Non-equilibrium phase transitions in biomolecular signal transduction

We study a mechanism for reliable switching in biomolecular signal-transduction cascades. Steady bistable states are created by system-size cooperative effects in populations of proteins, in spite of the fact that the phosphorylation-state transitions of any molecule, by means of which the switch is implemented, are highly stochastic. The emergence of switching is a nonequilibrium phase transition in an energetically driven, dissipative system described by a master equation. We use operator and functional integral methods from reaction-diffusion theory to solve for the phase structure, noise spectrum, and escape trajectories and first-passage times of a class of minimal models of switches, showing how all critical properties for switch behavior can be computed within a unified framework

Cumulative signal transmission in nonlinear reaction-diffusion networks

Quantifying signal transmission in biochemical systems is key to uncover the mechanisms that cells use to control their responses to environmental stimuli. In this work we use the time-integral of chemical species as a measure of a network’s ability to cumulatively transmit signals encoded in spatiotemporal concentrations. We identify a class of nonlinear reaction-diffusion networks in which the time-integrals of some species can be computed analytically. The derived time-integrals do not require knowledge of the solution of the reaction-diffusion equation, and we provide a simple graphical test to check if a given network belongs to the proposed class. The formulae for the time-integrals reveal how the kinetic parameters shape signal transmission in a network under spatiotemporal stimuli. We use these to show that a canonical complex-formation mechanism behaves as a spatial low-pass filter, the bandwidth of which is inversely proportional to the diffusion length of the ligand

Control structure and limitations of biochemical networks

Biochemical networks typically exhibit intricate topologies that hinder their analysis with control-theoretic tools. In this work we present a systematic methodology for the identification of the control structure of a reaction network. The method is based on a bandwidth reduction technique applied to the incidence matrix of the network’s graph. In addition, in the case of mass-action and stable networks we show that it is possible to identify linear algebraic dependencies between the time-domain integrals of some species’ concentrations. We consider the extrinsic apoptosis pathway and an activation– inhibition mechanism to illustrate the application of our result

The interplay of intrinsic and extrinsic bounded noises in genetic networks

After being considered as a nuisance to be filtered out, it became recently clear that biochemical noise plays a complex role, often fully functional, for a genetic network. The influence of intrinsic and extrinsic noises on genetic networks has intensively been investigated in last ten years, though contributions on the co-presence of both are sparse. Extrinsic noise is usually modeled as an unbounded white or colored gaussian stochastic process, even though realistic stochastic perturbations are clearly bounded. In this paper we consider Gillespie-like stochastic models of nonlinear networks, i.e. the intrinsic noise, where the model jump rates are affected by colored bounded extrinsic noises synthesized by a suitable biochemical state-dependent Langevin system. These systems are described by a master equation, and a simulation algorithm to analyze them is derived. This new modeling paradigm should enlarge the class of systems amenable at modeling. We investigated the influence of both amplitude and autocorrelation time of a extrinsic Sine-Wiener noise on: $(i)$ the Michaelis-Menten approximation of noisy enzymatic reactions, which we show to be applicable also in co-presence of both intrinsic and extrinsic noise, $(ii)$ a model of enzymatic futile cycle and $(iii)$ a genetic toggle switch. In $(ii)$ and $(iii)$ we show that the presence of a bounded extrinsic noise induces qualitative modifications in the probability densities of the involved chemicals, where new modes emerge, thus suggesting the possibile functional role of bounded noises

Stochastic focusing coupled with negative feedback enables robust regulation in biochemical reaction networks

Nature presents multiple intriguing examples of processes which proceed at high precision and regularity. This remarkable stability is frequently counter to modelers' experience with the inherent stochasticity of chemical reactions in the regime of low copy numbers. Moreover, the effects of noise and nonlinearities can lead to "counter-intuitive" behavior, as demonstrated for a basic enzymatic reaction scheme that can display stochastic focusing (SF). Under the assumption of rapid signal fluctuations, SF has been shown to convert a graded response into a threshold mechanism, thus attenuating the detrimental effects of signal noise. However, when the rapid fluctuation assumption is violated, this gain in sensitivity is generally obtained at the cost of very large product variance, and this unpredictable behavior may be one possible explanation of why, more than a decade after its introduction, SF has still not been observed in real biochemical systems. In this work we explore the noise properties of a simple enzymatic reaction mechanism with a small and fluctuating number of active enzymes that behaves as a high-gain, noisy amplifier due to SF caused by slow enzyme fluctuations. We then show that the inclusion of a plausible negative feedback mechanism turns the system from a noisy signal detector to a strong homeostatic mechanism by exchanging high gain with strong attenuation in output noise and robustness to parameter variations. Moreover, we observe that the discrepancy between deterministic and stochastic descriptions of stochastically focused systems in the evolution of the means almost completely disappears, despite very low molecule counts and the additional nonlinearity due to feedback. The reaction mechanism considered here can provide a possible resolution to the apparent conflict between intrinsic noise and high precision in critical intracellular processes

Trends in modeling Biomedical Complex Systems

In this paper we provide an introduction to the techniques for multi-scale complex biological systems, from the single bio-molecule to the cell, combining theoretical modeling, experiments, informatics tools and technologies suitable for biological and biomedical research, which are becoming increasingly multidisciplinary, multidimensional and information-driven. The most important concepts on mathematical modeling methodologies and statistical inference, bioinformatics and standards tools to investigate complex biomedical systems are discussed and the prominent literature useful to both the practitioner and the theoretician are presented

Trends in modeling Biomedical Complex Systems.

