Control Theory Concepts for Modeling Uncertainty in Enzyme Kinetics of Biochemical Networks

Abstract

Analysis of the dynamic and steady-state properties of biochemical networks hinge on information about the parameters of enzyme kinetics. The lack of experimental data characterizing enzyme activities and kinetics along with the associated uncertainties impede the development of kinetic models, and researchers commonly use Monte Carlo sampling to explore the parameter space. However, the sampling of parameter spaces is a computationally expensive task for larger biochemical networks. To address this issue, we exploit the fact that reaction rates of biochemical reactions and network responses can be expressed as a function of displacements from thermodynamic equilibrium of elementary reaction steps and concentrations of free enzymes and their intermediary complexes. For a set of kinetic mechanisms ubiquitously found in biochemistry, we express kinetic responses of enzymes to changes in network metabolite concentrations through these quantities both analytically and schematically. The tailor-made sampling of these quantities allows for characterizing the missing kinetic parameters and accelerating the efforts towards building genome-scale kinetic metabolic models.

Uncertainty Reduction in Biochemical Kinetic Models: Enforcing Desired Model Properties

“…Otherwise, we performed the stratified sampling where we imposed the σA distributions obtained from the classification algorithm in Step VII (Fig 7A and 7B). An alternative to sampling σA values would be to sample the enzyme states (27,28).…”

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

“…We found that all reaction directionalities within the obtained thermodynamically feasible steady-state flux and metabolite concentration profile were in agreement with the preassigned directionalities from iJN1411 [15] (Additional file 1: Table S1). We used ORACLE [34,[41][42][43][44][45][46][47][48][49][50] to construct a population of 50,000 nonlinear kinetic models around the computed steady-state flux and concentration profile ("Methods"). The constructed models contained the experimental values for 21 Michaelis constants (K m 's) available for the Pseudomonas genus in the Brenda database [81][82][83][84].…”

“…However, as the model complexity increases, the portion of available data of intracellular metabolite concentration and metabolic flux is rapidly decreasing, i.e., uncertainty in the system is increasing [19]. Next, we applied ORA-CLE [34,[41][42][43][44][45][46][47][48][49][50], a computational framework based on Monte Carlo sampling, to construct large-scale kinetic metabolic models of P. putida KT2440. The potential of developed kinetic models for the design of improved production strains of P. putida was demonstrated through two studies: (i) predicting metabolic responses of a wildtype P. putida strain to single-gene knockouts; and (ii) improving the responses of this organism to the stress conditions of increased ATP demand.…”

Understanding biochemical design principles with ensembles of canonical non-linear models

“…Although our emphasis is on finding general design principles, this method can be 705 prepended to any modeling pipeline as a way to accelerate parameter estimation by 706 filtering our bad models and integrating qualitative biochemical knowledge into the 707 modeling process. In fact, the method presented here can be considered the natural 708 continuation of the ensemble modeling approaches developed by Liao's group [13,14] by 709 way of incorporating the attention to thermodynamics and the use of power-law kinetics 710 exemplified by Hatzimanikatis' lab [15,21,29]. What this method adds is the possibility 711 of partitioning the design space into subspaces that can be sampled and tested 712 independently.…”

“…130 Using easy to measure values to reduce the dimensionality of the parameter space has 131 proven to be a very effective strategy for ensemble modeling [19] that works particularly 132 well with the power-law formalism [20]. Using models based on the power-law formalism 133 or similar approaches such as Metabolic Control Analysis (MCA) offers a series of 134 advantages [21] and does not result in a loss of generality. Once a set of the 135 above-mentioned parameters is obtained, it can always be translated to more traditional 136 biochemical parameters such as Michaelis constants or Hill coefficients [22,23].…”