Modeling the complex dynamics of enzyme-pathway coevolution.

Peer reviewedPostprin

Describing the complexity of systems: multi-variable "set complexity" and the information basis of systems biology

Context dependence is central to the description of complexity. Keying on the pairwise definition of "set complexity" we use an information theory approach to formulate general measures of systems complexity. We examine the properties of multi-variable dependency starting with the concept of interaction information. We then present a new measure for unbiased detection of multi-variable dependency, "differential interaction information." This quantity for two variables reduces to the pairwise "set complexity" previously proposed as a context-dependent measure of information in biological systems. We generalize it here to an arbitrary number of variables. Critical limiting properties of the "differential interaction information" are key to the generalization. This measure extends previous ideas about biological information and provides a more sophisticated basis for study of complexity. The properties of "differential interaction information" also suggest new approaches to data analysis. Given a data set of system measurements differential interaction information can provide a measure of collective dependence, which can be represented in hypergraphs describing complex system interaction patterns. We investigate this kind of analysis using simulated data sets. The conjoining of a generalized set complexity measure, multi-variable dependency analysis, and hypergraphs is our central result. While our focus is on complex biological systems, our results are applicable to any complex system.Comment: 44 pages, 12 figures; made revisions after peer revie

Multiomics Integration by Non-Negative Tri-Matrix Factorization Reveals New Target Genes in Parkinson’s Disease

Parkinson’s disease (PD) is the second most common neurodegenerative disease which is characterized by neuronal loss of dopaminergic neurons (mDA) in the substantia nigra. The underlying complexity of the disease and limited amount of patient material limits current interventions to only symptomatic and no curative treatment despite intensive research. We use patient-derived induced pluripotent stem cells to generate mDAs and investigate disease mechanisms by multiomics characterization including single cell RNA-sequencing and bulk proteomics and metabolomics. For this purpose, we developed an extended Non- Negative TriMatrix Factorization approache that allows to integrate the heterogeneous omics data with knowledge of molecular databases including protein-protein, genetic and metabolic interactions as well as co-expression profiles. Our approach was able to identify already PD-associated but also new druggable candidate genes of PD development.Book of abstract: 4th Belgrade Bioinformatics Conference, June 19-23, 202

On the phase space structure of IP3 induced Ca2+ signalling and concepts for predictive modeling

The correspondence between mathematical structures and experimental systems is the basis of the generalizability of results found with specific systems, and is the basis of the predictive power of theoretical physics. While physicists have confidence in this correspondence, it is less recognized in cellular biophysics. On the one hand, the complex organization of cellular dynamics involving a plethora of interacting molecules and the basic observation of cell variability seem to question its possibility. The practical difficulties of deriving the equations describing cellular behaviour from first principles support these doubts. On the other hand, ignoring such a correspondence would severely limit the possibility of predictive quantitative theory in biophysics. Additionally, the existence of functional modules (like pathways) across cell types suggests also the existence of mathematical structures with comparable universality. Only a few cellular systems have been sufficiently investigated in a variety of cell types to follow up these basic questions. IP3 induced Ca2+ signalling is one of them, and the mathematical structure corresponding to it is subject of ongoing discussion. We review the system’s general properties observed in a variety of cell types. They are captured by a reaction diffusion system. We discuss the phase space structure of its local dynamics. The spiking regime corresponds to noisy excitability. Models focussing on different aspects can be derived starting from this phase space structure. We discuss how the initial assumptions on the set of stochastic variables and phase space structure shape the predictions of parameter dependencies of the mathematical models resulting from the derivation

Data-driven dynamical model indicates that the heat shock response in Chlamydomonas reinhardtii is tailored to handle natural temperature variation

Global warming exposes plants to severe heat stress, with consequent crop yield reduction. Organisms exposed to high temperature stresses typically protect themselves with a heat shock response (HSR), where accumulation of unfolded proteins initiates the synthesis of heat shock proteins through the heat shock transcription factor HSF1. While the molecular mechanisms are qualitatively well characterized, our quantitative understanding of the under- lying dynamics is still very limited. Here, we study the dynamics of HSR in the photosynthetic model organism Chlamydomonas reinhardtii with a data-driven mathematical model of HSR. We based our dynamical model mostly on mass action kinetics, with a few nonlinear terms. The model was parametrized and validated by several independent datasets obtained from the literature. We demonstrate that HSR quantitatively and significantly differs if an increase in temperature of the same magnitude occurs abruptly, as often applied under laboratory conditions, or gradually, which would rather be expected under natural conditions. In contrast to rapid temperature increases, under gradual changes only negligible amounts of misfolded proteins accumulate, indicating that the HSR of C. reinhardtii efficiently avoids the accumulation of misfolded proteins under conditions most likely to prevail in nature. The mathematical model we developed is a flexible tool to simulate the HSR to different conditions and complements the current experimental approaches

