Modeling

Energy system

Why

Aerobic respiration is the main way to provide energy to bacteria . In aerobic respiration, one Acetyl-CoA was consumed away and 10 ATP are produced. The electron transport chain was supposed as the main part to produce ATP. But the fact is that the system we designed to fix carbon is derived from anaerobic bacteria and the enzymes with metal active center in it may be oxidated by oxygen. Therefore a model was built to get the solution to make the two system compatible.

Fig. 1. CARBON FIXATION SYSTEM. In one cycle, one ATP is cost and one CoA is acetylated to Acetyl-CoA.

It is reported that all the reactions is not very fast and the enzyme damaged by oxygen is can be repaired in other way. What the oxygen effects is reversible. Therefore it is believe that some concentration of oxygen can make both two systems work at the same time.

What we did

At first, all the reactions are assumed as elementary reaction.

V=KS₁^r¹X S₂^r² …S_i^rⁱ…S_n^rⁿ

V: the velocity of reaction

K: a constant of the reaction

n: the species’number of substrates and enzymes in the reaction

Si: the concentration of substrate or enzyme

ri: the cost of substrate during one reaction

Fig. 2. Simplified pathway of energy system designed by us.

The result was assumed to be related to the degree of equation. All the unknown parameters and original moles were assumed to be 1 0.1(for enzymes). These settings make the computation easier. Then we got all the equations in the table.

id	reactants	products	modifiers	Math
re1	s3,s18	s5	s6	(v2*s3)/(k3+s3)
re2	s5,s9,s10	s7,s11	s8	s5 * s9 * s10 * s8 * k1
re3	s7	s13,s15	s14	v1 * s7 / (k2 + s7) * s14 / 0.1
re4	s13,s18	s16	s17	(v1s13)/(k2+s13)s17/0.1
re5	s16,s18	s19	s20	(v1*s16)/(k2+s16)
re7	s19	s21,s9	s27	s19k1s27
re8	s3,s18	s28	s29	s3s18k1*s29
re9	s21	s30	s29	s21k1s29
re10	s30,s28,s32	s31		s30s28s32*k1
re12	s6	s34	s33	s6s33k2*s33/9.375
re21	s29	s34	s33	s29 * k2 * s33 / 9.375
re24	s21	s34	s33	s21 * s33 * k2*s33/9.375
re25	s31,s33,s11	s32,s10,s15		s31 * s33^3 * s11^10 * k1
re26	s34	s6		(v1*s34)/(k1+s34)
re27	s34	s29		(v1*s34)/(k1+s34)
re28	s34	s21		(v1*s34)/(k1+s34)

table : Reaction Equations in the modeling: The concentration of oxygen in air is 9.375 mol/m3 which was assumed as the perfect condition. The efficiency of all the enzyme are 100%. All the enzymes’ working efficiency are proportional to the concentration of oxygen. the number of ATP and ADP involved in re25 is 10; all the enzyme was thought as regent.

We changed the concentration of oxygen in our assumed environment to investigate the concentration’s change of ATP and ADP.

Results are as follows

**Fig. 3. The best concentration of oxygen: the concentration of oxygen in our environment is 0.65*9.375mole/m3. Concentration of ATP and ADP can keep in a ratio similar to original environment.**

Fig. 4. Low oxygen concentration: ATP is used up and the energy system can not work.

Fig. 5. High concentration of oxygen: system can not work.

The right concentration of oxygen can make our energy system feasible and increase the ratio of ATP/ADP. The extra ATP can be used by nitrogen fixation.

Improved Modeling of verification(BBa_K137502):

As Rhl and Las complex competitively bind reversibly with the target DNA-35, and furthermore control the transcription of DNA, we can work out a set of equations based on the balance of the reaction and the conserved Improved Modeling of verification(BBa_K137502):

As Rhl and Las complex competitively bind reversibly with the target DNA-35, and furthermore control the transcription of DNA, we can work out a set of equations based on the balance of the reaction and the conservation law while the reaction is at equilibrium state. Finally we figured out the equation representing the equilibrium state of the reaction.

To simplify the expressions, Rr represents the amount of free Rhl complex; DRr represents the amount of DNA binding with Rhl complex; Rtr represents the amount of Rhl complex; Rl represents the amount of free Las complex; DRl represents the amount of Las complex binding with DNA;Rtl represents the amount of Las complex.

Based on reservation law, we have the following equation:

Rr + DRr = Rtr

Rl + DRl = Rtl

kr represents the equilibrium constant of the reaction between Rhl complex and free DNA. kl represents the equilibrium constant of the reaction between Las complex and free DNA. The equations are as follow:

kr [D] [Rr] = [DRr]

kl [D] [Rl] = [DRl]

Based on conservation law, we set Dt as the amount of all DNA:

D + Dr + Dl = Dt

Solving the equations:

[k2(Rt1-DR1)+k1DR1][(Dt-DR1)(Rt1-DR1)-k1DR1]=Rt2k1DR1

Based on conservation law, the reaction is at equilibrium state. Finally we figured out the equation representing the equilibrium state of the reaction.