Uncertainty Quantification of Bacterial Microcompartment Permeability

Abstract

Salmonella expresses bacterial microcompartments (MCPs) upon 1,2-propanediol exposure. MCPs are nanoscale protein-bound shells that encase enzymes for the cofactor-dependent 1,2-propanediol metabolism. They are hypothesized to limit exposure to the toxic intermediate, propionaldehyde, decrease cofactor involvement in competing reactions, and enhance flux. We construct a mass-action mathematical model of purified MCPs and calibrate parameters to measured metabolite concentrations. We constrain mass-action kinetic parameters to previously estimated Michaelis-Menten parameters. We identified two distinct fits with different dynamics in the pathway product, propionate, but similar goodness of fit. Across fits, we inferred that the MCP 1,2-propanediol and propionaldehyde permeability should be greater than 10^{-6} and 10^{-8} m/s, respectively. Our results identify parameter ranges consistent with prevailing theories that MCPs impose preferential diffusion to 1,2-propanediol over propionaldehyde, and sequester toxic propionaldehyde away from the cell cytosol. The bimodality of the posterior distribution arises from bimodality in the estimated coenzyme-A (CoA) permeability and inhibition rates. The MCP permeability to CoA was inferred to be either less than 10^{-8.8} m/s or greater than 10^{-7.3} m/s. In a high CoA permeability environment with low rates of CoA inhibition, enzymes produced metabolites by recycling (NAD+)/(NADH). In a low CoA permeability environment with high rates of CoA inhibition, enzymes required external NAD+/H to produce metabolites. Dynamics are consistent with prevailing hypotheses about MCP function to sequester toxic propionaldehyde, and additional collection of data points between 6 and 24 hours or characterization of enzyme inhibition rates could further reduce uncertainty and provide better permeability estimates.

Figures (45)

• Figure 1: Pdu Metabolic Pathway Network. Pdu MCPs house metabolic reactions that convert 1,2-propanediol to 1-propanol and propionyl-CoA while producing propionaldehyde, a growth-inhibiting intermediate. Downstream PduL-facilitated reactions convert propionyl-CoA to propionate. Enzyme-inhibiting mechanisms, such as PduQ oxidation and PduP inhibition through complex formation, may occur in the compartment. Cobalamin activation and diol dehydratase reactivation encapsulated pathways also occur in the compartment (not shown or modeled explicitly).
• Figure 2: Mass-action decomposition reaction of A) Pdu enzymes and B) inhibition of PduQ and PduP. Reactions occur from left to right, with the sequence of substrates, intermediate complexes, and products indicated (below the line). A vertical downward-facing arrow indicates a binding event, and a vertical upward arrow indicates an unbinding event. From top to bottom, Figure A details PduCDE conversion of 1,2-propanediol to propionaldehyde Toraya2000, PduQ reduction of propionaldehyde to 1-propanol, PduP oxidation of propionaldehyde to propionyl-CoA, PduL convert of propionyl-CoA to propionyl-phosphate Smith1980 and AckA conversion of propionyl-phosphate to propionate. We assume that PduQ, PduL, and AckA sequentially bind to cofactors first and their organic substrate second. From top to bottom, Figure B outlines the mass-action decomposition of PduQ oxidation and PduP-CoA inhibition Smith1980. We assume that PduQ oxidation follows first-order elimination.
• Figure 3: (A) Bayesian calibration pipeline. The in vitro model was calibrated to prior parameter beliefs and metabolite time series using PyMC pymc2023. (B) Mass-action kinetic parameter relationship to PduCDE binding events. Odd and even indexed kinetic parameters represent reaction rates for the forward and reverse reaction, respectively. (C) Transformation between free mass-action (MA) & measured Michaelis-Menten (MM) space, and MA kinetic parameter space. (i) PyMC computes the leading MA variables from the measured MM space and free MA parameters. (ii) Combining free and leading MA variables, PyMC computes all MA parameters. Likelihood gradients are generated in terms of the mass-action parameter set. PyMC transforms the likelihood derivative to free MA and the measured MM parameter space via fundamental back-propagation operations.
• Figure 4: Modes 1 and 2 fit to A) 1,2-propanediol, B) propionaldehyde, C) propionate, and D) 1-propanol. Mode 1 and mode 2 differed primarily in propionate dynamics. There is a discrepancy between estimated propionaldehyde dynamics and experimental measurements because of unexplained mass loss at the time of study (see Section \ref{['ssec:BayesianInference']}). Later experiments showed mass loss was due to evaporation. The inclusion of mass loss did not affect downstream propionate and 1-propanol dynamics.
• Figure 5: Prior to Posterior kinetic parameter update of PduCDE and Keq parameters. A) Corner plot of prior and posterior (mode 1 and mode 2) PduCDE parameter samples. Shown are all PduCDCE mass-action kinetic parameters, measured Michaelis-Menten kinetic parameters, and MCP enzyme number. Strip plot comparing mode 1 and mode 2 inferred B) kcat,PduCDEf and KM,PduLCoA, and C) Keq of all reactions. The uniform prior range is overlaid as an orange pointplot interval.