Model-Based Optimal Design of a Gene Metabolator System

Model-based optimal design of a gene oscillator system

Asif Bhatti, Vivek Dua

Synthetic biology has garnered much interest in recent years and looks to revolutionise a wide range of industries including genetics and protein engineering. It is a novel, multidisciplinary approach utilising engineering principles and biology to enhance naturally occurring systems. First described by Szybalski and Skalka ^[1], it heralds a new age where genes can not only be described, but re-evaluated to give better arrangements of the gene network. Modelling and designing engineered biological systems to predict system performance before fabrication is an important component of synthetic biology ^[2,3]. In this sense it is similar to systems biology as they both rely heavily on computer modelling.

The main aim of this work is to optimally design a metabolator, which is a metabolic enzyme process of Acetyl-CoA and its co-factors. The metabolic process can be described using a dynamic model involving nonlinear differential equations ^[4].The metabolator consists of two metabolite pools, one with the enzyme and another with its co-factors, acetyl phosphate (AcP) and acetate kinase (Ack). The two pools are connected by a negative feedback reaction from the enzyme to the co-factors involving phosphate acetyltransferase (Pta), and a positive feed-forward reaction from the co-factors back to the enzyme involving acetyl synthase (Acs). The influx of glycerol, fatty acids and sugars (glycolytic flux) into the enzyme, Acetyl-CoA, causes its concentration to oscillate. As a result Pta feeds into the co-factor metabolite pool to produce acetate. Acetate is then transported to the cell for further intrinsic use. However the process is cyclical and can have a positive feed–forward reaction whereby the presence of acetate in the metabolite pool (AcP and Ack) can upregulate Acs formation to feed back to the enzyme. The process reacts to circadian rhythm in the body, and will continue to oscillate as a result.

The dynamic model of the metabolator is transformed into a system of simultaneous algebraic equations using an artificial neural network (ANN) transformation ^[5]. The metabolator design is formulated as an optimisation problem, where the objective is to control the concentration of Acetyl-CoA at a desired set-point by manipulating the glycolytic flux. Also, when acetate levels are increased to large values the system can be inhibited and will no longer oscillate, a property that could be useful for systems requiring a ‘shut-off' feature. To ensure robustness of the numerical convergence of the optimisation problem, the solution of the dynamic equations was also verified by the fourth order Runge-Kutta method, and the effect of the numerical integration step-size was also analysed

The metabolator performance is subject to uncertain parameters such as the surrounding environmental conditions (pH, temperature, availability of nutrients and age) and degradation of the enzyme. In the future work, the effect of these uncertain parameters on the design will be analysed, and a new design that can effectively take into account the uncertain parameters and yet deliver the performance required will be obtained.

[1]    Szybalski, W. & Skalka, A., Nobel-Prizes and Restriction Enzymes. Gene, 4, 181-182, 1978

[2]    Dasika, M. S. & Maranas, C. D., OptCircuit: An optimization based method for computational design of genetic circuits. Bmc Systems Biology, 2, 2008

[3]    Purcell, O., Savery, N. J., Grierson, C. S. & Di Bernado, M., A comparative analysis of synthetic genetic oscillators, Journal of the Royal Society Interface, 2010

[4]    Fung, E., Wong, W. W., Suen, J. K., Butler, T., Lee, S. G. & Liao, J. C., A synthetic gene-metabolic oscillator. Nature, 435, 118-122, 2005

[5]    Dua, V. & Dua, P., A simultaneous approach for parameter estimation of a system of ordinary differential equations, using artificial neural network approximation. Industrial and Engineering Chemistry Research, 51 (4), 1809-1814, 2012