Data-driven dynamical model indicates that the heat shock response in Chlamydomonas reinhardtii is tailored to handle natural temperature variation

Global warming exposes plants to severe heat stress, with consequent crop yield reduction. Organisms exposed to high temperature stresses typically protect themselves with a heat shock response (HSR), where accumulation of unfolded proteins initiates the synthesis of heat shock proteins through the heat shock transcription factor HSF1. While the molecular mechanisms are qualitatively well characterized, our quantitative understanding of the under- lying dynamics is still very limited. Here, we study the dynamics of HSR in the photosynthetic model organism Chlamydomonas reinhardtii with a data-driven mathematical model of HSR. We based our dynamical model mostly on mass action kinetics, with a few nonlinear terms. The model was parametrized and validated by several independent datasets obtained from the literature. We demonstrate that HSR quantitatively and significantly differs if an increase in temperature of the same magnitude occurs abruptly, as often applied under laboratory conditions, or gradually, which would rather be expected under natural conditions. In contrast to rapid temperature increases, under gradual changes only negligible amounts of misfolded proteins accumulate, indicating that the HSR of C. reinhardtii efficiently avoids the accumulation of misfolded proteins under conditions most likely to prevail in nature. The mathematical model we developed is a flexible tool to simulate the HSR to different conditions and complements the current experimental approaches

Carbohydrate-active enzymes exemplify entropic principles in metabolism

Statistical thermodynamics and in vitro experimentation demonstrate that metabolic enzymes can be driven by an increase in the entropy of a reaction system, and point to a role for entropy gradients in the emergence of robust metabolic functions in vivo

A cut finite element method for spatially resolved energy metabolism models in complex neuro-cell morphologies with minimal remeshing

A thorough understanding of brain metabolism is essential to tackle neurodegenerative diseases. Astrocytes are glial cells which play an important metabolic role by supplying neurons with energy. In addition, astrocytes provide scaffolding and homeostatic functions to neighboring neurons and contribute to the blood–brain barrier. Recent investigations indicate that the complex morphology of astrocytes impacts upon their function and in particular the efficiency with which these cells metabolize nutrients and provide neurons with energy, but a systematic understanding is still elusive. Modelling and simulation represent an effective framework to address this challenge and to deepen our understanding of brain energy metabolism. This requires solving a set of metabolic partial differential equations on complex domains and remains a challenge. In this paper, we propose, test and verify a simple numerical method to solve a simplified model of metabolic pathways in astrocytes. The method can deal with arbitrarily complex cell morphologies and enables the rapid and simple modification of the model equations by users also without a deep knowledge in the numerical methods involved. The results obtained with the new method (CutFEM) are as accurate as the finite element method (FEM) whilst CutFEM disentangles the cell morphology from its discretisation, enabling us to deal with arbitrarily complex morphologies in two and three dimensions

Fundamental properties of Ca²⁺ signals

Background Ca²⁺ is a ubiquitous and versatile second messenger that transmits information through changes of the cytosolic Ca²⁺ concentration. Recent investigations changed basic ideas on the dynamic character of Ca²⁺ signals and challenge traditional ideas on information transmission. Scope of review We present recent findings on key characteristics of the cytosolic Ca²⁺ dynamics and theoretical concepts that explain the wide range of experimentally observed Ca²⁺ signals. Further, we relate properties of the dynamical regulation of the cytosolic Ca²⁺ concentration to ideas about information transmission by stochastic signals. Major conclusions We demonstrate the importance of the hierarchal arrangement of Ca²⁺ release sites on the emergence of cellular Ca²⁺ spikes. Stochastic Ca²⁺ signals are functionally robust and adaptive to changing environmental conditions. Fluctuations of interspike intervals (ISIs) and the moment relation derived from ISI distributions contain information on the channel cluster open probability and on pathway properties. General significance Robust and reliable signal transduction pathways that entail Ca²⁺ dynamics are essential for eukaryotic organisms. Moreover, we expect that the design of a stochastic mechanism which provides robustness and adaptivity will be found also in other biological systems. Ca2 + dynamics demonstrate that the fluctuations of cellular signals contain information on molecular behavior. This article is part of a Special Issue entitled Biochemical, biophysical and genetic approaches to intracellular calcium signaling. Highlights ► We review recent findings on key characteristics of cytosolic Ca²⁺ dynamics. ► We demonstrate the importance of the hierarchal arrangement of Ca²⁺ release sites. ► New theoretical concepts exploit emergent behavior of cellular Ca²⁺ spikes. ► We relate the dynamical regulation of [Ca²⁺] to information transmission. ► Stochastic Ca²⁺ signals are functionally robust and adaptive to changing conditions