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At least 37 records · Page 2

De novo design of protein structure and function with RFdiffusion

Abstract There has been considerable recent progress in designing new proteins using deep-learning methods 1–9 . Despite this progress, a general deep-learning framework for protein design that enables solution of a wide range of design challenges, including de novo binder design and design of higher-order symmetric architectures, has yet to be described. Diffusion models 10,11 have had considerable success in image and language generative modelling but limited success when applied to protein modelling, probably due to the complexity of protein backbone geometry and sequence–structure relationships. Here we show that by fine-tuning the RoseTTAFold structure prediction network on protein structure denoising tasks, we obtain a generative model of protein backbones that achieves outstanding performance on unconditional and topology-constrained protein monomer design, protein binder design, symmetric oligomer design, enzyme active site scaffolding and symmetric motif scaffolding for therapeutic and metal-binding protein design. We demonstrate the power and generality of the method, called RoseTTAFold diffusion (RFdiffusion), by experimentally characterizing the structures and functions of hundreds of designed symmetric assemblies, metal-binding proteins and protein binders. The accuracy of RFdiffusion is confirmed by the cryogenic electron microscopy structure of a designed binder in complex with influenza haemagglutinin that is nearly identical to the design model. In a manner analogous to networks that produce images from user-specified inputs, RFdiffusion enables the design of diverse functional proteins from simple molecular specifications.

Science & Technology - Other Topics↗

Substrate Channeling via a Transient Protein-Protein Complex: The case of D-Glyceraldehyde-3-Phosphate Dehydrogenase and L-Lactate Dehydrogenase

Molecular dynamics studies showed that LDH and GAPDH tetramers can form a complex which can breakdown when the enzymes are saturated with NADH molecules. The interaction sites are conserved between LDH isozymes from heart and muscle cells, and between GAPDH molecules from rabbit and yeast cells. Positive electric fields between the NAD(H) binding sites showed that NAD(H) channeling within LDH-GAPDH complex can be an extension of NAD(H) channeling between the adjacent subunits within LDH and GAPDH tetramers. Analytical ultracentrifugation and enzyme kinetics studies indicated that LDH and GAPDH molecules can form a transient channeling complex. The transient complex can support the channeled and the diffusive paths in parallel, the relative contribution from each path depends on the off-rates for (GAPDH-NADH)-LDH complex and GAPDH-NADH complex. Negative cooperativity in NADH binding to different subunits in GAPDH tetramers can provide allosteric regulation of NADH channeling from GAPDH to LDH.

INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMI↗

Identification of a carbonic anhydrase–Rubisco complex within the alpha-carboxysome

Carboxysomes are proteinaceous organelles that encapsulate key enzymes of CO 2 fixation—Rubisco and carbonic anhydrase—and are the centerpiece of the bacterial CO 2 concentrating mechanism (CCM). In the CCM, actively accumulated cytosolic bicarbonate diffuses into the carboxysome and is converted to CO 2 by carbonic anhydrase, producing a high CO 2 concentration near Rubisco and ensuring efficient carboxylation. Self-assembly of the α-carboxysome is orchestrated by the intrinsically disordered scaffolding protein, CsoS2, which interacts with both Rubisco and carboxysomal shell proteins, but it is unknown how the carbonic anhydrase, CsoSCA, is incorporated into the α-carboxysome. Here, we present the structural basis of carbonic anhydrase encapsulation into α-carboxysomes from Halothiobacillus neapolitanus . We find that CsoSCA interacts directly with Rubisco via an intrinsically disordered N-terminal domain. A 1.98 Å single-particle cryoelectron microscopy structure of Rubisco in complex with this peptide reveals that CsoSCA binding is predominantly mediated by a network of hydrogen bonds. CsoSCA's binding site overlaps with that of CsoS2, but the two proteins utilize substantially different motifs and modes of binding, revealing a plasticity of the Rubisco binding site. Our results advance the understanding of carboxysome biogenesis and highlight the importance of Rubisco, not only as an enzyme but also as a central hub for mediating assembly through protein interactions.

