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

Partial mean-field model for neurotransmission dynamics

This article addresses reaction networks in which spatial and stochastic effects are of crucial importance. For such systems, particle-based models allow us to describe all microscopic details with high accuracy. However, they suffer from computational inefficiency if particle numbers and density get too large. Alternative coarse-grained-resolution models reduce computational effort tremendously, e.g., by replacing the particle distribution by a continuous concentration field governed by reaction-diffusion PDEs. We demonstrate how models on the different resolution levels can be combined into hybrid models that seamlessly combine the best of both worlds, describing molecular species with large copy numbers by macroscopic equations with spatial resolution while keeping the spatial-stochastic particle-based resolution level for the species with low copy numbers. To this end, we introduce a simple particle-based model for the binding dynamics of ions and vesicles at the heart of the neurotransmission process. Within this framework, we derive a novel hybrid model and present results from numerical experiments which demonstrate that the hybrid model allows for an accurate approximation of the full particle-based model in realistic scenarios.

Machine learning predicts system-wide metabolic flux control in cyanobacteria

Metabolic fluxes and their control mechanisms are fundamental in cellular metabolism, offering insights for the study of biological systems and biotechnological applications. However, quantitative and predictive understanding of controlling biochemical reactions in microbial cell factories, especially at the system level, is limited. In this work, we present ARCTICA, a computational framework that integrates constraint-based modelling with machine learning tools to address this challenge. Using the model cyanobacterium Synechocystis sp. PCC 6803 as chassis, we demonstrate that ARCTICA effectively simulates global-scale metabolic flux control. Key findings are that (i) the photosynthetic bioproduction is mainly governed by enzymes within the Calvin-Benson-Bassham (CBB) cycle, rather than by those involve in the biosynthesis of the end-product, (ii) the catalytic capacity of the CBB cycle limits the photosynthetic activity and downstream pathways and (iii) ribulose-1,5-bisphosphate carboxylase/oxygenase (RuBisCO) is a major, but not the most, limiting step within the CBB cycle. Predicted metabolic reactions qualitatively align with prior experimental observations, validating our modelling approach. ARCTICA serves as a valuable pipeline for understanding cellular physiology and predicting rate-limiting steps in genome-scale metabolic networks, and thus provides guidance for bioengineering of cyanobacteria.

Reversible Intracellular Gelation of MCF10A Cells Enables Programmable Control Over 3D Spheroid Growth

In nature, some organisms survive extreme environments by inducing a biostatic state wherein cellular contents are effectively vitrified. Recently, a synthetic biostatic state in mammalian cells is achieved via intracellular network formation using bio-orthogonal strain-promoted azide-alkyne cycloaddition (SPAAC) reactions between functionalized poly(ethylene glycol) (PEG) macromers. In this work, the effects of intracellular network formation on a 3D epithelial MCF10A spheroid model are explored. Macromer-transfected cells are encapsulated in Matrigel, and spheroid area is reduced by ≈50% compared to controls. The intracellular hydrogel network increases the quiescent cell population, as indicated by increased p21 expression. Additionally, bioenergetics (ATP/ADP ratio) and functional metabolic rates are reduced. To enable reversibility of the biostasis effect, a photosensitive nitrobenzyl-containing macromer is incorporated into the PEG network, allowing for light-induced degradation. Following light exposure, cell state, and proliferation return to control levels, while SPAAC-treated spheroids without light exposure (i.e., containing intact intracellular networks) remain smaller and less proliferative through this same period. These results demonstrate that photodegradable intracellular hydrogels can induce a reversible slow-growing state in 3D spheroid culture.

Macromolecular crowding potently stimulates DNA supercoiling activity of Mycobacterium tuberculosis DNA gyrase

Macromolecular crowding, manifested by high concentrations of proteins and nucleic acids in living cells, significantly influences biological processes such as enzymatic reactions. Studying these reactions in vitro, using agents such as polyetthylene glycols (PEGs) and polyvinyl alcohols (PVAs) to mimic intracellular crowding conditions, is essential due to the notable differences from enzyme behaviors observed in diluted aqueous solutions. In this article, we studied Mycobacterium tuberculosis (Mtb) DNA gyrase under macromolecular crowding conditions by incorporating PEGs and PVAs into the DNA supercoiling reactions. We discovered that high concentrations of potassium glutamate, glycine betaine, PEGs, and PVA substantially stimulated the DNA supercoiling activity of Mtb DNA gyrase. Steady-state kinetic studies showed that glycine betaine and PEG400 significantly reduced the KM of Mtb DNA gyrase and simultaneously increased the Vmax or kcat of Mtb DNA gyrase for ATP and the plasmid DNA molecule. Molecular dynamics simulation studies demonstrated that PEG molecules kept the ATP lid of DNA gyrase subunit B in a closed or semiclosed conformation, which prevented ATP molecules from leaving the ATP-binding pocket of DNA gyrase subunit B. The stimulation of the DNA supercoiling activity of Mtb DNA gyrase by these molecular crowding agents likely results from a decrease in water activity and an increase in excluded volume.

