoter can change its level of expression from low to high by passing through an intermediate state with a much smaller increase of fluctuations than by means of a direct transition.

Transcriptional Stochasticity as a Key Aspect of HIV-1 Latency.

This review summarizes current advances in the role of transcriptional stochasticity in HIV-1 latency, which were possible in a large part due to the development of single-cell approaches. HIV-1 transcription proceeds in bursts of RNA production, which stem from the stochastic switching of the viral promoter between ON and OFF states. This switching is caused by random binding dynamics of transcription factors and nucleosomes to the viral promoter and occurs at several time scales from minutes to hours. Transcriptional bursts are mainly controlled by the core transcription factors TBP, SP1 and NF-κb, the chromatin status of the viral promoter and RNA polymerase II pausing. In particular, spontaneous variability in the promoter chromatin creates heterogeneity in the response to activators such as TNF-α, which is then amplified by the Tat feedback loop to generate high and low viral transcriptional states. This phenomenon is likely at the basis of the partial and stochastic response of latent T cells from HIV-1 patients to latency-reversing agents, which is a barrier for the development of shock-and-kill strategies of viral eradication. A detailed understanding of the transcriptional stochasticity of HIV-1 and the possibility to precisely model this phenomenon will be important assets to develop more effective therapeutic strategies.

Canalization of gene expression in the Drosophila blastoderm by gap gene cross regulation.

Developing embryos exhibit a robust capability to reduce phenotypic variations that occur naturally or as a result of experimental manipulation. This reduction in variation occurs by an epigenetic mechanism called canalization, a phenomenon which has resisted understanding because of a lack of necessary molecular data and of appropriate gene regulation models. In recent years, quantitative gene expression data have become available for the segment determination process in the Drosophila blastoderm, revealing a specific instance of canalization. These data show that the variation of the zygotic segmentation gene expression patterns is markedly reduced compared to earlier levels by the time gastrulation begins, and this variation is significantly lower than the variation of the maternal protein gradient Bicoid. We used a predictive dynamical model of gene regulation to study the effect of Bicoid variation on the downstream gap genes. The model correctly predicts the reduced variation of the gap gene expression patterns and allows the characterization of the canalizing mechanism. We show that the canalization is the result of specific regulatory interactions among the zygotic gap genes. We demonstrate the validity of this explanation by showing that variation is increased in embryos mutant for two gap genes, Krüppel and knirps, disproving competing proposals that canalization is due to an undiscovered morphogen, or that it does not take place at all. In an accompanying article in PLoS Computational Biology (doi:10.1371/journal.pcbi.1000303), we show that cross regulation between the gap genes causes their expression to approach dynamical attractors, reducing initial variation and providing a robust output. These results demonstrate that the Bicoid gradient is not sufficient to produce gap gene borders having the low variance observed, and instead this low variance is generated by gap gene cross regulation. More generally, we show that the complex multigenic phenomenon of canalization can be understood at a quantitative and predictive level by the application of a precise dynamical model.

ODEbase: a repository of ODE systems for systems biology.

Summary: Recently, symbolic computation and computer algebra systems have been successfully applied in systems biology, especially in chemical reaction network theory. One advantage of symbolic computation is its potential for qualitative answers to biological questions. Qualitative methods analyze dynamical input systems as formal objects, in contrast to investigating only part of the state space, as is the case with numerical simulation. However, corresponding tools and libraries have a different set of requirements for their input data than their numerical counterparts. A common format used in mathematical modeling of biological processes is Systems Biology Markup Language (SBML). We illustrate that the use of SBML data in symbolic computation requires significant pre-processing, incorporating external biological and mathematical expertise. ODEbase provides suitable input data derived from established existing biomodels, covering in particular the BioModels database. Availability and implementation: ODEbase is available free of charge at https://odebase.org.

Computational Model of Heterogeneity in Melanoma: Designing Therapies and Predicting Outcomes.

Cutaneous melanoma is a highly invasive tumor and, despite the development of recent therapies, most patients with advanced metastatic melanoma have a poor clinical outcome. The most frequent mutations in melanoma affect the BRAF oncogene, a protein kinase of the MAPK signaling pathway. Therapies targeting both BRAF and MEK are effective for only 50% of patients and, almost systematically, generate drug resistance. Genetic and non-genetic mechanisms associated with the strong heterogeneity and plasticity of melanoma cells have been suggested to favor drug resistance but are still poorly understood. Recently, we have introduced a novel mathematical formalism allowing the representation of the relation between tumor heterogeneity and drug resistance and proposed several models for the development of resistance of melanoma treated with BRAF/MEK inhibitors. In this paper, we further investigate this relationship by using a new computational model that copes with multiple cell states identified by single cell mRNA sequencing data in melanoma treated with BRAF/MEK inhibitors. We use this model to predict the outcome of different therapeutic strategies. The reference therapy, referred to as "continuous" consists in applying one or several drugs without disruption. In "combination therapy", several drugs are used sequentially. In "adaptive therapy" drug application is interrupted when the tumor size is below a lower threshold and resumed when the size goes over an upper threshold. We show that, counter-intuitively, the optimal protocol in combination therapy of BRAF/MEK inhibitors with a hypothetical drug targeting cell states that develop later during the tumor response to kinase inhibitors, is to treat first with this hypothetical drug. Also, even though there is little difference in the timing of emergence of the resistance between continuous and adaptive therapies, the spatial distribution of the different melanoma subpopulations is more zonated in the case of adaptive therapy.

