Computational modelling predicts impaired barrier function and higher sensitivity to skin inflammation following pH elevation.

Skin surface pH has been identified as a key regulator of the epidermal homeostasis through its action on serine protease activity. These enzymes, like kallikreins (KLK), are responsible for the degradation of corneodesmosomes, the protein structures linking together corneocytes, and are regulated by Lympho-Epithelial Kazal-Type-related Inhibitor (LEKTI). KLK activity increases at pH levels higher than physiological. An increase in skin surface pH has been observed in patients suffering from skin diseases characterized by impaired barrier function, like atopic dermatitis. In this work, we introduce an agent-based model of the epidermis to study the impact of a change in skin surface pH on the structural and physiological properties of the epidermis, through the LEKTI-KLK mechanism. We demonstrate that a less acidic pH, compared to the slightly acidic pH observed in healthy skin, is sufficient to significantly affect the water loss at the surface and the amount of irritant permeating through the epidermis. This weakening of the skin barrier function eventually results in a more intense skin inflammation following exposure to an external irritant. This work provides additional evidence that skin surface pH and serine proteases can be therapeutic targets to improve skin barrier integrity.

Mathematical modeling of the microtubule detyrosination/tyrosination cycle for cell-based drug screening design.

Microtubules and their post-translational modifications are involved in major cellular processes. In severe diseases such as neurodegenerative disorders, tyrosinated tubulin and tyrosinated microtubules are in lower concentration. We present here a mechanistic mathematical model of the microtubule tyrosination cycle combining computational modeling and high-content image analyses to understand the key kinetic parameters governing the tyrosination status in different cellular models. That mathematical model is parameterized, firstly, for neuronal cells using kinetic values taken from the literature, and, secondly, for proliferative cells, by a change of two parameter values obtained, and shown minimal, by a continuous optimization procedure based on temporal logic constraints to formalize experimental high-content imaging data. In both cases, the mathematical models explain the inability to increase the tyrosination status by activating the Tubulin Tyrosine Ligase enzyme. The tyrosinated tubulin is indeed the product of a chain of two reactions in the cycle: the detyrosinated microtubule depolymerization followed by its tyrosination. The tyrosination status at equilibrium is thus limited by both reaction rates and activating the tyrosination reaction alone is not effective. Our computational model also predicts the effect of inhibiting the Tubulin Carboxy Peptidase enzyme which we have experimentally validated in MEF cellular model. Furthermore, the model predicts that the activation of two particular kinetic parameters, the tyrosination and detyrosinated microtubule depolymerization rate constants, in synergy, should suffice to enable an increase of the tyrosination status in living cells.

Model learning to identify systemic regulators of the peripheral circadian clock.

MOTIVATION: Personalized medicine aims at providing patient-tailored therapeutics based on multi-type data toward improved treatment outcomes. Chronotherapy that consists in adapting drug administration to the patient's circadian rhythms may be improved by such approach. Recent clinical studies demonstrated large variability in patients' circadian coordination and optimal drug timing. Consequently, new eHealth platforms allow the monitoring of circadian biomarkers in individual patients through wearable technologies (rest-activity, body temperature), blood or salivary samples (melatonin, cortisol) and daily questionnaires (food intake, symptoms). A current clinical challenge involves designing a methodology predicting from circadian biomarkers the patient peripheral circadian clocks and associated optimal drug timing. The mammalian circadian timing system being largely conserved between mouse and humans yet with phase opposition, the study was developed using available mouse datasets. RESULTS: We investigated at the molecular scale the influence of systemic regulators (e.g. temperature, hormones) on peripheral clocks, through a model learning approach involving systems biology models based on ordinary differential equations. Using as prior knowledge our existing circadian clock model, we derived an approximation for the action of systemic regulators on the expression of three core-clock genes: Bmal1, Per2 and Rev-Erbα. These time profiles were then fitted with a population of models, based on linear regression. Best models involved a modulation of either Bmal1 or Per2 transcription most likely by temperature or nutrient exposure cycles. This agreed with biological knowledge on temperature-dependent control of Per2 transcription. The strengths of systemic regulations were found to be significantly different according to mouse sex and genetic background. AVAILABILITY AND IMPLEMENTATION: https://gitlab.inria.fr/julmarti/model-learning-mb21eccb. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Graphical requirements for multistationarity in reaction networks and their verification in BioModels.