59 BASIC BIOLOGICAL SCIENCES↗

Development of a scalable, robust electrocatalytic technology for conversion of CO 2 to formic acid via microstructured materials

This project was funded by the Bioenergy Engineering for Product Synthesis (BEEPS) program under the Funding Opportunity Announcement (FOA) DE-FOA-0001916 Topic Area 5 “Rewiring Carbon Utilization”. This FOA sought projects that would electrocatalytically reduce CO 2 to a carbon intermediate and then upconvert to a multi-carbon product or fuel via non-photosynthetic biological system engineering. The project sought to combine the expertise of OCO Chem, whose chief scientist had previously developed an efficient electrocatalytic reactor for conversion of CO 2 to formate with potential to scale, Montana State University investigators who had recently patented a method for laterally grading membranes with the potential of improving reactant distribution and more uniform efficiency across membrane-based reactors, and University of South Florida which had recently discovered a novel C-C bond forming reaction not known to naturally occur in biological systems and which uses C1 substrates and circumvents the central microbial metabolism.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Strategies for Post-Synthetic Functionalization of Mesoporous Carbon Nanomaterial Surfaces

Most widely used carbon-based materials feature a bulk framework tolerant of extreme pH and temperature conditions while maintaining physical robustness, electrical conductivity, and biological relevance due to its inherent nontoxicity. At the nanoscale, the study of porous carbons has been of interest because of the enhanced accessible surface area relative to nonporous analogues. The evolution of synthetic techniques has developed structural allotropes with tunable internal pore diameter averages spanning from sub-nanometer to micron-plus sizes. Within the mesopore range, surface chemical phenomena abide by a kinetic-limited ruleset (ignoring the effects of bulk diffusion, as they do not pertain to this size regime). Further, mesopores provide sufficient volume and surface area for hosting guest species, including metal nanoparticles (MNP), polymers, small organics, and enzymes. These two unique features of mesoporous carbon (MC) drive interest in surface modifications to create new physicochemical functionality to these systems and their hosted species. As a result, the evolution of surface modification techniques has been scattered to disparate niches across the literature. This review compiles the array of elegant methods by which these carbon systems are topically engineered.

functionalization↗

Inhibition of MALT1 and BCL2 Induces Synergistic Antitumor Activity in Models of B-Cell Lymphoma

The activated B cell (ABC) subset of diffuse large B-cell lymphoma (DLBCL) is characterized by chronic B-cell receptor signaling and associated with poor outcomes when treated with standard therapy. In ABC-DLBCL, MALT1 is a core enzyme that is constitutively activated by stimulation of the B-cell receptor or gain-of-function mutations in upstream components of the signaling pathway, making it an attractive therapeutic target. We discovered a novel small-molecule inhibitor, ABBV-MALT1, that potently shuts down B-cell signaling selectively in ABC-DLBCL preclinical models leading to potent cell growth and xenograft inhibition. We also identified a rational combination partner for ABBV-MALT1 in the BCL2 inhibitor, venetoclax, which when combined significantly synergizes to elicit deep and durable responses in preclinical models. This work highlights the potential of ABBV-MALT1 monotherapy and combination with venetoclax as effective treatment options for patients with ABC-DLBCL.

59 BASIC BIOLOGICAL SCIENCES↗

Nitric Oxide Production from Nitrite plus Ascorbate during Ischemia upon Hippocampal Glutamate NMDA Receptor Stimulation

Nitric oxide (•NO), a diffusible free radical, is an intercellular messenger, playing a crucial role in several key brain physiological processes, including in neurovascular coupling (NVC). In the brain, glutamatergic activation of the neuronal nitric oxide synthase (nNOS) enzyme constitutes its main synthesis pathway. However, when oxygen (O2) supply is compromised, such as in stroke, ischemia, and aging, such •NO production pathway may be seriously impaired. In this context, evidence suggests that, as already observed in the gastric compartment, the reduction of nitrite by dietary compounds (such as ascorbate and polyphenols) or by specific enzymes may occur in the brain, constituting an important rescuing or complementary mechanism of •NO production. Here, using microsensors selective for •NO, we show that nitrite enhanced the •NO production in a concentration-dependent manner and in the presence of ascorbate evoked by N-methyl-D-aspartate (NMDA) and glutamate stimulation of rat hippocampal slices. Additionally, nitrite potentiated the •NO production induced by oxygen-glucose deprivation (OGD). Overall, these observations support the notion of a redox interaction of ascorbate with nitrite yielding •NO upon neuronal glutamatergic activation and given the critical role of NO as the direct mediator of neurovascular coupling may represents a key physiological mechanism by which •NO production for cerebral blood flow (CBF) responses to neuronal activation is sustained under hypoxic/acidic conditions in the brain.

