Team:UC San Diego/Modeling/Kinetics

Introduction

We developed a mathematical model to understand the relationship between the enzymes in our genetic constructs and their immediate microenvironment a priori. Using the MATLAB numerical solver ode23 and kinetic information from in vitro experiments found in literature (Table 1 and 2), we modeled the bioluminescence reaction network as an isolated system under steady state conditions and acquired preliminary light emission results for our different genetic constructs.

Chemical Reaction Network

The microbial Lux system can be interpreted as a two-component module, the aldehyde synthesis pathway and the light production pathway, coupled by an aldehyde and fatty acid.

Figure 1. The reactions in the aldehyde synthesis pathway are tightly coupled by the LuxCDE genes given the 1:1 ratio amongst substrate and product¹⁵.

In the aldehyde synthesis pathway (Fig. 1), the transferase (LuxD) first cleaves acyl-ACP and forms a fatty acid (RCOOH), via hydrolysis, which is subsequently activated by the synthetase subunit (LuxE) and reversibly transferred to the reductase subunit (LuxC) before being reduced with NADPH to an aldehyde (RCHO)^5,8,18,19,20. The fatty acid activation process in the synthetase subunit occurs at very low levels in the absence of reductase15. However, when the synthetase and reductase subunits are co-expressed with luciferase, the system proceeds to emit light in the absence of transferase¹⁶; albeit at lower levels.

Figure 2. The light production pathway is controlled by an enzyme complex luciferase (LuxA+LuxB, we used a LuxA+B fusion protein for enhanced luminescence²³) and its immediate microenvironment (molecular oxygen, aldehyde, and reduced flavin concentrations).

In effort to parallel our in vivo experiments, the light production network (Fig. 2) was extended to incorporate alternate reactions, such as aldehyde inhibition and the autoxidation of reduced flavin.

In the absence of RCHO, the reduced enzyme-oxygen adduct complex (intermediate II) dissociates and shifts the light producing pathway to the dark pathway^4,7,12,11,17. Under conditions in which the aldehyde concentration is high and the reduced flavin concentration insufficient, the aldehyde binds to luciferase prior to reduced flavin or to luciferase-bound hyrdroperoxyflavin and inhibits the system^1,2. Further light emission is limited by the autoxidation of reduced flavin and the slow dissociation of the aldehyde from the aldehyde-luciferase complex¹⁰ in addition to the release of fatty acid from peroxyhemiacetal (LuxAB-FMNH2O2-RCHO)^11,13. The presence of functional luciferase, which governs light production, is therefore determined controlled by the presence of specific cofactors.

Modeling

To study the relationship between light emission and different conditions, a model for the light production pathway was constructed to analyze single-burst assays in addition to studying the sensitivity of certain parameters that have been suggested to control light emission.

LIST OF ASSUMPTIONS

SYSTEM OF EQUATIONS

Induction Curves and Parameter Sensitivity

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FIGURES

Model Reduction

SYSTEM OF EQUATIONS

Velocity Equations

EQUATIONS

Results

Future Directions

Parameter Table

Rate Constant	Value	Reference
k¹	unknown
k²	unknown
k³	unknown
k⁴	unknown
k⁵	unknown
k⁶	unknown
k⁷	21.2 s^-1	(14)
k⁸	10 s^-1	(9)
k⁹	6.0*10₅ M^-1s^-1	(12)
k¹⁰	4.6 s^-1	(12)
k¹¹	2.4*10₆ M^-1s^-1	(12)
k¹²	0.1 s^-1	(12)
k¹³	1.2*10₅ M^-1s^-1	(12)
k¹⁴	0.1 s^-1	(12)
k¹⁵	9.5 s^-1	(12)
k¹⁶	0.5 s^-1	(12)
k¹⁷	3*10₃ M^-1s^-1	(2)
k¹⁸	0.06 s^-1	(2)
k¹⁹	1.9*10_-3 s^-1	(3)
k²⁰	1*10₅ M^-1s^-1	(12)
k²¹	40 s^-1	(12)

Enzyme Table

Enzyme	Parameter	Value
lux AB	Vmax^luxAB	71.58
	r²²	0.62
	k⁴¹	0.22
	k⁴²	81.5
	k⁴³	72.2
lux EC	Vmax^luxEC	198.93
	r⁴⁴	0.04
	k⁶¹	90.9
	k⁶²	95.3
	k⁶³	24.35
	k⁶⁴	76.5
frp	Vmax^frp	51.8
	r¹²	1
	k³¹	0.72
	k³²	49.5
lux D	Vmax^luxD	45.8
	r³³	unknown
	k⁵¹	0.37
	k⁵²	unknown

Cofactor Table

Chemical Species	Concentration (uM)	Reference
NADPH	560	(6)
ATP	1310	(6)
O²	550	(27)
H²O	500	unknown
H+	300	unknown

Scripts

Link to Enzyme Kinetics Scripts

References

REFERENCES