Model-driven insights into the effects of temperature on metabolism

Temperature affects cellular processes at different spatiotemporal scales, and identifying the genetic and molecular mechanisms underlying temperature responses paves the way to develop approaches for mitigating the effects of future climate scenarios. A systems view of the effects of temperature on cellular physiology can be obtained by focusing on metabolism since: (i) its functions depend on transcription and translation and (ii) its outcomes support organisms' development, growth, and reproduction. Here we provide a systematic review of modelling efforts directed at investigating temperature effects on properties of single biochemical reactions, system-level traits, metabolic subsystems, and whole-cell metabolism across different prokaryotes and eukaryotes. We compare and contrast computational approaches and theories that facilitate modelling of temperature effects on key properties of enzymes and their consideration in constraint-based as well as kinetic models of metabolism. In addition, we provide a summary of insights from computational approaches, facilitating integration of omics data from temperature-modulated experiments with models of metabolic networks, and review the resulting biotechnological applications. Lastly, we provide a perspective on how different types of metabolic modelling can profit from developments in machine learning and models of different cellular layers to improve model-driven insights into the effects of temperature relevant for biotechnological applications.

Optimal enzyme utilization suggests that concentrations and thermodynamics determine binding mechanisms and enzyme saturations

Deciphering the metabolic functions of organisms requires understanding the dynamic responses of living cells upon genetic and environmental perturbations, which in turn can be inferred from enzymatic activity. In this work, we investigate the optimal modes of operation for enzymes in terms of the evolutionary pressure driving them toward increased catalytic efficiency. We develop a framework using a mixed-integer formulation to assess the distribution of thermodynamic forces and enzyme states, providing detailed insights into the enzymatic mode of operation. We use this framework to explore Michaelis-Menten and random-ordered multi-substrate mechanisms. We show that optimal enzyme utilization is achieved by unique or alternative operating modes dependent on reactant concentrations. We find that in a bimolecular enzyme reaction, the random mechanism is optimal over any other ordered mechanism under physiological conditions. Our framework can investigate the optimal catalytic properties of complex enzyme mechanisms. It can further guide the directed evolution of enzymes and fill in the knowledge gaps in enzyme kinetics.

Stress-dependent macromolecular crowding in the mitochondrial matrix

Macromolecules of various sizes induce crowding of the cellular environment. This crowding impacts on biochemical reactions by increasing solvent viscosity, decreasing the water-accessible volume and altering protein shape, function, and interactions. Although mitochondria represent highly protein-rich organelles, most of these proteins are somehow immobilized. Therefore, whether the mitochondrial matrix solvent exhibits macromolecular crowding is still unclear. Here, we demonstrate that fluorescent protein fusion peptides (AcGFP1 concatemers) in the mitochondrial matrix of HeLa cells display an elongated molecular structure and that their diffusion constant decreases with increasing molecular weight in a manner typical of macromolecular crowding. Chloramphenicol (CAP) treatment impaired mitochondrial function and reduced the number of cristae without triggering mitochondrial orthodox-to-condensed transition or a mitochondrial unfolded protein response. CAP-treated cells displayed progressive concatemer immobilization with increasing molecular weight and an eightfold matrix viscosity increase, compatible with increased macromolecular crowding. These results establish that the matrix solvent exhibits macromolecular crowding in functional and dysfunctional mitochondria. Therefore, changes in matrix crowding likely affect matrix biochemical reactions in a manner depending on the molecular weight of the involved crowders and reactants.

Symbolic kinetic models in python (SKiMpy): intuitive modeling of large-scale biological kinetic models

MOTIVATION

Large-scale kinetic models are an invaluable tool to understand the dynamic and adaptive responses of biological systems. The development and application of these models have been limited by the availability of computational tools to build and analyze large-scale models efficiently. The toolbox presented here provides the means to implement, parameterize and analyze large-scale kinetic models intuitively and efficiently.

