(333g) 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