Fig. 1: Using Bayesian statistical learning to integrate temperature dependence in enzyme-constrained GEMs.

a An illustration of the temperature effects on enzyme-catalyzed reactions and their integration into an etcGEM (see detailed description and equations in “Methods” section). The metabolic network ecYeast7.6¹⁶ is shown. b A two-state denaturation model^20,21,58 was used to describe the temperature-dependent unfolding process. [E]_N is the concentration of the enzyme in the native state; T_opt is the optimal temperature at which the specific activity is maximized; T_m and T₉₀ are temperatures at which there is a 50 and 90% probability that an enzyme is in the denatured state, respectively. c Macromolecular rate theory^31,33 describing the temperature dependence of enzyme turnover number k_cat. Inset shows the heat capacity difference between ground state (E + S) and transition state (E − TS), adapted from Hobbs et al.³¹. d Temperature dependence of enzyme-specific activity r, which is a product of (b) and (c). e Overview the Bayesian statistical learning approach, where the problem can be formulated as given a generative model (M) (enzyme and temperature constrained genome-scale metabolic model, etcGEM in this study) corresponding to a set of parameters θ and a set of measurements D (phenome data), Bayes’ theorem provides a direct way of updating the Prior distribution of parameters P(θ) to a Posterior distribution P(θ|D): \(P(\theta |D) = \frac{{P(D|\theta ) \times P(\theta)}}{{P(D)}}\). P(θ|D) is thereby a less uncertain description of the real θ. Since P(D|θ) is, in most applications, computationally expensive or even infeasible to obtain, a sequential Monte Carlo based approximate Bayesian computation (SMC-ABC) approach was implemented (“Methods”) to sample a list of parameter sets from the Posterior.