In this paper we provide an introduction to the techniques for multi-scale complex biological systems, from the single bio-molecule to the cell, combining theoretical modeling, experiments, informatics tools and technologies suitable for biological and biomedical research, which are becoming increasingly multidisciplinary, multidimensional and information-driven. The most important concepts on mathematical modeling methodologies and statistical inference, bioinformatics and standards tools to investigate complex biomedical systems are discussed and the prominent literature useful to both the practitioner and the theoretician are presented.RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are

Optimal Design of Signaling Modules:Key Drivers, Trade-Offs and Sustainability

One of the basic characteristics of every living system is the ability to respond to extracellular signals. This is carried out through a limited number of protein-based signaling networks, whose function is not based only on simple transmission of the received signals, but incorporates the processing, encoding and integration of both external and internal signals. The results than lead to different changes in gene expression and regulate cell growth, mitogenesis, differentiation, embryo development, and stress responses in mammalian cells, whereas the malfunction is in correlation with diseases such as cancer, asthma and diabetes. In signaling networks, the basic units are covalent modification cycles, which comprise the activation and deactivation of proteins by other proteins. Protein modification in cell signaling – typically a phosphorylation and dephosphorylation – is a general mechanism responsible for the transfer of a wide variety of chemical signals in biological systems. Although the concept does not seem to be complex from a biochemical point of view, these simple systems can nevertheless provide a large diapason of dynamical responses and are therefore ubiquitous building blocks of signaling pathways. These cycles are often linked, forming multiple layers of cycles, the so-called cascades. Commonly observed instance of signal transduction through a series of protein kinase reactions are the kinases of the mitogen-activated protein kinase (MAPK) cascades. These pathways, which are found in almost all eukaryotes, play an important role in controlling different cellular processes, including fundamental functions. The activation of the cellular response by MAPK pathways typically involves at least three phosphorylation steps. In order to better understand the nature of this regulation and to gain greater insight into the mechanisms that determine the function of cells, signaling modules have been intensively studied using mathematical modeling and computational simulations, through the fast growing field of systems biology and its disciplines. The primary aim is to faithfully describe the system and to be able to predict the system behavior. Synergistically with experimental analysis, the reported observations have allowed one to identify properties of these pathways, such as fast signal propagation, large amplification, short signal duration and noise resistance. Since biochemical parameters in signaling pathways are not easily accessible experimentally, it is necessary to use advanced mathematical tools for their correct estimation. Using the paradigm of man-made optimal signal transduction systems, we chose to take the research path for discovering optimal design of cellular signaling modules. To approach the main thesis objective, we first identified the key system parameters through global sensitivity analysis. Comparative analysis of differences and similarities within different system architectures revealed some insights for initial parameter classification and starting point for optimal system design. In order to be able to interpret a broader range of phenotypes, we take into account both steady-state and dynamic properties simultaneously. Furthermore, we investigated the trade-offs between optimal characteristics. As a result, we found the biochemical and biophysical parameters that determine these trade-offs and we analyzed if there exist conditions under which we can simultaneously achieve optimal steady-state and dynamic performance. We first analyze what are the design principles that lead the system to have the minimal signaling times, subject to a certain level of amplification gain. In this setup, we bring out our main research question: are there any trade-offs and interplay between different steady-state and dynamic properties? Furthermore, we include the property of ultrasensitivity and eventually solve multi-objective optimization problems. A particularly insightful finding of this work is that, upon judicious selection of the kinetic parameters, a simple covalent modification cycle is able to meet multiple objectives simultaneously. In particular, this analysis may help explain why signaling cycles are so ubiquitous in cell signaling. The enhancement of ultrasensitivity and faster signal propagation in the multicyclic systems clearly show the advantages of the natural choice of designing signaling pathways in the form of signaling cascades. The thesis concludes with the potential research steps that could be taken along the same path, and that would gather more quantitative knowledge about signaling pathways

Modeling the Transcriptional Landscape of in vitro Neuronal Differentiation and ALS Disease

The spinal cord is a complex structure responsible for processing sensory inputs and motor outputs. As such, the developmental and spatial organization of cells is highly organized. Diseases affecting the spinal cord, such as Amyotrophic Lateral Sclerosis (ALS), result in the disruption of normal cellular function and intercellular interactions, culminating in neurodegeneration. Deciphering disease mechanisms requires a fundamental understanding of both the normal development of cells within the spinal cord as well as the homeostatic environment that allows for proper function. Biological processes such as cellular differentiation, maturation, and disease progression proceed in an asynchronous and cell type-specific manner. Until recently, bulk measurements of a mixed population of cells have been key in understanding these events. However, bulk measurements can obscure the molecular mechanisms involved in branched or coinciding processes, such as differential transcriptional responses occurring between subpopulations of cells. Measurements in individual cells have largely been restricted to 4 color immunofluorescence assays, which provide a solid but limited view of molecular-level changes. Recently, developments in single cell RNA-sequencing (scRNA-Seq) have provided an avenue of accurately profiling the RNA expression levels of thousands of genes concomitantly in an individual cell. With this increased experimental precision comes the ability to explore pathways that are differentially activated in subpopulations of cells, and to determine the transcriptional programs that underlie complex biological processes. In this dissertation, I will first review the key features of scRNA-Seq and downstream analysis. I will then discuss two applications of scRNA-seq: 1) the in vitro differentiation of mouse embryonic stem cells into motor neurons, and 2) the effect of the ALS-associated gene SOD1G93A expression on cultured motor neurons in a cellular model of ALS