# Modeling in biology

Modern biology is more and more quantitative and produces huge amounts of data. A main challenge is therefore to develop strategies and methods to analyze and interpret experimental data in order extract novel, quantitative information.

Existing approaches can be typically divided into two families: (1) top-down or data-driven methods consisting in developing statistical analysis or visualization tools based on the data; (2) bottom-up or hypothesis-driven methods consisting in formalizing biological hypotheses into mechanistic models. While the former family is extensively used in the SYMER project, the main planned original developments will concern the latter.

Bottom-up methods are usually based on the translation of basic biological, physical or chemical mechanisms into a mathematical or computational predictive framework. The general philosophy of mechanistic approaches can be summarized by a virtuous cycle (Fig.1) of model implementation based on existing knowledge and first principles, confrontation with data to infer model parameters, formulation of predictions followed by an experimental test, and utilization of differences between predictions and new data to improve the quality of the models.

Such approaches allow to (in)validate hypotheses when direct experimental tests are hardly achievable, but also to provide a quantitative framework to formalize novel concepts and to guide new experiments or discoveries. Moreover, it is well known in physics or applied mathematics that complex behaviors might emerge from simple mechanisms in a dynamical system [1]. Therefore, predicting the outcome of systems of interacting components, such as biological systems, is not easy and requires a systematic analysis via efficient modeling.

*Fig.1: Virtuous cycle of bottom-up, hypothesis-driven approaches driven by an iterative exchange between experiments and theory. Image from [2].*

### Modeling in the SYMER project

In the SYMER project, we aim to use and develop several original approaches at different levels to infer the key players and mechanisms involved in the metabolo-epigenetic coupling. From large-scale, statistical analysis to detailed mechanistic modeling, we aim at generating frameworks to formalize precisely biological hypotheses as well as to test and validate putative mechanisms. Achievement of this goal is possible only through the strong interactions between various disciplines, from experimental biology and biochemistry to mathematics, computer science and physics.In particular, we are developing mathematical and physical models capturing the dynamical coupling between metabolism and epigenetics (Fig.2). Previously, many efforts have been devoted to model metabolism and epigenetics separately (see [3] and [4] for reviews). On one hand, metabolism is a set of biochemical reactions occurring within the cells to produce mainly energy-carrying molecules but also to provide the cell chemicals that may serve as building blocks for the formation or modification of macromolecules. Some of these chemicals may also play a role as intra-cellular signals or information carriers. The basic kinetic laws of biochemical reactions being rather well-known, specific metabolic pathways are usually described in terms of differential equations (Fig.2, right) or of metabolic flux balances [5]. On the other hand, epigenetic regulation was mostly modeled using generic frameworks describing the stochastic dynamics of epigenetic marks (Fig.2, left). Such approaches suggested that the cooperative, long-range spreading capacity of these biochemical marks is a prerequisite to maintain a robust, coherent epigenetic state.

However, very few theoretical approaches have addressed the information transfer between these two important classes of cellular processes. In the SYMER project, we are using quantitative modeling, in close interactions with experimental biologists, to formalize the concept of metabolo-epigenetics. Combining dynamical systems, stochastic modeling, statistical analysis and information theory, we are developing mechanistic frameworks to investigate the role of metabolism in controlling gene expression via epigenetic regulation. We expect our approach to generate new theoretical notions and biological paradigms that will be tested experimentally, going beyond our current understanding of the metabolo-epigenetic coupling.

Fig.2 : (Left) Metabolism is commonly modeled by sets of differential equations describing the time-evolution of the cellular concentrations of metabolites and enzymes driven by biochemical reactions. Image from [6]. (Right) Epigenetic regulation is usually described using stochastic models considering that, locally, the chromatin biochemical composition may fluctuate between various states that spread along the genome thanks to reader-writer enzymes. (Center) In SYMER, we are coupling both parts by accounting (i) for the control of enzymatic activities and of resources by the metabolism, and (ii) for the epigenetic regulation of the expression of proteins involved in energy or metabolite production chains.

Fig.2 : (Left) Metabolism is commonly modeled by sets of differential equations describing the time-evolution of the cellular concentrations of metabolites and enzymes driven by biochemical reactions. Image from [6]. (Right) Epigenetic regulation is usually described using stochastic models considering that, locally, the chromatin biochemical composition may fluctuate between various states that spread along the genome thanks to reader-writer enzymes. (Center) In SYMER, we are coupling both parts by accounting (i) for the control of enzymatic activities and of resources by the metabolism, and (ii) for the epigenetic regulation of the expression of proteins involved in energy or metabolite production chains.

[1] May (1976) Simple mathematical models with very complicated dynamics. Nature 261: 459-467.

[2] Szekely et al (2014) Stochastic simulation in systems biology. Comp. Struct. Biotech. J. 12: 14-25.

[3] Machado et al (2015) Current challenges in modeling cellular metabolism. Front. Bioeng. Biotechnol. 3: 193.

[4] Cortini, et al (2016) The physics of epigenetics. Rev. Mod. Phys. 88: 025002.

[5] Lee et al (2006) Flux balance analysis in the era of metabolomics. Briefings in Bioinformatics 7: 140–50.

[6] Sivanand et al (2018) Spatiotemporal Control of Acetyl-CoA Metabolism in Chromatin Regulation. Trends Biochem. Sci. 43: 61-74.

[2] Szekely et al (2014) Stochastic simulation in systems biology. Comp. Struct. Biotech. J. 12: 14-25.

[3] Machado et al (2015) Current challenges in modeling cellular metabolism. Front. Bioeng. Biotechnol. 3: 193.

[4] Cortini, et al (2016) The physics of epigenetics. Rev. Mod. Phys. 88: 025002.

[5] Lee et al (2006) Flux balance analysis in the era of metabolomics. Briefings in Bioinformatics 7: 140–50.

[6] Sivanand et al (2018) Spatiotemporal Control of Acetyl-CoA Metabolism in Chromatin Regulation. Trends Biochem. Sci. 43: 61-74.

## Responsables

**Daniel Jost**

TIMC-IMAG

daniel.jost@univ-grenoble-alpes.fr

**Eric Fanchon**

TIMC-IMAG

eric.fanchon@univ-grenoble-alpes.fr