Difference between revisions of "Team:UC San Diego/Modeling/Kinetics"

Line 42: Line 42:
  
 
<center><img src="https://static.igem.org/mediawiki/2015/9/92/UCSDlight_production.jpeg"></center>
 
<center><img src="https://static.igem.org/mediawiki/2015/9/92/UCSDlight_production.jpeg"></center>
<i><p>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).</p></i>
+
<i><p>Figure 2. The light production pathway is controlled by an enzyme complex luciferase (LuxA+LuxB, we used a LuxA+B fusion protein for enhanced luminescence<sup>23</sup>) and its immediate microenvironment (molecular oxygen, aldehyde, and reduced flavin concentrations).</p></i>
  
 
<p>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.</p>  
 
<p>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.</p>  
Line 52: Line 52:
 
<h3>Modeling</h3>
 
<h3>Modeling</h3>
  
<p>Lorem ipsum dolor sit amet, consectetur adipiscing elit. Mauris eu suscipit lectus. Pellentesque ut risus rhoncus, congue tortor at, aliquam augue. Vestibulum ex mi, varius quis sollicitudin at, blandit ac lorem. Vivamus mattis sapien turpis, in fringilla nulla cursus id. Vestibulum vestibulum velit et accumsan aliquet. Aenean nulla justo, scelerisque id pulvinar eu, fringilla et nisl. Cras sapien magna, tincidunt in sapien et, sagittis sodales lacus. Praesent a ex ut augue fringilla interdum.</p>
+
<p>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. </p>
  
 
<p>LIST OF ASSUMPTIONS</p>
 
<p>LIST OF ASSUMPTIONS</p>

Revision as of 23:54, 18 September 2015

post image

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 pathway4,7,12,11,17. 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 system1,2. 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




Lorem ipsum dolor sit amet, consectetur adipiscing elit. Mauris eu suscipit lectus. Pellentesque ut risus rhoncus, congue tortor at, aliquam augue. Vestibulum ex mi, varius quis sollicitudin at, blandit ac lorem. Vivamus mattis sapien turpis, in fringilla nulla cursus id. Vestibulum vestibulum velit et accumsan aliquet. Aenean nulla justo, scelerisque id pulvinar eu, fringilla et nisl. Cras sapien magna, tincidunt in sapien et, sagittis sodales lacus. Praesent a ex ut augue fringilla interdum.

FIGURES

Lorem ipsum dolor sit amet, consectetur adipiscing elit. Mauris eu suscipit lectus. Pellentesque ut risus rhoncus, congue tortor at, aliquam augue. Vestibulum ex mi, varius quis sollicitudin at, blandit ac lorem. Vivamus mattis sapien turpis, in fringilla nulla cursus id. Vestibulum vestibulum velit et accumsan aliquet. Aenean nulla justo, scelerisque id pulvinar eu, fringilla et nisl. Cras sapien magna, tincidunt in sapien et, sagittis sodales lacus. Praesent a ex ut augue fringilla interdum.

Lorem ipsum dolor sit amet, consectetur adipiscing elit. Mauris eu suscipit lectus. Pellentesque ut risus rhoncus, congue tortor at, aliquam augue. Vestibulum ex mi, varius quis sollicitudin at, blandit ac lorem. Vivamus mattis sapien turpis, in fringilla nulla cursus id. Vestibulum vestibulum velit et accumsan aliquet. Aenean nulla justo, scelerisque id pulvinar eu, fringilla et nisl. Cras sapien magna, tincidunt in sapien et, sagittis sodales lacus. Praesent a ex ut augue fringilla interdum.

Model Reduction

Lorem ipsum dolor sit amet, consectetur adipiscing elit. Mauris eu suscipit lectus. Pellentesque ut risus rhoncus, congue tortor at, aliquam augue. Vestibulum ex mi, varius quis sollicitudin at, blandit ac lorem. Vivamus mattis sapien turpis, in fringilla nulla cursus id. Vestibulum vestibulum velit et accumsan aliquet. Aenean nulla justo, scelerisque id pulvinar eu, fringilla et nisl. Cras sapien magna, tincidunt in sapien et, sagittis sodales lacus. Praesent a ex ut augue fringilla interdum.

