scholarly journals Elementary vectors and autocatalytic sets for computational models of cellular growth

2021 ◽  
Author(s):  
Stefan Müller ◽  
Diana Széliová ◽  
Jürgen Zanghellini
Keyword(s):  
Growth Rate ◽  
Computational Models ◽  
Lipid Synthesis ◽  
Cellular Growth ◽  
Ammonium Uptake ◽  
Biomass Composition ◽  
Elementary Flux Modes ◽  
Autocatalytic Sets ◽  
Growth Modes ◽  
Cellular Phenotypes

Traditional models of cellular growth involve an approximative biomass ''reaction'' which specifies biomass composition in terms of precursor metabolites (such as amino acids and nucleotides). On the one hand, biomass composition is often not known exactly and may vary drastically between extreme conditions; on the other hand, the predictions of computational models crucially depend on biomass. Even elementary flux modes (EFMs) depend on the biomass reaction. (To be specific: not just the numerical values of the EFMs, but also their supports and their number.) To better understand cellular phenotypes across conditions, we introduce and analyze new classes of elementary vectors for more comprehensive models of cellular growth, involving explicit synthesis reactions for all macromolecules. Growth modes (GMs) are given by stoichiometry, and elementary growth modes (EGMs) are GMs that cannot be decomposed without cancellations. Unlike EFMs, EGMs need not be support-minimal. Most importantly, every GM can be written as a sum of EGMs. In models with additional (capacity) constraints, growth vectors (GVs) and elementary growth vectors (EGVs) also depend on growth rate. In any case, EGMs/EGVs do not depend on the biomass composition. In fact, they cover all possible biomass compositions and can be seen as unbiased versions of elementary flux modes/vectors (EFMs/EFVs) used in traditional models. To relate the new concepts to other branches of theory, we define autocatalytic GMs and the corresponding autocatalytic sets of reactions. Further, we illustrate our results in a small model of a self-fabricating cell, involving glucose and ammonium uptake, amino acid and lipid synthesis, and the expression of all enzymes and the ribosome itself. In particular, we study the variation of biomass composition as a function of growth rate. In agreement with experimental data, low nitrogen uptake correlates with high carbon (lipid) storage.

scholarly journals Elementary growth modes/vectors and minimal autocatalytic sets for kinetic/constraint-based models of cellular growth

2021 ◽  
Author(s):  
Stefan Müller
Keyword(s):  
Growth Rate ◽  
Maximum Growth ◽  
Linear Constraints ◽  
Maximum Growth Rate ◽  
Cellular Growth ◽  
Metabolic Pathway Analysis ◽  
Elementary Flux Modes ◽  
Autocatalytic Sets ◽  
Growth Modes ◽  
Cellular Phenotypes

AbstractElementary vectors are fundamental objects in polyhedral geometry. In metabolic pathway analysis, elementary vectors range from elementary flux modes (of the flux cone) and elementary flux vectors (of a flux polyhedron) via elementary conversion modes (of the conversion cone) to minimal cut sets (of a dual polyhedron) in computational strain design.To better understand cellular phenotypes with optimal (or suboptimal) growth rate, we introduce and analyze classes of elementary vectors for models of cellular growth. Growth modes (GMs) only depend on stoichiometry, but not on growth rate or concentrations; they are elements of the growth cone. Elementary growth modes (EGMs) are conformally nondecomposable GMs; unlike elementary flux modes, they are not support-minimal, in general. Most importantly, every GM can be written as a conformal sum of EGMs. Growth vectors (GVs) and elementary growth vectors (EGVs) also depend on growth rate, concentrations, and linear constraints; they are elements of a growth polyhedron. Again, every GV can be written as a conformal sum of EGVs. To relate the new concepts to other branches of theory, we define autocatalytic GMs and the corresponding (minimal) autocatalytic sets of reactions.As a case study, we consider whole cell models (simple kinetic models of self-fabrication). First, we use EGMs to derive an upper bound for growth rate that only depends on enzyme kinetics. Next, we study growth rate maximization (via control parameters for ribosome kinetics). In particular, we analyze growth states (GSs) and elementary growth states (EGSs) as introduced in [de Groot et al, 2020]. Unlike EGMs, EGSs depend on (metabolite) concentrations and growth rate. Most importantly, (i) we show that EGSs are support-minimal, (ii) we give a simple proof for the fact that maximum growth rate is attained at an EGS, and (iii) we show that, at every optimal EGS, the ribosome capacity constraint is active. Finally, we determine the dependence of EGSs on growth rate, and we study the relation between EGSs and minimal autocatalytic sets, EGMs, and elementary flux modes. Along the way, we point out (and resolve) mathematical issues in [de Groot et al, 2020].

scholarly journals Elementary Growth Modes provide a molecular description of cellular self-fabrication

