Abstracts

Eugenio Cinquemani (Inria Grenoble)

Enhanced production of heterologous proteins by a synthetic microbial consortium: Conditions and trade-offs

Synthetic microbial consortia have been increasingly utilized in biotechnology and experimental evidence shows that suitably engineered consortia can outperform individual species in the synthesis of valuable products. Despite significant achievements, though, a quantitative understanding of the conditions that make this possible, and of the trade-offs due to the concurrent growth of multiple species, is still limited. In this work, we contribute to filling this gap by the investigation of a known prototypical synthetic consortium. A first E. coli strain, producing a heterologous protein, is sided by a second E. coli strain engineered to scavenge toxic byproducts, thus favoring the growth of the producer at the expense of diverting part of the resources to the growth of the cleaner. The simplicity of the consortium is ideal to perform an in depth-analysis and draw conclusions of more general interest. We develop a coarse-grained mathematical model that quantitatively accounts for literature data from different key growth phenotypes. Based on this, assuming growth in chemostat, we first investigate the conditions enabling stable coexistence of both strains and the effect of the metabolic load due to heterologous protein production. In these conditions, we establish when and to what extent the consortium outperforms the producer alone in terms of productivity. Finally, we show in chemostat as well as in a fed-batch scenario that gain in productivity comes at the price of a reduced yield, reflecting at the level of the consortium resource allocation trade-offs that are well-known for individual species.[1] Mauri, M., Gouzé, J. L., De Jong, H., & Cinquemani, E. (2020). Enhanced production of heterologous proteins by a synthetic microbial community: Conditions and trade-offs. PLOS Computational Biology, 16(4), e1007795.

Werner Haselmayr (Johannes Kepler Universität Linz)

Introduction to Synthetic Molecular Communications

Molecular communications (MC) is a new communication paradigm that uses biochemical signals for information exchange. MC is widely found in nature, for example bacteria use MC to coordinate their behavior (quorum sensing). MC mechanisms in nature are generally simple, energy efficient, and biocompatible. Hence, it has attracted the attention of communications engineers as a solution to communicate in environments, such as the human body, where conventional wireless communications using electromagnetic waves is not feasible. Such synthetic MC systems may enable transformative applications in nanomedicine, such as targeted drug delivery. In order to design and analyze synthetic MC systems, mathematical models for the release (transmitter), propagation (channel), and reception (receiver) mechanisms are required.This talk provides an overview on the existing models for the individual components of synthetic MC systems. Moreover, the latest MC testbeds are presented and open research problems as well as future research directions are discussed.

Stefan Müller (Universität Wien)

Mathematical models of chemical and metabolic networks

Many biological systems can be modeled as networks of chemical reactions, often with mass-action kinetics. Interestingly, for large classes of networks, the qualitative behavior of the resulting dynamical systems is independent of the rate constants. We consider chemical networks with generalized mass-action kinetics, where reaction rates are power laws in the species concentrations, leading to generalized polynomial ODEs (having real exponents). We characterize uniqueness/existence of positive "complex-balanced" equilibria (for all rate constants and all initial conditions) in terms of sign vectors of two linear subspaces (corresponding to stoichiometric coefficients and kinetic orders, respectively). In terms of real algebraic geometry, we obtain first multivariate generalizations of Descartes' rule of signs.As a particular cellular system, metabolism is modeled as a network of enzymatic reactions, however, often without knowledge of the kinetics. Traditionally, the analysis is based on stoichiometric information (and optimality principles), leading to linear programs.We consider metabolic networks with kinetic information and the resulting nonlinear programs. In particular, we are interested in enzyme allocation problems where a chosen reaction rate is maximized under an enzymatic capacity constraint. Most importantly, we characterize optimal solutions in abstract terms: For arbitrary enzyme kinetics, solutions that optimize rates correspond to sign vectors with minimal support (of the kernel of the stoichiometric matrix). Chemical and metabolic networks share common modeling paradigms (stoichiometry + kinetics) and mathematical methods (sign vectors = oriented matroids) which suggests to further exploit synergistic effects.

Maximilian Schäfer (FAU Erlangen-Nürnberg)

Modeling Molecular Communication Channels by Transfer Functions

The accurate modeling of Molecular Communication (MC) channels is crucial for the analysis of naturally occurring MC systems and for the design of synthetic ones. Ideally, a channel model should be able to capture the complete dynamics in an analytical form while fast numerical evaluation is preferable. As most practical MC systems try to mimic naturally occurring transport phenomena for information carrying particles, their transmission relies on a variety of different linear and non-linear mechanisms, i.e., different forms of reactions, advection and diffusion. The derivation of a channel model mostly starts with an abstraction of those effects in terms of mathematical equations. A well known mathematical description of MC systems is based on partial differential equations (PDEs). The prevalent modeling techniques may be roughly divided into numerical and analytical methods. While numerical methods try to solve PDEs e.g. by finite element methods, analytical modeling techniques try to find a closed form solution, e.g., in terms of Green’s function or transfer functions.This talk provides an overview on several relevant effects occurring in practical MC systems and shows how they can be abstracted into a mathematical formulation. Moreover, the modeling of MC channels in terms of transfer functions, an analytical modeling technique, is introduced by practical examples.

Florian Wodlei (Living Systems Research, Klagenfur)

Hydrodynamical Control of the Decoupling of Reaction, Diffusion and Convection in a Complex Chemical Reaction System

The interplay between reaction, diffusion and convection can lead to complex evolutions in a chemical system. These evolutions can also include the transition to and from chaos. The chemical system under investigation here is the Belousov-Zhabotinsky reaction, which is one of the most studied oscillatory chemical reaction systems. The reason for this is, on the one hand, surely its easy performance in the lab but, on the other hand, also its great importance to a better understanding of oscillations in chemical and biological systems, like for example in biological clocks, which are responsible for the day-night cycle in organisms. Encapsulated in micelles or vesicles (liposomes) the Belousov-Zhabotinsky reaction can also serve as a model system for molecular communications in multicellular organisms [2]. Most importantly, for this research, is that it is also a good system to study the appearance of chaos in chemical systems [1].In this work we study how the naturally occurring decoupling of reaction, diffusion and convection, which is connected to the transition to and from chaos, that takes place in a closed batch set-up of this system, can be controlled hydrodynamically. Our main goal is to understand the effect of a limited stirring phase on this transitions. So far, we could identify a relative shrinkage of the time length of the chaotic transient due to this type of hydrodynamical control [3].
[1] F. Wodlei., M. A. Budroni, and M. Rustici. Butterfly effect in a chemical oscillator. European Journal of Physics, Volume 35 Number 4, 2014 [2] P. Stano, F. Wodlei, P. Carrera, S. Ristori, N. Marchettini and F. Rossi: Approaches to molecular communication between synthetic compartments based on encapsulated chemical oscillators. Advances in Artificial Life and Evolutionary Computation, Communications in Computer and Information Science (CCIS), Vol. 445, 2014[3] F. Wodlei, M. R. Hristea. Effect of Limited Stirring on the Belousov Zhabotinsky Reaction. Proceedings of the European Conference on Complex Systems (September 2013)

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