RESULTS

We present a Python package (SKiMpy) bridging this gap by implementing an efficient kinetic modeling toolbox for the semiautomatic generation and analysis of large-scale kinetic models for various biological domains such as signaling, gene expression and metabolism. Furthermore, we demonstrate how this toolbox is used to parameterize kinetic models around a steady-state reference efficiently. Finally, we show how SKiMpy can implement multispecies bioreactor simulations to assess biotechnological processes.

AVAILABILITY AND IMPLEMENTATION

The software is available as a Python 3 package on GitHub: https://github.com/EPFL-LCSB/SKiMpy, along with adequate documentation.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Uricase Crowding via Polyelectrolyte Layers Coacervation for Carbon Fiber-Based Electrochemical Detection of Uric Acid

Urate oxidase (UOx) surrounded by synthetic macromolecules, such as polyethyleneimine (PEI), poly(allylamine hydrochloride) (PAH), and poly(sodium 4-styrenesulfonate) (PSS) is a convenient model of redox-active biomacromolecules in a crowded environment and could display high enzymatic activity towards uric acid, an important marker of COVID-19 patients. In this work, the carbon fiber electrode was modified with Prussian blue (PB) redox mediator, UOx layer, and a layer-by-layer assembled polyelectrolyte film, which forms a complex coacervate consisting of a weakly charged polyelectrolyte (PEI or PAH) and a highly charged one (PSS). The film deposition process was controlled by cyclic voltammetry and scanning electron microscopy coupled with energy-dispersive X-ray analysis (at the stage of PB deposition) and through quartz crystal microbalance technique (at latter stages) revealed uniform distribution of the polyelectrolyte layers. Variation of the polyelectrolyte film composition derived the following statements. (1) There is a linear correlation between electrochemical signal and concentration of uric acid in the range of 10^-4-10^-6 M. (2) An increase in the number of polyelectrolyte layers provides more reproducible values for uric acid concentration in real urine samples of SARS-CoV-2 patients measured by electrochemical enzyme assay, which are comparable to those of spectrophotometric assay. (3) The PAH/UOx/PSS/(PAH/PSS)₂-coated carbon fiber electrode displays the highest sensitivity towards uric acid. (4) There is a high enzyme activity of UOx immobilized into the hydrogel nanolayer (values of the Michaelis-Menten constant are up to 2 μM) and, consequently, high affinity to uric acid.

Experimental measurements of the bacterial oxidation of HT in soils: Impact over a zone influenced by an industrial release of tritium in HT form

Tritium is a radionuclide released to the atmosphere by nuclear industries in various forms, mainly HTO and to a lesser extent HT. However, some nuclear sites may emit predominantly HT in the atmosphere. The HT is oxidized to HTO essentially in the top cm of soils, and that the formed HTO is then possibly released into the atmosphere. HTO is an assimilable form by plants. Therefore, it is important to understand the environmental behaviour of HT. In this work, we adapt the bacterial oxidation model of HT in soils of Ota et al. (2007) by laboratory experiments on soils typical of western France, and we have in particular adapted the frequency factor A and the Michaelis-Menten enzymatic reaction parameter (Km) on the basis of an Arrhenius equation in function of the porosity of the soil. We then applied this model to the environment near the reprocessing plant of Orano la Hague (France), which emits a significant amount of HT. Based on the adapted model, and knowing the atmospheric variations of HTO and HT over the period 2013-2016, we estimated that the mean HTO activity in soil due to atmospheric HT reached 0.6 Bq.L^-1 (with a peak value of 5 Bq.L^-1) while the mean value with all sources taken into account is 6.2 Bq.L^-1. Then, in an environment such as that surrounding the Orano La Hague plant, where near-field atmospheric HT activity is very high, the bacterial oxydation contribution to produce HTO in the soil can be considered as approximately 10%. The flux to the atmosphere from these source representing approximately. 1.5 Bq.m^-2.d^-1. If we consider an area of 2 km around the plant (i.e. 13 km²), we estimate 218 Bq.s^-1 of HTO was released by the soil, representing less than 0.1% of the direct atmospheric release of HTO around the site. From this work, it appears clear that this secondary source term from the soil is insignificant at this specific site.

Generation of multicellular spatiotemporal models of population dynamics from ordinary differential equations, with applications in viral infection

BACKGROUND

The biophysics of an organism span multiple scales from subcellular to organismal and include processes characterized by spatial properties, such as the diffusion of molecules, cell migration, and flow of intravenous fluids. Mathematical biology seeks to explain biophysical processes in mathematical terms at, and across, all relevant spatial and temporal scales, through the generation of representative models. While non-spatial, ordinary differential equation (ODE) models are often used and readily calibrated to experimental data, they do not explicitly represent the spatial and stochastic features of a biological system, limiting their insights and applications. However, spatial models describing biological systems with spatial information are mathematically complex and computationally expensive, which limits the ability to calibrate and deploy them and highlights the need for simpler methods able to model the spatial features of biological systems.