2019 ◽  
Author(s):  
Daan H. de Groot ◽  
Josephus Hulshof ◽  
Bas Teusink ◽  
Frank J. Bruggeman ◽  
Robert Planqué
Keyword(s):  
Growth Rate ◽  
Building Blocks ◽  
Reaction Rates ◽  
Cellular Growth ◽  
Cellular Composition ◽  
Growth Modes ◽  
Phenotypic Complexity ◽  
A Cell ◽  
Autocatalytic Process ◽  
Basic Equations

AbstractA major aim of biology is to predict phenotype from genotype. Here we ask if we can describe all possible molecular states (phenotypes) for a cell that fabricates itself at a constant rate, given its enzyme kinetics and the stoichiometry of all reactions (the genotype). For this, we must understand the autocatalytic process of cellular growth which is inherently nonlinear: steady-state self-fabrication requires a cell to synthesize all of its components, including metabolites, enzymes and ribosomes, in the proportions that exactly match its own composition – the growth demand thus depends on the cellular composition. Simultaneously, the concentrations of these components should be tuned to accomplish this synthesis task – the cellular composition thus depends on the growth demand. We here derive a theory that describes all phenotypes that solve this circular problem; the basic equations show how the concentrations of all cellular components and reaction rates must be balanced to get a constant self-fabrication rate. All phenotypes can be described as a combination of one or more minimal building blocks, which we call Elementary Growth Modes (EGMs). EGMs can be used as the theoretical basis for all models that explicitly model self-fabrication, such as the currently popular Metabolism and Expression models. We then used our theory to make concrete biological predictions: we find that natural selection for maximal growth rate drives microorganisms to states of minimal phenotypic complexity: only one EGM will be active when cellular growth rate is maximised. The phenotype of a cell is only extended with one more EGM whenever growth becomes limited by an additional biophysical constraint, such as a limited solvent capacity of a cellular compartment. Our theory starts from basic biochemical and evolutionary considerations, and describes unicellular life, both in growth-promoting and in stress-inducing environments, in terms of EGMs, the universal building blocks of self-fabrication and a cell’s phenotype.

scholarly journals An analytical theory of balanced cellular growth

2019 ◽  
Author(s):  
Hugo Dourado ◽  
Martin J. Lercher
Keyword(s):  
Growth Rate ◽  
Mass Conservation ◽  
Dry Mass ◽  
Cellular Growth ◽  
Biomass Composition ◽  
Balanced Growth ◽  
Balance Analysis ◽  
Unicellular Organisms ◽  
Maximal Growth Rate ◽  
Cellular Components

ABSTRACTThe biological fitness of unicellular organisms is largely determined by their balanced growth rate, i.e., by the rate with which they replicate their biomass composition. Natural selection on this growth rate occurred under a set of physicochemical constraints, including mass conservation, reaction kinetics, and limits on dry mass per volume; mathematical models that maximize the balanced growth rate while accounting explicitly for these constraints are inevitably nonlinear and have been restricted to small, non-realistic systems. Here, we lay down a general theory of balanced growth states, providing explicit expressions for protein concentrations, fluxes, and the growth rate. These variables are functions of the concentrations of cellular components, for which we calculate marginal fitness costs and benefits that can be related to metabolic control coefficients. At maximal growth rate, the net benefits of all concentrations are equal. Based solely on physicochemical constraints, the growth balance analysis (GBA) framework introduced here unveils fundamental quantitative principles of cellular growth and leads to experimentally testable predictions.

scholarly journals Massive Phenotypic Measurements Reveal Complex Physiological Consequences of Differential Translation Efficacies

2017 ◽  
Author(s):  
Adam Paul Arkin ◽  
Guillaume Cambray
Keyword(s):  
Growth Rate ◽  
Translation Initiation ◽  
Protein Production ◽  
Protein Biosynthesis ◽  
Cellular Growth ◽  
Sequence Variants ◽  
Release Rates ◽  
Trade Offs ◽  
Fluctuating Environments ◽  
Protein Overproduction

ABSTRACTControl of protein biosynthesis is at the heart of resource allocation and cell adaptation to fluctuating environments. One gene’s translation often occurs at the expense of another’s, resulting in global energetic and fitness trade-offs during differential expression of various functions. Patterns of ribosome utilization—as controlled by initiation, elongation and release rates—are central to this balance. To disentangle their respective determinants and physiological impacts, we complemented measurements of protein production with highly parallelized quantifications of transcripts’ abundance and decay, ribosome loading and cellular growth rate for 244,000 precisely designed sequence variants of an otherwise standard reporter. We find highly constrained, non-monotonic relationships between measured phenotypes. We show that fitness defects derive either from protein overproduction, with efficient translation initiation and heavy ribosome flows; or from unproductive ribosome sequestration by highly structured, slowly initiated and overly stabilized transcripts. These observations demonstrate physiological impacts of key sequence features in natural and designed transcripts.