SYSTEM OF EQUATIONS

Lorem ipsum dolor sit amet, consectetur adipiscing elit. Mauris eu suscipit lectus. Pellentesque ut risus rhoncus, congue tortor at, aliquam augue. Vestibulum ex mi, varius quis sollicitudin at, blandit ac lorem. Vivamus mattis sapien turpis, in fringilla nulla cursus id. Vestibulum vestibulum velit et accumsan aliquet. Aenean nulla justo, scelerisque id pulvinar eu, fringilla et nisl. Cras sapien magna, tincidunt in sapien et, sagittis sodales lacus. Praesent a ex ut augue fringilla interdum.

Velocity Equations

Lorem ipsum dolor sit amet, consectetur adipiscing elit. Mauris eu suscipit lectus. Pellentesque ut risus rhoncus, congue tortor at, aliquam augue. Vestibulum ex mi, varius quis sollicitudin at, blandit ac lorem. Vivamus mattis sapien turpis, in fringilla nulla cursus id. Vestibulum vestibulum velit et accumsan aliquet. Aenean nulla justo, scelerisque id pulvinar eu, fringilla et nisl. Cras sapien magna, tincidunt in sapien et, sagittis sodales lacus. Praesent a ex ut augue fringilla interdum.

EQUATIONS

Lorem ipsum dolor sit amet, consectetur adipiscing elit. Mauris eu suscipit lectus. Pellentesque ut risus rhoncus, congue tortor at, aliquam augue. Vestibulum ex mi, varius quis sollicitudin at, blandit ac lorem. Vivamus mattis sapien turpis, in fringilla nulla cursus id. Vestibulum vestibulum velit et accumsan aliquet. Aenean nulla justo, scelerisque id pulvinar eu, fringilla et nisl. Cras sapien magna, tincidunt in sapien et, sagittis sodales lacus. Praesent a ex ut augue fringilla interdum.

EQUATIONS

Lorem ipsum dolor sit amet, consectetur adipiscing elit. Mauris eu suscipit lectus. Pellentesque ut risus rhoncus, congue tortor at, aliquam augue. Vestibulum ex mi, varius quis sollicitudin at, blandit ac lorem. Vivamus mattis sapien turpis, in fringilla nulla cursus id. Vestibulum vestibulum velit et accumsan aliquet. Aenean nulla justo, scelerisque id pulvinar eu, fringilla et nisl. Cras sapien magna, tincidunt in sapien et, sagittis sodales lacus. Praesent a ex ut augue fringilla interdum.

Results


Lorem ipsum dolor sit amet, consectetur adipiscing elit. Mauris eu suscipit lectus. Pellentesque ut risus rhoncus, congue tortor at, aliquam augue. Vestibulum ex mi, varius quis sollicitudin at, blandit ac lorem. Vivamus mattis sapien turpis, in fringilla nulla cursus id. Vestibulum vestibulum velit et accumsan aliquet. Aenean nulla justo, scelerisque id pulvinar eu, fringilla et nisl. Cras sapien magna, tincidunt in sapien et, sagittis sodales lacus. Praesent a ex ut augue fringilla interdum.

Lorem ipsum dolor sit amet, consectetur adipiscing elit. Mauris eu suscipit lectus. Pellentesque ut risus rhoncus, congue tortor at, aliquam augue. Vestibulum ex mi, varius quis sollicitudin at, blandit ac lorem. Vivamus mattis sapien turpis, in fringilla nulla cursus id. Vestibulum vestibulum velit et accumsan aliquet. Aenean nulla justo, scelerisque id pulvinar eu, fringilla et nisl. Cras sapien magna, tincidunt in sapien et, sagittis sodales lacus. Praesent a ex ut augue fringilla interdum.

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 VmaxluxAB 71.58
r22 0.62
k41 0.22
k42 81.5
k43 72.2
lux EC VmaxluxEC 198.93
r44 0.04
k61 90.9
k62 95.3
k63 24.35
k64 76.5
frp Vmaxfrp 51.8
r12 1
k31 0.72
k32 49.5
lux D VmaxluxD 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