Catalyst: Fast and flexible modeling of reaction networks

A Nudge to the Truth: Atom Conservation as a Hard Constraint in Models of Atmospheric Composition Using a Species-Weighted Correction

Computational models of atmospheric composition are not always physically consistent. For example, not all models respect fundamental conservation laws such as conservation of atoms in an interconnected chemical system. In well performing models, these unphysical deviations are often ignored because they are frequently minor, and thus only need a small nudge to perfectly conserve mass. Here we introduce a method that anchors a prediction from any numerical model to physically consistent hard constraints, nudging concentrations to the nearest solution that respects the conservation laws. This closed-form model-agnostic correction uses a single matrix operation to minimally perturb the predicted concentrations to ensure that atoms are conserved to machine precision. To demonstrate this approach, we train a gradient boosting decision tree ensemble to emulate a small reference model of ozone photochemistry and test the effect of the correction on accurate but nonconservative predictions. The nudging approach minimally perturbs the already well-predicted results for most species, but decreases the accuracy of important oxidants, including radicals. We develop a weighted extension of this nudging approach that considers the uncertainty and magnitude of each species in the correction. This species-level weighting approach is essential to accurately predict important low concentration species such as radicals. We find that applying the species-weighted correction slightly improves overall accuracy by nudging unphysical predictions to a more likely mass-conserving solution.

Kinetic Modeling Enables Understanding of Off-Cycle Processes in Pd-Catalyzed Amination of Five-Membered Heteroaryl Halides

The mechanism of Pd-catalyzed amination of five-membered heteroaryl halides was investigated by integrating experimental kinetic analysis with kinetic modeling through predictive testing and likelihood ratio analysis, revealing an atypical productive coupling pathway and multiple off-cycle events. The GPhos-supported Pd catalyst, along with the moderate-strength base NaOTMS, was previously found to promote efficient coupling between five-membered heteroaryl halides and secondary amines. However, slight deviations from the optimal concentration, temperature, and/or solvent resulted in significantly lower yields, contrary to typical reaction optimization trends. We found that the coupling of 4-bromothiazole with piperidine proceeds through an uncommon mechanism in which the NaOTMS base, rather than the amine, binds first to the oxidative addition complex; the resulting OTMS-bound Pd species is the resting state. Formation of the Pd-amido complex via base/amine exchange was identified as the turnover-limiting step, unlike other reported catalyst systems for which reductive elimination is turnover-limiting. We determined that the amine-bound Pd complex, usually an on-cycle intermediate, is instead a reversibly generated off-cycle species, and that base-mediated decomposition of 4-bromothiazole is the primary irreversible catalyst deactivation pathway. Predictive testing and kinetic modeling were key to the identification of these off-cycle processes, providing insight into minor mechanistic pathways that are difficult to observe experimentally. Collectively, this report reveals the unique enabling features of the Pd-GPhos/NaOTMS system, implementing mechanistic insights to improve the yields of particularly challenging coupling reactions. Moreover, these findings highlight the utility of applying predictive tests to kinetic models for the rapid evaluation of mechanistic possibilities in small-molecule catalytic systems.

Advancing Mathematical Epidemiology and Chemical Reaction Network Theory via Synergies Between Them

Our paper reviews some key concepts in chemical reaction network theory and mathematical epidemiology, and examines their intersection, with three goals. The first is to make the case that mathematical epidemiology (ME), and also related sciences like population dynamics, virology, ecology, etc., could benefit by adopting the universal language of essentially non-negative kinetic systems as developed by chemical reaction network (CRN) researchers. In this direction, our investigation of the relations between CRN and ME lead us to propose for the first time a definition of ME models, stated in Open Problem 1. Our second goal is to inform researchers outside ME of the convenient next generation matrix (NGM) approach for studying the stability of boundary points, which do not seem sufficiently well known. Last but not least, we want to help students and researchers who know nothing about either ME or CRN to learn them quickly, by offering them a Mathematica package "bootcamp", including illustrating notebooks (and certain sections below will contain associated suggested notebooks; however, readers with experience may safely skip the bootcamp). We hope that the files indicated in the titles of various sections will be helpful, though of course improvement is always possible, and we ask the help of the readers for that.

Codiscovering graphical structure and functional relationships within data: A Gaussian Process framework for connecting the dots

Most problems within and beyond the scientific domain can be framed into one of the following three levels of complexity of function approximation. Type 1: Approximate an unknown function given input/output data. Type 2: Consider a collection of variables and functions, some of which are unknown, indexed by the nodes and hyperedges of a hypergraph (a generalized graph where edges can connect more than two vertices). Given partial observations of the variables of the hypergraph (satisfying the functional dependencies imposed by its structure), approximate all the unobserved variables and unknown functions. Type 3: Expanding on Type 2, if the hypergraph structure itself is unknown, use partial observations of the variables of the hypergraph to discover its structure and approximate its unknown functions. These hypergraphs offer a natural platform for organizing, communicating, and processing computational knowledge. While most scientific problems can be framed as the data-driven discovery of unknown functions in a computational hypergraph whose structure is known (Type 2), many require the data-driven discovery of the structure (connectivity) of the hypergraph itself (Type 3). We introduce an interpretable Gaussian Process (GP) framework for such (Type 3) problems that does not require randomization of the data, access to or control over its sampling, or sparsity of the unknown functions in a known or learned basis. Its polynomial complexity, which contrasts sharply with the super-exponential complexity of causal inference methods, is enabled by the nonlinear ANOVA capabilities of GPs used as a sensing mechanism.