Effects of carbon monoxide on cardiac muscle cells in culture

1988 ◽  
Vol 255 (3) ◽  
pp. C291-C296 ◽  
Author(s):  
A. C. Nag ◽  
K. C. Chen ◽  
M. Cheng
Keyword(s):  
Growth Rate ◽  
Cardiac Muscle ◽  
Structural Organization ◽  
Optimal Growth ◽  
Muscle Cells ◽  
Cellular Growth ◽  
Cardiac Muscle Cells ◽  
Cells In Culture ◽  
Significant Difference

Embryonic rat cardiac muscle cells grown in the presence of various tensions of CO (5-95%) without the presence of O2 survived and exhibited reduced cell growth, which was concentration dependent. When cardiac muscle cells were grown in the presence of a mixture of CO (10-20%) and O2 (10-20%), the growth rate of these cells was comparable to that of the control cells. Cardiac myocytes continued to beat when exposed to varying tensions of CO, except in the case of 95% CO. The cells exposed to different concentrations of CO contained fewer myofibrils of different stages of differentiation compared with the control and the culture exposed to a mixture of 20% O2 and 20% CO, with cells that contained abundant, highly differentiated myofibrils. There was no significant difference in the structural organization of mitochondria between the control and the surviving experimental cells. It is evident from the present studies that O2 is required for the optimum in vitro cellular growth of cardiac muscle. Furthermore, CO in combination with O2 at a concentration of 10 or 20% can produce optimal growth of cardiac muscle cells in culture.

Influence of Initiation Site and Lamellar Divergency on the Overall Kinetics of Cellular Growth and Coarsening in Aged U-Nb Alloys

2018 ◽  
Vol 941 ◽  
pp. 863-868
Author(s):  
Robert E. Hackenberg ◽  
Megan G. Emigh ◽  
Pallas A. Papin ◽  
Ann M. Kelly ◽  
Robert T. Forsyth ◽  
...  
Keyword(s):  
Growth Rate ◽  
Initiation Site ◽  
Nucleation Site ◽  
Cellular Growth ◽  
Constant Growth Rate ◽  
Rate Behavior ◽  
Apparent Activation Energies ◽  
Aging Kinetics ◽  
Kinetics Of ◽  
Overall Kinetics

Overall kinetics of lamellar overaging reactions in U-5.5Nb and U-7.5Nb were analyzed by Avrami-Arrhenius analyses of volume fractions measured from an extensive temperature-time (T-t) matrix of specimens. The cellular initiation site (grain boundaries, inclusions) and regimes of lamellar divergency-cum-slowing growth rate were explicitly accounted for. Avrami exponents n from T-t regimes of constant-growth rate were consistent with theory (1<n<3); those from divergent T-t regimes were smaller, n~0.7, which is not surprising given their different growth rate behavior. The apparent activation energies Q were similar for grain-boundary and inclusion-nucleated discontinuous precipitation, indicating that their nucleation site does not alter their overall kinetics. Avrami Analysis of Isothermal Aging Kinetics

scholarly journals Bacterial Quorum Sensing Stabilizes Cooperation by Optimizing Growth Strategies

2016 ◽  
Vol 82 (22) ◽  
pp. 6498-6506 ◽  
Author(s):  
Eric L. Bruger ◽  
Christopher M. Waters
Keyword(s):  
Growth Rate ◽  
Quorum Sensing ◽  
Experimental Evidence ◽  
Fundamental Problem ◽  
Growth Yield ◽  
Cellular Growth ◽  
Growth Strategies ◽  
High Cell ◽  
Content Type ◽  
Cell Densities

ABSTRACTCommunication has been suggested as a mechanism to stabilize cooperation. In bacteria, chemical communication, termed quorum sensing (QS), has been hypothesized to fill this role, and extracellular public goods are often induced by QS at high cell densities. Here we show, with the bacteriumVibrio harveyi, that QS provides strong resistance against invasion of a QS defector strain by maximizing the cellular growth rate at low cell densities while achieving maximum productivity through protease upregulation at high cell densities. In contrast, QS mutants that act as defectors or unconditional cooperators maximize either the growth rate or the growth yield, respectively, and thus are less fit than the wild-type QS strain. Our findings provide experimental evidence that regulation mediated by microbial communication can optimize growth strategies and stabilize cooperative phenotypes by preventing defector invasion, even under well-mixed conditions. This effect is due to a combination of responsiveness to environmental conditions provided by QS, lowering of competitive costs when QS is not induced, and pleiotropic constraints imposed on defectors that do not perform QS.IMPORTANCECooperation is a fundamental problem for evolutionary biology to explain. Conditional participation through phenotypic plasticity driven by communication is a potential solution to this dilemma. Thus, among bacteria, QS has been proposed to be a proximate stabilizing mechanism for cooperative behaviors. Here, we empirically demonstrate that QS inV. harveyiprevents cheating and subsequent invasion by nonproducing defectors by maximizing the growth rate at low cell densities and the growth yield at high cell densities, whereas an unconditional cooperator is rapidly driven to extinction by defectors. Our findings provide experimental evidence that QS regulation prevents the invasion of cooperative populations by QS defectors even under unstructured conditions, and they strongly support the role of communication in bacteria as a mechanism that stabilizes cooperative traits.

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