Thomas' necessary conditions for the existence of multiple steady states in gene networks have been proved by Soulé with high generality for dynamical systems defined by differential equations. When applied to (protein) reaction networks however, those conditions do not provide information since they are trivially satisfied as soon as there is a bimolecular or a reversible reaction. Refined graphical requirements have been proposed to deal with such cases. In this paper, we present for the first time a graph rewriting algorithm for checking the refined conditions given by Soliman, and evaluate its practical performance by applying it systematically to the curated branch of the BioModels repository. This algorithm analyzes all reaction networks (of size up to 430 species) in less than 0.05 second per network, and permits to conclude to the absence of multistationarity in 160 networks over 506. The short computation times obtained in this graphical approach are in sharp contrast to the Jacobian-based symbolic computation approach. We also discuss the case of one extra graphical condition by arc rewiring that allows us to conclude on 20 more networks of this benchmark but with a high computational cost. Finally, we study with some details the case of phosphorylation cycles and MAPK signalling models which show the importance of modelling the intermediate complexations with the enzymes in order to correctly analyze the multistationarity capabilities of such biochemical reaction networks.

Influence Networks Compared with Reaction Networks: Semantics, Expressivity and Attractors.

Biochemical reaction networks are one of the most widely used formalisms in systems biology to describe the molecular mechanisms of high-level cell processes. However, modellers also reason with influence diagrams to represent the positive and negative influences between molecular species and may find an influence network useful in the process of building a reaction network. In this paper, we introduce a formalism of influence networks with forces, and equip it with a hierarchy of Boolean, Petri net, stochastic and differential semantics, similarly to reaction networks with rates. We show that the expressive power of influence networks is the same as that of reaction networks under the differential semantics, but weaker under the discrete semantics. Furthermore, the hierarchy of semantics leads us to consider a (positive) Boolean semantics that cannot test the absence of a species, that we compare with the (negative) Boolean semantics with test for absence of a species in gene regulatory networks à la Thomas. We study the monotonicity properties of the positive semantics and derive from them an algorithm to compute attractors in both the positive and negative Boolean semantics. We illustrate our results on models of the literature about the p53/Mdm2 DNA damage repair system, the circadian clock, and the influence of MAPK signaling on cell-fate decision in urinary bladder cancer.

Computer-aided biochemical programming of synthetic microreactors as diagnostic devices.

Biological systems have evolved efficient sensing and decision-making mechanisms to maximize fitness in changing molecular environments. Synthetic biologists have exploited these capabilities to engineer control on information and energy processing in living cells. While engineered organisms pose important technological and ethical challenges, de novo assembly of non-living biomolecular devices could offer promising avenues toward various real-world applications. However, assembling biochemical parts into functional information processing systems has remained challenging due to extensive multidimensional parameter spaces that must be sampled comprehensively in order to identify robust, specification compliant molecular implementations. We introduce a systematic methodology based on automated computational design and microfluidics enabling the programming of synthetic cell-like microreactors embedding biochemical logic circuits, or protosensors, to perform accurate biosensing and biocomputing operations in vitro according to temporal logic specifications. We show that proof-of-concept protosensors integrating diagnostic algorithms detect specific patterns of biomarkers in human clinical samples. Protosensors may enable novel approaches to medicine and represent a step toward autonomous micromachines capable of precise interfacing of human physiology or other complex biological environments, ecosystems, or industrial bioprocesses.

Logical model specification aided by model-checking techniques: application to the mammalian cell cycle regulation.

MOTIVATION: Understanding the temporal behaviour of biological regulatory networks requires the integration of molecular information into a formal model. However, the analysis of model dynamics faces a combinatorial explosion as the number of regulatory components and interactions increases. RESULTS: We use model-checking techniques to verify sophisticated dynamical properties resulting from the model regulatory structure in the absence of kinetic assumption. We demonstrate the power of this approach by analysing a logical model of the molecular network controlling mammalian cell cycle. This approach enables a systematic analysis of model properties, the delineation of model limitations, and the assessment of various refinements and extensions based on recent experimental observations. The resulting logical model accounts for the main irreversible transitions between cell cycle phases, the sequential activation of cyclins, and the inhibitory role of Skp2, and further emphasizes the multifunctional role for the cell cycle inhibitor Rb. AVAILABILITY AND IMPLEMENTATION: The original and revised mammalian cell cycle models are available in the model repository associated with the public modelling software GINsim (http://ginsim.org/node/189). CONTACT: thieffry@ens.fr SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Model-based investigation of the circadian clock and cell cycle coupling in mouse embryonic fibroblasts: Prediction of RevErb-α up-regulation during mitosis.