Nunes, Carla (ORCID:0000000274521592)↗

Spatiotemporal 4D Whole-cell Modeling of a Minimal Autotroph Reveals Central Carbon Metabolism Regulated Locally by Protein Megacomplexes via Post-translational Modifications under Light Disturbance

Photosynthetic microorganisms rely on multiple pathways in central carbon metabolism to adapt to fluctuating light and energy availability across diel cycles. Mechanistic insight into the regulatory dynamics of this adaptation requires integrating processes spanning disparate timescales, from rapid redox-dependent post-translational modifications (PTMs) to slower changes in protein expression and metabolic pathway usage. To address this complexity beyond genome-based inference and traditional modeling, we develop a whole-cell four-dimensional (3D + time) model of the marine cyanobacterium Prochlorococcus marinus MED4 that explicitly represents the spatial organization of enzymatic and molecular processes in central carbon metabolism under light perturbation. We employ a perturbation-based research design to experimentally generate time-series, multi-omics measurements that provide molecular descriptors and cryo-ET derived 3D segmented volumes as constraints for this dynamic 4D framework. The integration of experiments and modeling across defined light regimes enables quantitative validation of system-level responses and forecasting under distinct light disturbances. We test the hypothesis that light-dependent redox PTMs regulating the structural assembly of a protein megacomplex, the “dark complex,” modulate metabolic flux at a conserved regulatory node of the Calvin–Benson cycle (CBC) in cyanobacteria. Our model shows that subcellular spatial organization buffers rapid light-induced changes in thylakoid reaction rates, which are followed by redox-PTM-mediated sequestration or release of CBC enzymes in the dark complex, ultimately impacting carbon fixation dynamics within carboxysomes. Comparison with an equivalently parameterized well-mixed stochastic model demonstrates that post-translational regulation not only buffers transcriptional noise and diffusion-driven fluctuations but also stabilizes phenotypic outcomes, underscoring the importance of spatial heterogeneity in phenotypic robustness. This ability to probe adaptive, spatiotemporally resolved mechanisms in photosynthetic machinery and central carbon metabolism addresses a critical gap in genotype-to-phenotype inference and expands modeling and design capabilities for understudied or genetically intractable autotrophs such as P. marinus MED4.

Johnson, Connah G.↗

Development of energetic and enzymatic limitations on microbial carbon cycling in soils

Soil organic carbon (SOC) constitutes an important reservoir in the global carbon cycle that is vulnerable to transformation and loss from land use and climate change. Anoxic conditions protect SOC from microbial degradation through limiting the energetics of respiration and inhibiting extracellular oxidative enzymes. Given growing evidence of prevalent anaerobic microsites in upland soils, we designed an experiment testing the development of dissolved organic carbon (DOC) signatures of energetic and enzymatic limitations on microbial carbon utilization across simulated soil aggregates or peds. Reactors comprised a soil column “aggregate” underlying an advective “macropore” channel. Soils received downward diffusive inputs of aerated porewater media with added nitrate, sulfate, or no amendment—where native ferrihydrite served as dominant anaerobic terminal electron acceptor (TEA). After 40 days, added nitrate resulted in highest bulk respiration and DOC production while sulfate did not differ from the control. Nominal oxidation state of carbon (NOSC) was higher (more favorable) with added TEAs at soil surfaces and decreased with depth, while NOSC in the non-amended soil remained lower and constant with depth. DOC generally increased with depth, which along with decreasing NOSC values indicates joint electron-donor and acceptor control over respiration energetics. Of all organic compound classes, only the relative abundance of phenolics increased between 0 and 0.5 cm depth, which aligns with the oxic-anoxic transition and suggests oxidative enzyme inhibition. Furthermore, our results suggest that oxygen limitation within upland soil aggregates may preserve SOC via both energetic and enzymatic C protection mechanisms, which are vulnerable upon exposure to oxygen.

