Growth Mechanics: General principles of optimal cellular resource allocation in balanced growth

Abstract

The physiology of biological cells evolved under physical and chemical constraints such as mass conservation, nonlinear reaction kinetics, and limits on cell density. For unicellular organisms, the fitness that governs this evolution is mainly determined by the balanced cellular growth rate. We previously introduced Growth Balance Analysis (GBA) as a general framework to model such nonlinear systems, and we presented analytical conditions for optimal balanced growth in the special case that the active reactions are known. Here, we develop Growth Mechanics (GM) as a more general, succinct, and powerful analytical description of the growth optimization of GBA models, which we formulate in terms of a minimal number of dimensionless variables. GM uses Karush-Kuhn-Tucker (KKT) conditions in a Lagrangian formalism. It identifies fundamental principles of optimal resource allocation in GBA models of any size and complexity, including the analytical conditions that determine the set of active reactions at optimal growth. We identify from first principles the economic values of biochemical reactions, expressed as marginal changes in cellular growth rate; these economic values can be related to the costs and benefits of proteome allocation into the reactions' catalysts. Our formulation also generalizes the concepts of Metabolic Control Analysis to models of growing cells. GM unifies and extends previous approaches of cellular modeling and analysis, putting forward a program to analyze cellular growth through the stationarity conditions of a Lagrangian function. GM thereby provides a general theoretical toolbox for the study of fundamental mathematical properties of balanced cellular growth.

Turnover number predictions for kinetically uncharacterized enzymes using machine and deep learning

“…If we were not able to find the identical reaction in the BiGG database, we selected the most similar one using a similarity score (see Methods). To calculate how much variance of the k cat values can be explained by the calculated fluxes, we fitted a linear regression model to the training set, with the log k 10 -transformed fluxes as the only input. The fitted model achieves a coefficient of determination R 2 = 0.021, a MSE = 1.40, and a Pearson correlation coefficient r = 0.15 on the test set ( Figure S4 ).…”

“…k cat is a central parameter for quantitative studies of enzymatic activities, and is of key importance for understanding cellular metabolism, physiology, and resource allocation. In particular, comprehensive sets of k cat values are essential for metabolic models that consider the cost of producing or maintaining enzymes [1][2][3][4][5][6][7][8][9] , a prerequisite for accurate simulations of cellular physiology and growth 10 . Currently, no high-throughput experimental assays exist for k cat , and experiments are both time consuming and expensive.…”

Growth balance analysis models of cyanobacteria for understanding resource allocation strategies

“…an internal stoichiometric matrix normalized by corresponding molecular masses, including a column "R" for a ribosome reaction producing proteins, and a row "a" for the total protein concentration), 𝝉 denotes reaction turnover times determined by some given kinetic rate laws, and 𝜌 denotes biomass density. For any given GBA model, a simple set of equations determining the balanced growth problem can be derived from first principles (Dourado et al, 2022). These equations depend only on the mass balance of reactions contained in the matrix M, kinetic parameters, and cell density data, which are only a subset of all parameters used in the Synechocystis model from (Faizi et al, 2018).…”

“…The fixed cellular density 𝜌 constrains the sum of all metabolite concentrations 𝑐 𝑚 and total protein concentration 𝑐 𝑎 (itself defined as the sum of all individual protein concentrations 𝑝 𝑗 ). The growth rate optimization problem at given environment 𝒙 = (𝑥 𝐶 , 𝑥 𝐼 ) can be entirely formulated on flux fractions 𝒇 = 𝒗/𝜇𝜌, greatly simplifying analytical and numerical studies (Dourado et al, 2022).…”

“…Nonlinear optimization problems are however difficult to be solved numerically for large scale models (Wortel, Noor, Ferris, Bruggeman, & Liebermeister, 2018), and nonlinear kinetics have been currently accounted for only in small, simplified cell models (Burnap, 2015;Faizi et al, 2018;Jahn et al, 2018;Molenaar et al, 2009). Recent studies have shown how the mathematical formulation of such nonlinear problems can be greatly simplified, potentially facilitating the simulation of larger nonlinear cell models (Dourado & Lercher, 2020;Dourado, Liebermeister, Ebenhöh, & Lercher, 2022).…”