Considering Dynamic Constraints during Strain Optimization

Microbial cells have been successfully engineered to produce a large variety of biomolecules useful as biofuels, drugs and drug-precursors, and bioplastics.  One challenge in maximizing the production of a target metabolite within a microbial cell is identifying gene modifications in the form of up-regulation, down-regulation, or knockout. While many such interventions are identified in an ad hoc manner based on experimental expertise, several computational tools have been developed for strain optimization.  Strain optimization is formulated as an optimization problem specified in terms of two variables: flux variables and control (decision) variables that correspond to the presence or absence of regulation for each reaction and in each direction (up/down).  Importantly, solutions to strain optimization problems must respect new bounds imposed due to regulation modification. A gene knock out modifies the upper and lower flux bounds to be zero, while up/down regulation defines new upper/lower bounds on reaction fluxes. Changes in bounds due to gene modifications impose new steady-state constraints, referred to as dynamic constraints, on the system as a whole.  Another challenge in strain optimization is identifying an optimal fold change (e.g., 0.5, 2x, 5x, or 10x), instead of just identifying the fold change direction (up or down regulation).  Prior computational approaches do not consider updating the steady state boundaries nor identify gene fold modification.

We propose a new strain optimization formulation that identifies fold changes required to maximize cellular yield.  The fold changes are treated as a random variable with a probability distribution reflecting uncertainty in implementing engineering interventions.  Each fold change can be one of three values, 2x, 5x, or 10x, compared to a 1x non-regulated fold change.  Simulated Annealing (SA) is used to identify the optimal interventions and their fold changes.  Flux Balance Analysis is utilized as a fitness function, evaluating the product yield using updated steady state conditions.   We have applied this method to maximize the production of antibody in the Chinese Hamster Ovary (CHO) cell, and pyruvate in Escherichia coli.  Our results show that SA is capable of identifying several intervention sets with different fold changes values that result in the same yield value of a desired product.   Our results also show increased predicted maximum yield value due to utilizing dynamic constraints that update steady-state bounds.