54 ENVIRONMENTAL SCIENCES↗

Insights from designing an artificial cascade catalysis system using principles from substrate channeling in enzymes

Generalizing the key requirements of highly-selective, multi-step chemical conversions involving spatially separated reaction centers remains one of the grand challenges of chemistry. Much work towards this effort has focused on decomposing multi-step conversions into their constituent reactions, whose intermediates are successively upgraded in a chemical cascade via diffusion from center to center. This approach for synthesizing more complex molecules takes its cues from biochemical networks, where near-unit conversion of even complex carbohydrates is achieved by upgrading chemical precursors via enzymatic cascades. In this computational study we examine a simple cascade involving coupled Ag and Cu catalysts that sequentially converts CO2 to CO and then CO2 and CO to reduced products, generically named CO2Product and COProduct. The system architecture is inspired by the phenomenon of biological substrate channeling, and components are examined to evaluate their effects on conversion efficiency in the cascade. Aside from a substrate channel linking two reaction centers, we find efficient cascades must also incorporate directional substrate diffusion, compartmentalization of the reaction centers, and proper timing of substrate arrival at the active center. We make explicit linkages between these requirements and chemical conversion in known biological systems, revealing additional control elements that could be incorporated.

CO 2 reduction↗

BETO 2021 Peer Review - Biochemical Process Modeling and Simulation (BPMS)

The Biochemical Process Modeling and Simulation project aims to reduce the cost and time of research by applying theory, modeling, and simulation to the most relevant bottlenecks in the biochemical process. We use molecular modeling, quantum mechanics, metabolic modeling, fluid dynamics, and reaction-diffusion methods in close collaboration with pretreatment, hydrolysis, upgrading, and TEA. The project's outcomes are increased yields and efficiency of the biochemical process, added value to products, and reduced price of fuels by specifically targeting catalytic efficiency, reactor design, enzyme efficiency, and microbial design.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Biochemical Process Modeling and Simulation (BPMS)

The Biochemical Process Modeling and Simulation project aims to reduce the cost and time of research by applying theory, modeling, and simulation to the most relevant bottlenecks in the biochemical process. We use molecular modeling, quantum mechanics, metabolic modeling, fluid dynamics, and reaction-diffusion methods in close collaboration with pretreatment, hydrolysis, upgrading, and TEA. The project's outcomes are increased yields and efficiency of the biochemical process, added value to products, and reduced price of fuels by specifically targeting catalytic efficiency, reactor design, enzyme efficiency, and microbial design. We work closely with experimental projects to identify problems and iterate with experiments to find and refine solutions. By working with experimentalists, we decide on problems that can be solved with simulation that could otherwise not be solved or would take too long with experiment alone to reach BETO's targets. Over the years, we have produced solutions that have resulted in determining the most likely fatty-acid derivative for passive transport out of bacteria that upgrade biomass, and we have also designed enzyme mutations for enhanced lignin upgrading. Metabolic models have been developed to tune the activity of 2,3 butanediol production for the 2030 target. A computational method to deliver understanding of how complex omics data can be interpreted in the metabolic pathways of organisms used in the Agile Biofoundry. We have found methods to overcome specific barriers and continue to develop those methods. Our reactor studies have guided the design of both the microbes and reactors for aerobic and micro-aerobic production at all scales and have been instrumental in improving the accuracy of techno-economic analysis models. This project is essential in the process of selecting the final processes for 2030 SAF production targets. More specifically, recently, we have: 1) Predicted the strength of the basic structural interactions in commodity plastics to provide guidance for plastics upcycling strategies. 2) Developed computational tool to improve the characterization of lignin-derived compounds 3) Developed new methodologies to enable Machine Learning-based Directed Evolution for protein engineering. 4) Developed Machine Learning methods to predict protein promiscuity and mutations to further improve microbial and enzymatic driven processes and demonstrated the utility of ML approaches to engineering proteins from sparse experimental datasets. 5) Developed new methods to enable high-fidelity simulation of aerobic fermentation at industrial scale and resolving mismatch of time scales through subcycling/operator splitting 7) Identified the difficulty in preventing local high-oxygen conditions in industrial bubble columns, which leads to less-desirable acetoin production, suggesting future research directions in alternative reactor configurations (e.g loop reactors, shallow-channel reactors).