Experimental observations have put in evidence autonomous self-sustained circadian oscillators in most mammalian cells, and proved the existence of molecular links between the circadian clock and the cell cycle. Some mathematical models have also been built to assess conditions of control of the cell cycle by the circadian clock. However, recent studies in individual NIH3T3 fibroblasts have shown an unexpected acceleration of the circadian clock together with the cell cycle when the culture medium is enriched with growth factors, and the absence of such acceleration in confluent cells. In order to explain these observations, we study a possible entrainment of the circadian clock by the cell cycle through a regulation of clock genes around the mitosis phase. We develop a computational model and a formal specification of the observed behavior to investigate the conditions of entrainment in period and phase. We show that either the selective activation of RevErb-α or the selective inhibition of Bmal1 transcription during the mitosis phase, allow us to fit the experimental data on both period and phase, while a uniform inhibition of transcription during mitosis seems incompatible with the phase data. We conclude on the arguments favoring the RevErb-α up-regulation hypothesis and on some further predictions of the model.

Synthesizing Configurable Biochemical Implementation of Linear Systems from Their Transfer Function Specifications.

The ability to engineer synthetic systems in the biochemical context is constantly being improved and has a profound societal impact. Linear system design is one of the most pervasive methods applied in control tasks, and its biochemical realization has been proposed by Oishi and Klavins and advanced further in recent years. However, several technical issues remain unsolved. Specifically, the design process is not fully automated from specification at the transfer function level, systems once designed often lack dynamic adaptivity to environmental changes, matching rate constants of reactions is not always possible, and implementation may be approximative and greatly deviate from the specifications. Building upon the work of Oishi and Klavins, this paper overcomes these issues by introducing a design flow that transforms a transfer-function specification of a linear system into a set of chemical reactions, whose input-output response precisely conforms to the specification. This system is implementable using the DNA strand displacement technique. The underlying configurability is embedded into primitive components and template modules, and thus the entire system is adaptive. Simulation of DNA strand displacement implementation confirmed the feasibility and superiority of the proposed synthesis flow.

Reconfigurable neuromorphic computation in biochemical systems.

Implementing application-specific computation and control tasks within a biochemical system has been an important pursuit in synthetic biology. Most synthetic designs to date have focused on realizing systems of fixed functions using specifically engineered components, thus lacking flexibility to adapt to uncertain and dynamically-changing environments. To remedy this limitation, an analog and modularized approach to realize reconfigurable neuromorphic computation with biochemical reactions is presented. We propose a biochemical neural network consisting of neuronal modules and interconnects that are both reconfigurable through external or internal control over the concentrations of certain molecular species. Case studies on classification and machine learning applications using the DNA strain displacement technology demonstrate the effectiveness of our design in both reconfiguration and autonomous adaptation.

In silico control of biomolecular processes.

By implementing an external feedback loop one can tightly control the expression of a gene over many cell generations with quantitative accuracy. Controlling precisely the level of a protein of interest will be useful to probe quantitatively the dynamical properties of cellular processes and to drive complex, synthetically-engineered networks. In this chapter we describe a platform for real-time closed-loop control of gene expression in yeast that integrates microscopy for monitoring gene expression at the cell level, microfluidics to manipulate the cells environment, and original software for automated imaging, quantification, and model predictive control. By using an endogenous osmo-stress responsive promoter and playing with the osmolarity of the cells environment, we demonstrate that long-term control can indeed be achieved for both time-constant and time-varying target profiles, at the population level, and even at the single-cell level.

A constraint solving approach to model reduction by tropical equilibration.

Model reduction is a central topic in systems biology and dynamical systems theory, for reducing the complexity of detailed models, finding important parameters, and developing multi-scale models for instance. While singular perturbation theory is a standard mathematical tool to analyze the different time scales of a dynamical system and decompose the system accordingly, tropical methods provide a simple algebraic framework to perform these analyses systematically in polynomial systems. The crux of these methods is in the computation of tropical equilibrations. In this paper we show that constraint-based methods, using reified constraints for expressing the equilibration conditions, make it possible to numerically solve non-linear tropical equilibration problems, out of reach of standard computation methods. We illustrate this approach first with the detailed reduction of a simple biochemical mechanism, the Michaelis-Menten enzymatic reaction model, and second, with large-scale performance figures obtained on the http://biomodels.net repository.

Long-term model predictive control of gene expression at the population and single-cell levels.

Gene expression plays a central role in the orchestration of cellular processes. The use of inducible promoters to change the expression level of a gene from its physiological level has significantly contributed to the understanding of the functioning of regulatory networks. However, from a quantitative point of view, their use is limited to short-term, population-scale studies to average out cell-to-cell variability and gene expression noise and limit the nonpredictable effects of internal feedback loops that may antagonize the inducer action. Here, we show that, by implementing an external feedback loop, one can tightly control the expression of a gene over many cell generations with quantitative accuracy. To reach this goal, we developed a platform for real-time, closed-loop control of gene expression in yeast that integrates microscopy for monitoring gene expression at the cell level, microfluidics to manipulate the cells' environment, and original software for automated imaging, quantification, and model predictive control. By using an endogenous osmostress responsive promoter and playing with the osmolarity of the cells environment, we show that long-term control can, indeed, be achieved for both time-constant and time-varying target profiles at the population and even the single-cell levels. Importantly, we provide evidence that real-time control can dynamically limit the effects of gene expression stochasticity. We anticipate that our method will be useful to quantitatively probe the dynamic properties of cellular processes and drive complex, synthetically engineered networks.

