Modeling biochemical reaction networks in complex intracellular environments

Whether one aims to design treatments for diseases such as cancer or diabetes, engineer cells to produce valuable biochemicals sustainably, or to grasp the behavior of living organisms, it is essential to understand how cells react to genetic, environmental, and biochemical perturbations. Responses of living systems to such perturbations are tied to the dynamics of the biochemical networks implementing the various biological functions necessary for its survival. Thus, knowledge about the dynamics of these biochemical networks is crucial to understand how living entities react to changes in their environment, genes, or biochemistry. The environment within cells is filled with proteins, lipids, polysaccharides, RNA, and DNA, creating various kinds of structures such as droplets, aggregates, and filaments and occupying up to 40% of the intracellular volume. Many of the reactions within the biochemical reaction networks can only be studied in detail when isolated from the intracellular environment. Interaction of the reactants with these structures and other molecules within the cellular volume affects the dynamics properties of the biochemical reactions. The data obtained from experiments that measure the reaction dynamics isolated from the intracellular environment in a dilute setup, omit the effects originating from the interactions with this complex intracellular environment. This discrepancy can result in misinformed models unable to capture the cellular responses. Theoretical and computational models can provide insight into how the reaction kinetics is altered due to the structures inside the cell.

In this thesis, we studied the behavior of reactions confined to different structures inside the cell. Therefore, we focused our efforts on the dynamic capture of chromatin-binding proteins as well as the effects of macromolecular crowding on enzyme kinetics and enzyme reaction networks. Firstly, we used computational modeling and parameter estimation methods to identify the binding mechanism of a heterochromatin effector protein binding to a posttranslational modification mark. We then identified the key parameters of this binding mechanism to investigate the potential effects of the intracellular environment on the binding behavior. Secondly, we investigated the reaction kinetics of enzymes in a solution of macromolecules, such as other enzymes, proteins, DNA, and others. We, therefore, developed a new computational framework that allowed us to parameterize approximate reaction kinetic based on particle simulations. This method allowed us to show that maximal enzyme rates and Michaelis-Menten constants are reduced up to 10 fold upon introducing macromolecules into the system. We continued the analysis of crowded enzyme kinetics by developing a new theoretical model of crowded diffusion-controlled reaction networks. We then used this model to study the role of diffusion in crowded enzyme kinetics. Thirdly, we combined the approximate kinetics with the theoretical model to investigate the impact of crowding on prototypical metabolic networks consisting of multiple enzymatic reactions. Our results suggest that crowding can have significant and unintuitive effects on the sensitivities of the reaction network, making a strong for the application of the derived methods in large scale metabolic models. Finally, we outline the path towards application-specific in vivo like models from the integration of revaluated in vitro data.