[Resistance to BRAF inhibitors: A lesson from clinical observations]. / La résistance aux inhibiteurs de BRAF - Les leçons de la clinique.

The MAPK/ERK pathway is an essential intracellular signaling pathway. Its deregulation is involved in tumor transformation and progression. The discovery of activating mutations of BRAF in various cancers has opened new therapeutic avenues with BRAF protein kinase inhibitors. Depending on the type of cancers, these inhibitors have shown either insufficient efficacy due to primary resistance of tumor cells or transient efficacy due to the development of acquired resistance. In this review, we revisit the discoveries that led to the development of BRAF inhibitors and detail the molecular and cellular mechanisms of resistance in cancers treated with these inhibitors. Understanding these mechanisms is crucial for developing more efficient therapeutic strategies.

Title: La résistance aux inhibiteurs de BRAF - Les leçons de la clinique. Abstract: La voie de signalisation MAPK/ERK est une voie centrale de la signalisation intracellulaire. Sa dérégulation participe à la transformation et la progression tumorales. Dans plusieurs cancers, la découverte de mutations activatrices de BRAF, à l'origine de l'activation de cette voie, a ouvert de nouvelles perspectives thérapeutiques avec le développement d'inhibiteurs spécifiques de la protéine. Selon les cancers, ces inhibiteurs ont cependant montré soit une efficacité insuffisante, due à la résistance primaire des cellules tumorales, soit une efficacité transitoire, due à l'apparition d'une résistance acquise. Dans cette revue, nous revenons sur les découvertes qui ont conduit au développement de ces inhibiteurs de BRAF. Nous détaillons également les mécanismes moléculaires et cellulaires de la résistance à ces inhibiteurs observée dans différents types de cancers. Comprendre ces mécanismes est en effet primordial pour développer des stratégies thérapeutiques qui soient plus efficaces.

The control of transcriptional memory by stable mitotic bookmarking.

To maintain cellular identities during development, gene expression profiles must be faithfully propagated through cell generations. The reestablishment of gene expression patterns upon mitotic exit is mediated, in part, by transcription factors (TF) mitotic bookmarking. However, the mechanisms and functions of TF mitotic bookmarking during early embryogenesis remain poorly understood. In this study, taking advantage of the naturally synchronized mitoses of Drosophila early embryos, we provide evidence that GAGA pioneer factor (GAF) acts as a stable mitotic bookmarker during zygotic genome activation. We show that, during mitosis, GAF remains associated to a large fraction of its interphase targets, including at cis-regulatory sequences of key developmental genes with both active and repressive chromatin signatures. GAF mitotic targets are globally accessible during mitosis and are bookmarked via histone acetylation (H4K8ac). By monitoring the kinetics of transcriptional activation in living embryos, we report that GAF binding establishes competence for rapid activation upon mitotic exit.

Quantitative imaging of transcription in living Drosophila embryos reveals the impact of core promoter motifs on promoter state dynamics.

Genes are expressed in stochastic transcriptional bursts linked to alternating active and inactive promoter states. A major challenge in transcription is understanding how promoter composition dictates bursting, particularly in multicellular organisms. We investigate two key Drosophila developmental promoter motifs, the TATA box (TATA) and the Initiator (INR). Using live imaging in Drosophila embryos and new computational methods, we demonstrate that bursting occurs on multiple timescales ranging from seconds to minutes. TATA-containing promoters and INR-containing promoters exhibit distinct dynamics, with one or two separate rate-limiting steps respectively. A TATA box is associated with long active states, high rates of polymerase initiation, and short-lived, infrequent inactive states. In contrast, the INR motif leads to two inactive states, one of which relates to promoter-proximal polymerase pausing. Surprisingly, the model suggests pausing is not obligatory, but occurs stochastically for a subset of polymerases. Overall, our results provide a rationale for promoter switching during zygotic genome activation.

Comparison of SYK Signaling Networks Reveals the Potential Molecular Determinants of Its Tumor-Promoting and Suppressing Functions.

Spleen tyrosine kinase (SYK) can behave as an oncogene or a tumor suppressor, depending on the cell and tissue type. As pharmacological SYK inhibitors are currently evaluated in clinical trials, it is important to gain more information on the molecular mechanisms underpinning these opposite roles. To this aim, we reconstructed and compared its signaling networks using phosphoproteomic data from breast cancer and Burkitt lymphoma cell lines where SYK behaves as a tumor suppressor and promoter. Bioinformatic analyses allowed for unveiling the main differences in signaling pathways, network topology and signal propagation from SYK to its potential effectors. In breast cancer cells, the SYK target-enriched signaling pathways included intercellular adhesion and Hippo signaling components that are often linked to tumor suppression. In Burkitt lymphoma cells, the SYK target-enriched signaling pathways included molecules that could play a role in SYK pro-oncogenic function in B-cell lymphomas. Several protein interactions were profoundly rewired in the breast cancer network compared with the Burkitt lymphoma network. These data demonstrate that proteomic profiling combined with mathematical network modeling allows untangling complex pathway interplays and revealing difficult to discern interactions among the SYK pathways that positively and negatively affect tumor formation and progression.