Competing G protein-coupled receptor kinases balance G protein and ß-arrestin signaling.

Seven-transmembrane receptors (7TMRs) are involved in nearly all aspects of chemical communications and represent major drug targets. 7TMRs transmit their signals not only via heterotrimeric G proteins but also through ß-arrestins, whose recruitment to the activated receptor is regulated by G protein-coupled receptor kinases (GRKs). In this paper, we combined experimental approaches with computational modeling to decipher the molecular mechanisms as well as the hidden dynamics governing extracellular signal-regulated kinase (ERK) activation by the angiotensin II type 1A receptor (AT(1A)R) in human embryonic kidney (HEK)293 cells. We built an abstracted ordinary differential equations (ODE)-based model that captured the available knowledge and experimental data. We inferred the unknown parameters by simultaneously fitting experimental data generated in both control and perturbed conditions. We demonstrate that, in addition to its well-established function in the desensitization of G-protein activation, GRK2 exerts a strong negative effect on ß-arrestin-dependent signaling through its competition with GRK5 and 6 for receptor phosphorylation. Importantly, we experimentally confirmed the validity of this novel GRK2-dependent mechanism in both primary vascular smooth muscle cells naturally expressing the AT(1A)R, and HEK293 cells expressing other 7TMRs.

Towards real-time control of gene expression: controlling the HOG signaling cascade.

To decipher the dynamical functioning of cellular processes, the method of choice is to observe the time response of cells subjected to well controlled perturbations in time and amplitude. Efficient methods, based on molecular biology, are available to monitor quantitatively and dynamically many cellular processes. In contrast, it is still a challenge to perturb cellular processes - such as gene expression - in a precise and controlled manner. Here, we propose a first step towards in vivo control of gene expression: in real-time, we dynamically control the activity of a yeast signaling cascade thanks to an experimental platform combining a micro-fluidic device, an epi-fluorescence microscope and software implementing control approaches. We experimentally demonstrate the feasibility of this approach, and we investigate computationally some possible improvements of our control strategy using a model of the yeast osmo-adaptation response fitted to our data.

A graphical method for reducing and relating models in systems biology.

MOTIVATION: In Systems Biology, an increasing collection of models of various biological processes is currently developed and made available in publicly accessible repositories, such as biomodels.net for instance, through common exchange formats such as SBML. To date, however, there is no general method to relate different models to each other by abstraction or reduction relationships, and this task is left to the modeler for re-using and coupling models. In mathematical biology, model reduction techniques have been studied for a long time, mainly in the case where a model exhibits different time scales, or different spatial phases, which can be analyzed separately. These techniques are however far too restrictive to be applied on a large scale in systems biology, and do not take into account abstractions other than time or phase decompositions. Our purpose here is to propose a general computational method for relating models together, by considering primarily the structure of the interactions and abstracting from their dynamics in a first step. RESULTS: We present a graph-theoretic formalism with node merge and delete operations, in which model reductions can be studied as graph matching problems. From this setting, we derive an algorithm for deciding whether there exists a reduction from one model to another, and evaluate it on the computation of the reduction relations between all SBML models of the biomodels.net repository. In particular, in the case of the numerous models of MAPK signalling, and of the circadian clock, biologically meaningful mappings between models of each class are automatically inferred from the structure of the interactions. We conclude on the generality of our graphical method, on its limits with respect to the representation of the structure of the interactions in SBML, and on some perspectives for dealing with the dynamics. AVAILABILITY: The algorithms described in this article are implemented in the open-source software modeling platform BIOCHAM available at http://contraintes.inria.fr/biocham The models used in the experiments are available from http://www.biomodels.net/.

Towards a systems biology approach of-G protein-coupled receptor signalling: challenges and expectations.

G protein-coupled receptors (GPCRs) control all the main physiological functions and are targeted by more than 50% of therapeutics. Our perception of GPCRs signalling has grown increasingly complex since it is now accepted that they activate large signalling networks which are integrating the information fluxes into appropriate biological responses. These concepts lead the way to the development of pathway-selective agonists (or antagonists) with fewer side effects. Systems biology approaches focused on GPCR-mediated signalling would help dealing with the huge complexity of these mechanisms therefore speeding-up the discovery of new drug classes. In this review, we present the various technical and conceptual possibilities allowing a systems approach of GPCR-mediated signalling. The main remaining limitations are also discussed.