Predicting Long-Time-Scale Kinetics under Variable Experimental Conditions with Kinetica.jl

Predicting the degradation processes of molecules over long time scales is a key aspect of industrial materials design. However, it is made computationally challenging by the need to construct large networks of chemical reactions that are relevant to the experimental conditions that kinetic models must mirror, with every reaction requiring accurate kinetic data. Here, we showcase Kinetica.jl, a new software package for constructing large-scale chemical reaction networks in a fully automated fashion by exploring chemical reaction space with a kinetics-driven algorithm; coupled to efficient machine-learning models of activation energies for sampled elementary reactions, we show how this approach readily enables generation and kinetic characterization of networks containing ∼103 chemical species and ≃104-105 reactions. Symbolic-numeric modeling of the generated reaction networks is used to allow for flexible, efficient computation of kinetic profiles under experimentally realizable conditions such as continuously variable temperature regimes, enabling direct connection between bottom-up reaction networks and experimental observations. Highly efficient propagation of long-time-scale kinetic profiles is required for automated reaction network refinement and is enabled here by a new discrete kinetic approximation. The resulting Kinetica.jl simulation package therefore enables automated generation, characterization, and long-time-scale modeling of complex chemical reaction systems. We demonstrate this for hydrocarbon pyrolysis simulated over time scales of seconds, using transient temperature profiles representing those of tubular flow reactor experiments.

Feedback between stochastic gene networks and population dynamics enables cellular decision-making

Phenotypic selection occurs when genetically identical cells are subject to different reproductive abilities due to cellular noise. Such noise arises from fluctuations in reactions synthesizing proteins and plays a crucial role in how cells make decisions and respond to stress or drugs. We propose a general stochastic agent-based model for growing populations capturing the feedback between gene expression and cell division dynamics. We devise a finite state projection approach to analyze gene expression and division distributions and infer selection from single-cell data in mother machines and lineage trees. We use the theory to quantify selection in multi-stable gene expression networks and elucidate that the trade-off between phenotypic switching and selection enables robust decision-making essential for synthetic circuits and developmental lineage decisions. Using live-cell data, we demonstrate that combining theory and inference provides quantitative insights into bet-hedging-like response to DNA damage and adaptation during antibiotic exposure in Escherichia coli.

Pattern formation by turbulent cascades

Fully developed turbulence is a universal and scale-invariant chaotic state characterized by an energy cascade from large to small scales at which the cascade is eventually arrested by dissipation1-6. Here we show how to harness these seemingly structureless turbulent cascades to generate patterns. Pattern formation entails a process of wavelength selection, which can usually be traced to the linear instability of a homogeneous state7. By contrast, the mechanism we propose here is fully nonlinear. It is triggered by the non-dissipative arrest of turbulent cascades: energy piles up at an intermediate scale, which is neither the system size nor the smallest scales at which energy is usually dissipated. Using a combination of theory and large-scale simulations, we show that the tunable wavelength of these cascade-induced patterns can be set by a non-dissipative transport coefficient called odd viscosity, ubiquitous in chiral fluids ranging from bioactive to quantum systems8-12. Odd viscosity, which acts as a scale-dependent Coriolis-like force, leads to a two-dimensionalization of the flow at small scales, in contrast with rotating fluids in which a two-dimensionalization occurs at large scales4. Apart from odd viscosity fluids, we discuss how cascade-induced patterns can arise in natural systems, including atmospheric flows13-19, stellar plasma such as the solar wind20-22, or the pulverization and coagulation of objects or droplets in which mass rather than energy cascades23-25.

SBMLToolkit.jl: a Julia package for importing SBML into the SciML ecosystem

Julia is a general purpose programming language that was designed for simplifying and accelerating numerical analysis and computational science. In particular the Scientific Machine Learning (SciML) ecosystem of Julia packages includes frameworks for high-performance symbolic-numeric computations. It allows users to automatically enhance high-level descriptions of their models with symbolic preprocessing and automatic sparsification and parallelization of computations. This enables performant solution of differential equations, efficient parameter estimation and methodologies for automated model discovery with neural differential equations and sparse identification of nonlinear dynamics. To give the systems biology community easy access to SciML, we developed SBMLToolkit.jl. SBMLToolkit.jl imports dynamic SBML models into the SciML ecosystem to accelerate model simulation and fitting of kinetic parameters. By providing computational systems biologists with easy access to the open-source Julia ecosystevnm, we hope to catalyze the development of further Julia tools in this domain and the growth of the Julia bioscience community. SBMLToolkit.jl is freely available under the MIT license. The source code is available at https://github.com/SciML/SBMLToolkit.jl.