RESULTS

In this work, we develop a formal method for deriving cell-based, spatial, multicellular models from ODE models of population dynamics in biological systems, and vice versa. We provide examples of generating spatiotemporal, multicellular models from ODE models of viral infection and immune response. In these models, the determinants of agreement of spatial and non-spatial models are the degree of spatial heterogeneity in viral production and rates of extracellular viral diffusion and decay. We show how ODE model parameters can implicitly represent spatial parameters, and cell-based spatial models can generate uncertain predictions through sensitivity to stochastic cellular events, which is not a feature of ODE models. Using our method, we can test ODE models in a multicellular, spatial context and translate information to and from non-spatial and spatial models, which help to employ spatiotemporal multicellular models using calibrated ODE model parameters. We additionally investigate objects and processes implicitly represented by ODE model terms and parameters and improve the reproducibility of spatial, stochastic models.

CONCLUSION

We developed and demonstrate a method for generating spatiotemporal, multicellular models from non-spatial population dynamics models of multicellular systems. We envision employing our method to generate new ODE model terms from spatiotemporal and multicellular models, recast popular ODE models on a cellular basis, and generate better models for critical applications where spatial and stochastic features affect outcomes.

Electrostatic Reaction Inhibition in Nanoparticle Catalysis

Electrostatic reaction inhibition in heterogeneous catalysis emerges if charged reactants and products with similar charges are adsorbed on the catalyst and thus repel the approaching reactants. In this work, we study the effects of electrostatic inhibition on the reaction rate of unimolecular reactions catalyzed on the surface of a spherical model nanoparticle using particle-based reaction-diffusion simulations. Moreover, we derive closed rate equations based on an approximate Debye-Smoluchowski rate theory, valid for diffusion-controlled reactions, and a modified Langmuir adsorption isotherm, relevant for reaction-controlled reactions, to account for electrostatic inhibition in the Debye-Hückel limit. We study the kinetics of reactions ranging from low to high adsorptions on the nanoparticle surface and from the surface- to diffusion-controlled limits for charge valencies 1 and 2. In the diffusion-controlled limit, electrostatic inhibition drastically slows down the reactions for strong adsorption and low ionic concentration, which is well described by our theory. In particular, the rate decreases with adsorption affinity because, in this case, the inhibiting products are generated at a high rate. In the (slow) reaction-controlled limit, the effect of electrostatic inhibition is much weaker, as semiquantitatively reproduced by our electrostatic-modified Langmuir theory. We finally propose and verify a simple interpolation formula that describes electrostatic inhibition for all reaction speeds ("diffusion-influenced" reactions) in general.

The geometry of the toxicity of silver nanoparticles to freshwater mussels

The question about the influence of the geometry of silver nanoparticle (nAg) towards toxicity in aquatic organisms is largely unanswered. The purpose of this study was to examine if different geometries of nAg could initiate biophysical stress in the soft tissues of mussels. Freshwater Dreissenna bugensis mussels were exposed for 48 h at 15 °C to 10 and 50 μg/L of ionic Ag and to 3 forms of polyvinylpyrrolidone (PVP)-coated nAg of similar size: sphere, cube and prism. At the end of the exposure period, mussels were allowed to depurate overnight and the post-mitochondrial fraction of the soft tissues were analyzed for the levels of liquid crystals (LCs), changes in the activity and fractal dimensions of pyruvate kinase-lactate dehydrogenase (PK-LDH), F-actin and protein-ubiquitin (UB) levels. The data revealed that exposure to nAg forms lead to increased formation of LCs in increasing order of intensity: prismatic > cubic > spherical nAg. The activity in PK-LDH was decreased by all forms of nAg but not by ionic Ag⁺ (as with the following effects). Fractal kinetics of the PK-LDH system revealed that the nAg forms increased the spectral dimension (sD) in increasing order: spherical > cubic > prismatic nAg. A decrease in the fractal diffusion rate (fDR) with small changes in the fractal dimension (fD) was also obtained. The levels of F-actin and protein-UB were significantly affected for most forms of nAg and followed a pattern similar to LCs levels. In conclusion, the geometry of nAg could influence the formation of LCs, alter the fractal kinetics of the PK-LDH system, F-actin levels and protein damage in the soft tissues of freshwater mussels.