BIOMASS FUELS↗

Self-generated electrokinetic flows from active-charged boundary patterns

We develop a hydrodynamic description of self-generated electrolyte flow in capillaries whose bounding walls feature nonuniform distributions of charge nonuniform active ionic fluxes. The hydrodynamic velocity arising in such a system has components that are forbidden by symmetry in the absence of charge and fluxes. However, when these two boundary mechanisms are simultaneously present, they can lead to a symmetry broken state where steady flows with both unidirectional and circulatory components emerge. We show that these flow states arise when modulated boundary patterns of charge and fluxes are offset by a flux-charge phase difference, which is associated with the separation between sites of their peak densities on the wall. Mismatch in diffusivity of cationic and anionic species can modify the flow states and becomes an enhancing factor when fluxes of both ion species are being produced together at the same site. We demonstrate that this mechanism can be realized with a microfluidic generator that is powered by enzyme-coated patches that catalyze reactants in the solution to produce fluxes of ions. The local ionic elevation or depletion, which disrupts a nonuniform double layer, promotes self-induced gradients yielding persistent body forces to generate bulk fluid motion. Our work quantifies a boundary-driven mechanism behind self-sustained electrolyte flow in confined environments that exists without any external bulk-imposed fields or gradients. It provides a theoretical framework for understanding the combined effect of active and charged boundaries that are relevant in biological or soft matter systems, and can be utilized in electrofluidic and iontronic applications.

active matter↗

Engineering quorum-sensing circuits in Synechococcus elongatus PCC 7942 towards self-inducible systems

Despite significant potential for cyanobacteria as sustainable bioproduction chases, there are limited examples of scaled cyanobacterial bioproduction. In part, this is because most cyanobacterial species are poorly adapted to bioreactor cultivation conditions and lack features that facilitate biomass growth and harvesting at scale. We explored quorum sensing (QS) pathways derived from heterotrophic microbes as a method for autoinduction of gene expression circuits coordinated to population density in cyanobacteria. Here, we integrated genetic modules designed to produce and detect the diffusible QS signal, acyl-homoserine lactones (AHLs), in the cyanobacterial model, Synechococcus elongatus PCC 7942 (S. elongatus). We demonstrate that S. elongatus heterologously produces sufficient AHL signals to activate gene expression in a dose-dependent and population density-responsive manner. A hybrid combination of AHL synthesis enzyme from Vibrio fischeri (Lux system) with the transcription factor receiver from Pseudomonas aeruginosa (Las system) provides an ideal activation ratio and mitigates toxicity observed with some AHL systems. As a proof of concept, we coupled the QS pathway to the expression of a cell division inhibitory gene, cdv3, facilitating late-phase cell elongation, cell sedimentation, and improved biomass recovery. Our findings provide a foundation for the development of auto-induction systems leverageable to improve cyanobacterial biotechnology applications.

Acyl homoserine lactones (AHL)↗

In Situ Identification of Reaction Intermediates and Mechanistic Understandings of Methane Oxidation over Hematite: A Combined Experimental and Theoretical Study

Effective methane utilization for either clean power generation or value-added chemical production has been a subject of growing attention worldwide for decades, yet challenges persist mostly in relation to methane activation under mild conditions. Here, we report hematite, an earth-abundant material, to be highly effective and thermally stable to catalyze methane combustion at low temperatures (<500 °C) with a low light-off temperature of 230 °C and 100% selectivity to CO 2 . The reported performance is impressive and comparable to those of precious-metal-based catalysts, with a low apparent activation energy of 17.60 kcal·mol –1 . Our theoretical analysis shows that the excellent performance stems from a tetra-iron center with an antiferromagnetically coupled iron dimer on the hematite (110) surface, analogous to that of the methanotroph enzyme methane monooxygenase that activates methane at ambient conditions in nature. Isotopic oxygen tracer experiments support a Mars van Krevelen redox mechanism where CH 4 is activated by reaction with a hematite surface oxygen first, followed by a catalytic cycle through a molecular-dioxygen-assisted pathway. Surface studies with in situ diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS) and density functional theory (DFT) calculations reveal the evolution of reaction intermediates from a methoxy CH 3 –O–Fe, to a bridging bidentate formate b-HCOO–Fe, to a monodentate formate m-HCOO–Fe, before CO 2 is eventually formed via a combination of thermal hydrogen-atom transfer (HAT) and proton-coupled electron transfer (PCET) processes. Finally, the elucidation of the reaction mechanism and the intermediate evolutionary profile may allow future development of catalytic syntheses of oxygenated products from CH 4 in gas-phase heterogeneous catalysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The Exometabolome of Xylella fastidiosa in Contact with Paraburkholderia phytofirmans Supernatant Reveals Changes in Nicotinamide, Amino Acids, Biotin, and Plant Hormones