Grid Filter Models for the Large Eddy Simulation of Fluid Flows

Marc Anthony David Habisreutinger

In fluid mechanics, turbulence can occur in very simple flow geometries, for Newtonian fluids and without the need for additional flow conditions such as temperature gradients or chemical reactions. In standard cases, intuitive assumptions on the physics of the subgrid scales coupled with the classical theories of turbulence can be well suited for subgrid modelling in large eddy simulation. However, considering more complex situations such as elastic or plasmas turbulence, the behaviour of the subgrid scales is not clearly identified, certainly not as intuitive and the corresponding theories are not available yet. The question is how to proceed when the functional modelling, which imposes a known behaviour to the subgrid scales of the flow, is not possible. For instance, this issue could be overcome using deconvolution-based subgrid models which aim at a partial recovery of the original quantities from their filtered counterpart. In principle, functional modelling is avoided by attempting to invert the filtering operator applied to the governing equations. However, this apparent advantage is completely lost since these models are usually coupled with auxiliary approaches, directly based on functional modelling, in order to account for the interactions with the scales which are not representable on the coarse spatial discretization used for large eddy simulation. The driving motivation of this work is to suppress the need for this secondary modelling which would allow to extend the use of deconvolution-based models to the large eddy simulation of flows whose behaviour of subgrid scales is not identified. Considering the effects of the coarse numerical discretization as the only effective filter applied to the macroscopic equations, an interpretation of the deconvolution models as a way to approximate the effect of the scales lost by numerical discretization on the resolved scales of the flow is demonstrated. Consequently, a new category of subgrid models, the grid filter models, is defined and gives a theoretical justification to the use of deconvolution models for the entire subgrid modelling process. In this perspective, a general method for the computation of the convolution filter which models the effect of the grid filter on the computable scales of the solution is proposed, thereby addressing the key issue of the numerical discretization in large eddy simulation. This modelling approach is validated performing the large eddy simulation of the incompressible flow of a Newtonian fluid in a lid-driven cubical cavity. Comparisons with classical subgrid models allow to assess the validity of this modelling approach and the suppression of the need for functional modelling. In order to extend the validity domain of the grid filter models, the large eddy simulation of an elastic turbulence problem is envisaged. Numerical simulations of elastic turbulence are limited by numerical instabilities which are particularly stringent at high elasticity. Moreover, the computational burden resulting from the required space-time resolutions is significantly increased as compared to the Newtonian case. Consequently, available direct numerical simulations are restricted to periodic and two-dimensional cases. Among these studies, the large eddy simulation of the viscoelastic Kolmogorov flow is chosen as benchmark problem.

EPFL2010

Perturbative Techniques in Hadron Collider Physics

Paolo Torrielli

High-energy particle physics is going through a crucial moment of its history, one in which it can finally aspire to give a precise answer to some of the fundamental questions it has been conceived for. On the one side, the theoretical picture describing the elementary strong and electroweak interactions below the TeV scale, the Standard Model, has been well consolidated over the decades by the observation and the precise characterization of its constituents. On the other hand, the enormous technological potentialities nowadays available, and the skills accumulated in decades of collider experiments with increasingly high complexity, render for the first time plausible the possibility of addressing complicated and conceptually deep questions like the ones at hand. The best incarnation of this high level of sophistication is the CERN Large Hadron Collider (LHC), the most powerful experimental apparatus ever built, which is designed to shed light on the true nature of fundamental interactions at energies never attained before, and which has already started to open a new era in physics with the recent discovery of the longed-for Higgs boson, a true milestone for the human knowledge as well as one of the most important discoveries in the modern epoch. The knowledge that has been and is going to be reached in these crucial years would of course not be conceivable without a deep interplay between the theoretical and the experimental efforts. In particular, on the theoretical side, not only there are wide groups of researchers devoted to building possible extensions to the Standard Model, which draws the guidelines of current and future experiments, but also there is a vast community whose research is rather aimed at the precise predictions of all the physical observables that could be measured at colliders, and at the systematic improvement of the approximations that currently constrain such predictions. On top of representing the state-of-the-art of the human understanding of the properties that regulate elementary-particle interactions and of the formalisms that describe them, the developments of this line of research have an immediate and significant impact on experiments. Firstly, these detailed calculations are the very theoretical predictions against which experimental data are compared, so they are crucial in establishing the validity or not of the theories according to which they are performed. Secondly, the signals one wants to extract from data at modern colliders are so tiny and difficult to single out that the experimental searches themselves need be supplemented by a detailed work of theoretical modelling and simulation. In this respect, high-precision computations play an essential role in all analysis strategies devised by experimental collaborations, and in many aspects of the detector calibration. It is clear that, for theoretical computations to be useful in experimental analyses and simulations, the predictions they yield should be reliable for all possible configurations of the particles to be detected. Thus the key feature for the present theoretical collider physics is not particularly the computation of observables with high precision only in a limited region of the phase space, but the capability of combining (‘matching’) in a consistent way different approaches, each of which is reliable in a particular kinematic regime. With this perspective, matching techniques represent one of the most promising and successful theoretical frameworks currently available, and are considered as eminently valuable tools both on the theoretical and on the experimental sides. Matched computations are based on a perturbation-theory approach for the description of configurations in which the scattering products are well separated and/or highly energetic: in particular the precision currently attained for all but a few of the relevant processes within the Standard Model is the next-to-leading order (NLO) in powers of the strong quantum-chromodynamics (QCD) coupling constant αS; for the description of configurations in which the particles outgoing the collisions are close to each other and/or have low energy, it can be shown that the perturbation-theory expansion breaks down, and then a complementary method, like the parton shower Monte Carlo (PSMC), has instead to be employed. The task of matching is precisely that of giving a prediction that interpolates between the two approaches in a smooth and theoretically-consistent way. This thesis is focused on MC@NLO, a high-energy physics formalism capable of matching computations performed at the NLO in QCD to PSMC generators, in such a way as to retain the virtues of both approaches while discarding their mutual deficiencies. In particular, the thesis reports on the work successfully achieved in extending MC@NLO from its original numerical implementation, tailored on the HERWIG PSMC, to the other main PSMC programs currently employed by experimental collaborations, PYTHIA and Herwig++, confirming the advocated universality of the method. Differences in the various realizations are explained in detail both at the formal level and through the simulation of various Standard-Model reactions. Moreover we describe how the MC@NLO framework has been developed so as to render its implementation automatic with respect to the physics process one is about to simulate: beyond yielding an enormous increase in its potential for present and future collider phenomenology, and upgrading the standard of precision for high-energy computations to the NLO+PSMC level, this development allows for the first time the application of the MC@NLO formalism to a huge number of relevant and highly complicated reactions, through an implementation which is also easily usable by people well-outside the community of experts in QCD calculations. As example of this new version, called aMC@NLO, recent results are presented for complex scattering processes, involving four or five final-state particles. Finally, possible extensions of the framework to theories beyond the Standard Model, like the supersymmetric version of QCD, are briefly introduced.