Optimal Design of Experiments for Hybrid Nonlinear Models, with Applications to Extended Michaelis–Menten Kinetics

Biochemical mechanism studies often assume statistical models derived from Michaelis–Menten kinetics, which are used to approximate initial reaction rate data given the concentration level of a single substrate. In experiments dealing with industrial applications, however, there are typically a wide range of kinetic profiles where more than one factor is controlled. We focus on optimal design of such experiments requiring the use of multifactor hybrid nonlinear models, which presents a considerable computational challenge. We examine three different candidate models and search for tailor-made D- or weighted-A-optimal designs that can ensure the efficiency of nonlinear least squares estimation. We also study a compound design criterion for discriminating between two candidate models, which we recommend for design of advanced kinetic studies.

Supplementary materials accompanying this paper appear on-line

Large-scale kinetic metabolic models of Pseudomonas putida KT2440 for consistent design of metabolic engineering strategies

BACKGROUND

Pseudomonas putida is a promising candidate for the industrial production of biofuels and biochemicals because of its high tolerance to toxic compounds and its ability to grow on a wide variety of substrates. Engineering this organism for improved performances and predicting metabolic responses upon genetic perturbations requires reliable descriptions of its metabolism in the form of stoichiometric and kinetic models.

RESULTS

In this work, we developed kinetic models of P. putida to predict the metabolic phenotypes and design metabolic engineering interventions for the production of biochemicals. The developed kinetic models contain 775 reactions and 245 metabolites. Furthermore, we introduce here a novel set of constraints within thermodynamics-based flux analysis that allow for considering concentrations of metabolites that exist in several compartments as separate entities. We started by a gap-filling and thermodynamic curation of iJN1411, the genome-scale model of P. putida KT2440. We then systematically reduced the curated iJN1411 model, and we created three core stoichiometric models of different complexity that describe the central carbon metabolism of P. putida. Using the medium complexity core model as a scaffold, we generated populations of large-scale kinetic models for two studies. In the first study, the developed kinetic models successfully captured the experimentally observed metabolic responses to several single-gene knockouts of a wild-type strain of P. putida KT2440 growing on glucose. In the second study, we used the developed models to propose metabolic engineering interventions for improved robustness of this organism to the stress condition of increased ATP demand.

CONCLUSIONS

The study demonstrates the potential and predictive capabilities of the kinetic models that allow for rational design and optimization of recombinant P. putida strains for improved production of biofuels and biochemicals. The curated genome-scale model of P. putida together with the developed large-scale stoichiometric and kinetic models represents a significant resource for researchers in industry and academia.

From Escherichia coli mutant 13C labeling data to a core kinetic model: A kinetic model parameterization pipeline

Kinetic models of metabolic networks offer the promise of quantitative phenotype prediction. The mechanistic characterization of enzyme catalyzed reactions allows for tracing the effect of perturbations in metabolite concentrations and reaction fluxes in response to genetic and environmental perturbation that are beyond the scope of stoichiometric models. In this study, we develop a two-step computational pipeline for the rapid parameterization of kinetic models of metabolic networks using a curated metabolic model and available 13C-labeling distributions under multiple genetic and environmental perturbations. The first step involves the elucidation of all intracellular fluxes in a core model of E. coli containing 74 reactions and 61 metabolites using 13C-Metabolic Flux Analysis (13C-MFA). Here, fluxes corresponding to the mid-exponential growth phase are elucidated for seven single gene deletion mutants from upper glycolysis, pentose phosphate pathway and the Entner-Doudoroff pathway. The computed flux ranges are then used to parameterize the same (i.e., k-ecoli74) core kinetic model for E. coli with 55 substrate-level regulations using the newly developed K-FIT parameterization algorithm. The K-FIT algorithm employs a combination of equation decomposition and iterative solution techniques to evaluate steady-state fluxes in response to genetic perturbations. k-ecoli74 predicted 86% of flux values for strains used during fitting within a single standard deviation of 13C-MFA estimated values. By performing both tasks using the same network, errors associated with lack of congruity between the two networks are avoided, allowing for seamless integration of data with model building. Product yield predictions and comparison with previously developed kinetic models indicate shifts in flux ranges and the presence or absence of mutant strains delivering flux towards pathways of interest from training data significantly impact predictive capabilities. Using this workflow, the impact of completeness of fluxomic datasets and the importance of specific genetic perturbations on uncertainties in kinetic parameter estimation are evaluated.