Microbial competition within plant tissues affects invading pathogens’ fitness. Metabolomics is a great tool for studying their biochemical interactions by identifying accumulated metabolites. Xylella fastidiosa, a Gram-negative bacterium causing Pierce’s disease (PD) in grapevines, secretes various virulence factors including cell wall-degrading enzymes, adhesion proteins, and quorum-sensing molecules. These factors, along with outer membrane vesicles, contribute to its pathogenicity. Previous studies demonstrated that co-inoculating X. fastidiosa with the Paraburkholderia phytofirmans strain PsJN suppressed PD symptoms. Here, we further investigated the interaction between the phytopathogen and the endophyte by analyzing the exometabolome of wild-type X. fastidiosa and a diffusible signaling factor (DSF) mutant lacking quorum sensing, cultivated with 20% P. phytofirmans spent media. Liquid chromatography–mass spectrometry (LC-MS) and the Method for Metabolite Annotation and Gene Integration (MAGI) were used to detect and map metabolites to genomes, revealing a total of 121 metabolites, of which 25 were further investigated. These metabolites potentially relate to host adaptation, virulence, and pathogenicity. Notably, this study presents the first comprehensive profile of X. fastidiosa in the presence of a P. phytofirmans spent media. The results highlight that P. phytofirmans and the absence of functional quorum sensing affect the ratios of glutamine to glutamate (Gln:Glu) in X. fastidiosa. Additionally, two compounds with plant metabolism and growth properties, 2-aminoisobutyric acid and gibberellic acid, were downregulated when X. fastidiosa interacted with P. phytofirmans. These findings suggest that P. phytofirmans-mediated disease suppression involves modulation of the exometabolome of X. fastidiosa, impacting plant immunity.

60 APPLIED LIFE SCIENCES↗

Reactive high-spin iron(IV)-oxo sites through dioxygen activation in a metal–organic framework

In nature, nonheme iron enzymes use dioxygen to generate high-spin iron(IV)=O species for a variety of oxygenation reactions. Although synthetic chemists have long sought to mimic this reactivity, the enzyme-like activation of O 2 to form high-spin iron(IV) = O species remains an unrealized goal. Here, we report a metal–organic framework featuring iron(II) sites with a local structure similar to that in α-ketoglutarate-dependent dioxygenases. The framework reacts with O 2 at low temperatures to form high-spin iron(IV) = O species that are characterized using in situ diffuse reflectance infrared Fourier transform, in situ and variable-field Mössbauer, Fe Kβ x-ray emission, and nuclear resonance vibrational spectroscopies. In the presence of O 2 , the framework is competent for catalytic oxygenation of cyclohexane and the stoichiometric conversion of ethane to ethanol.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A Kinetic Model for Predicting Trace Gas Uptake and Reaction

A model is developed to describe trace gas uptake and reaction with applications to aerosols and microdroplets. Gas uptake by the liquid is formulated as a coupled equilibria that links gas, surface, and bulk regions of the droplet or solution. Previously, this framework was used in explicit stochastic reaction-diffusion simulations to predict the reactive uptake kinetics of ozone with droplets containing aqueous aconitic acid, maleic acid, and sodium nitrite. With the use of prior data and simulation results, a new equation for the uptake coefficient is derived, which accounts for both surface and bulk reactions. Lambert W functions are used to obtain closed form solutions to the integrated rate laws for the multiphase kinetics; similar to previous expressions that describe Michaelis-Menten enzyme kinetics. Together these equations couple interface and bulk processes over a wide range of conditions and do not require many of the limiting assumptions needed to apply resistor model formulations to explain trace gas uptake and reaction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