EPFL2012

Particle-Based Simulation Reveals Macromolecular Crowding Effects on the Michaelis-Menten Mechanism

Vassily Hatzimanikatis, Daniel Robert Weilandt

Many computational models for analyzing and predicting cell physiology rely on in vitro data collected in dilute and controlled buffer solutions. However, this can mislead models because up to 40% of the intracellular volume-depending on the organism, the physiology, and the cellular compartment-is occupied by a dense mixture of proteins, lipids, polysaccharides, RNA, and DNA. These intracellular macromolecules interfere with the interactions of enzymes and their reactants and thus affect the kinetics of biochemical reactions, making in vivo reactions considerably more complex than the in vitro data indicates. In this work, we present a new, to our knowledge, type of kinetics that captures and quantifies the effect of volume exclusion and other spatial phenomena on the kinetics of elementary reactions. We further developed a framework that allows for the efficient parameterization of these kinetics using particle simulations. Our formulation, entitled generalized elementary kinetics, can be used to analyze and predict the effect of intracellular crowding on enzymatic reactions and was herein applied to investigate the influence of crowding on phosphoglycerate mutase in Escherichia coli, which exhibits prototypical reversible Michaelis-Menten kinetics. Current research indicates that many enzymes are reaction limited and not diffusion limited, and our results suggest that the influence of fractal diffusion is minimal for these reaction-limited enzymes. Instead, increased association rates and decreased dissociation rates lead to a strong decrease in the effective maximal velocities V-max and the effective Michaelis-Menten constants K-M under physiologically relevant volume occupancies. Finally, the effects of crowding were explored in the context of a linear pathway, with the finding that crowding can have a redistributing effect on the effective flux responses in the case of twofold enzyme overexpression. We suggest that this framework, in combination with detailed kinetics models, will improve our understanding of enzyme reaction networks under nonideal conditions.

CELL PRESS2019