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Methodology

To achieve each one of the previous proposals, we will follow this methodology:

Equations

For this model, it is firstly necessary to determine the reactions involved in the Calvin cycle, which are available in databases. If you would like to see the equations, click the below.

Carbon Dioxide

$${d[CO_2] \over dt} = 0 .$$

Erythrose 4-Phosphate

$${d[E4P] \over dt} = {{V_{max}^{F6P \rightarrow E4P} \cdot [F6P]} \over {K_m^{F6P \rightarrow E4P} + [F6P]}} - {{V_{max}^{E4P \rightarrow Sed17P2} \cdot [E4P]} \over {K_m^{E4P \rightarrow Sed17P2} + [E4P]}} - k_{deg}^{E4P}[E4P] .$$

Sedoheptulose 1,7-Bisphosphatase

$${d[Sed1,7P2] \over dt} = {{V_{max}^{E4P \rightarrow Sed17P2} \cdot [E4P]} \over {K_m^{E4P \rightarrow Sed17P2} + [E4P]}} - {{V_{max}^{Sed17P2 \rightarrow Sed7P} \cdot [Sed1,7P2]} \over {K_m^{Sed17P2 \rightarrow Sed7P} + [Sed1,7P2]}} - k_{deg}^{Sed17P2}[Sed1,7P2] .$$

Sedoheptulose 7-Phosphate

$${d[Sed7P] \over dt} = {{V_{max}^{Sed17P2 \rightarrow Sed7P} \cdot [Sed1,7P2]} \over {K_m^{Sed17P2 \rightarrow Sed7P} + [Sed1,7P2]}} - {{V_{max}^{Sed7P \rightarrow R5P} \cdot [Sed7P]} \over {K_m^{Sed7P \rightarrow R5P} + [Sed7P]}} - k_{deg}^{Sed7P} [Sed7P] .$$

Ribose 5-Phosphate

$${d[R5P] \over dt} = {{V_{max}^{Sed7P \rightarrow R5P} \cdot [Sed7P]} \over {K_m^{Sed7P \rightarrow R5P} + [Sed7P]}} - {{V_{max}^{R5P \rightarrow Rul5P} \cdot [R5P]} \over {K_m^{R5P \rightarrow Rul5P} + [R5P]}} - k_{deg}^{R5}[R5P] .$$

Ribolose 5-Phosphate

$${d[Rul5P] \over dt} = {{V_{max}^{R5P \rightarrow Rul5P} \cdot [R5P]} \over {K_m^{R5P \rightarrow Rul5P} + [R5P]}} - {{V_{max}^{Rul5P \rightarrow Rul15P2} \cdot [Rul5P]} \over {K_m^{Rul5P \rightarrow Rul15P2} + [Rul5P]}} - k_{deg}^{Rul5P}[Rul5P] .$$

Ribulose 1,5-Bisphosphate

$${d[Rul1,5P2] \over dt} = {{V_{max}^{Rul5P \rightarrow Rul15P2} \cdot [Rul5P]} \over {K_m^{Rul5P \rightarrow Rul15P2} + [Rul5P]}} - {{V_{max}^{Rul15P2 \rightarrow Gl3P} \cdot [Rul1,5P2][CO_2]} \over {K_m^{Rul15P2 \rightarrow Gl3P} + [Rul1,5P2][CO_2]}} - k_{deg}^{Rul15P2}[Rul1,5P2] .$$

Glycerate 3-phosphate

$${d[Gl3P] \over dt} = {{V_{max}^{Rul15P2 \rightarrow Gl3P} \cdot [Rul1,5P2][CO_2]} \over {K_m^{Rul15P2 \rightarrow Gl3P} + [Rul1,5P2][CO_2]}} - {{V_{max}^{Gl3P \rightarrow Gl13P2} \cdot [Gl3P]} \over {K_m^{Gl3P \rightarrow Gl13P2} + [Gl3P]}} - k_{deg}^{Gl3P}[Gl3P] .$$

Glycerate 1,3-Bisphosphate

$${d[Gl1,3P2] \over dt} = {{V_{max}^{Gl3P \rightarrow Gl13P2} \cdot [Gl3P]} \over {K_m^{Gl3P \rightarrow Gl13P2} + [Gl3P]}} - {{V_{max}^{Gl13P2 \rightarrow GlAl3P} \cdot [Gl1,3P2]} \over {K_m^{Gl13P2 \rightarrow GlAl3P} + [Gl1,3P2]}} - k_{deg}^{Gl13P2}[Gl1,3P2] .$$

Glyceraldehyde 3-Phosphate

$${d[GlAl3P] \over dt} = {{V_{max}^{Gl13P2 \rightarrow GlAl3P} \cdot [Gl1,3P2]} \over {K_m^{Gl13P2 \rightarrow GlAl3P} + [Gl1,3P2]}} - {{V_{max}^{GlAl3P \rightarrow F16P2} \cdot [GlAl3P]} \over {K_m^{GlAl3P \rightarrow F16P2} + [GlAl3P]}} - k_{deg}^{GlAl3P}[GlAl3P] .$$

Fructose 1,6-Bisphosphatase

$${d[F1,6P2] \over dt} = {{V_{max}^{GlAl3P \rightarrow F16P2} \cdot [GlAl3P]} \over {K_m^{GlAl3P \rightarrow F16P2} + [GlAl3P]}} - {{V_{max}^{F16P2 \rightarrow F6P} \cdot [F1,6P2]} \over {K_m^{F16P2 \rightarrow F6P} + [F1,6P2]}} - k_{deg}^{F16P2}[F1,6P2] .$$

Fructose 6-Phosphate

$${d[F6P] \over dt} = {{V_{max}^{F16P2 \rightarrow F6P} \cdot [F1,6P2]]} \over {K_m^{F16P2 \rightarrow F6P} + [F1,6P2]}} - {{V_{max}^{F6P \rightarrow E4P} \cdot [F6P]} \over {K_m^{F6P \rightarrow E4P} + [F6P]}} - k_{deg}^{F6P}[F6P] .$$

RNA(FBP/SBP)

$${d[RNA(FBP/SBP)] \over dt} = k_{transc}^{FBP/SBP}[ADN] - k_{deg}^{RNA(FBP/SBP)}[RNA(FBP/SBP)].$$

FBP/SBP

$${d[FBP/SBP] \over dt} = k_{trad}^{FBP/SBP}[RNA(FBP/SBP)] - k_{deg}^{FBP/SBP}[FBP/SBP].$$

Glucose 6-Phospate

$${d[G6P] \over dt} = {{V_{max}^{F6P \rightarrow G6P} \cdot [F6P]} \over {K_m^{F6P \rightarrow G6P} + [F6P}} - {{V_{max}^{G6P \rightarrow G1P} \cdot [G6P]} \over {K_m^{G6P \rightarrow G1P} + [G6P]}} - k_{deg}^{G6P}[G6P] .$$

Glucose 1-Phospate

$${d[G1P] \over dt} = {{V_{max}^{G6P \rightarrow G1P} \cdot [G6P]} \over {K_m^{G6P \rightarrow G1P} + [G6P]}} - {{V_{max}^{G1P \rightarrow ADPG} \cdot [G1P]} \over {K_m^{G1P \rightarrow ADPG} + [G1P]}} - {{V_{max}^{G1P \rightarrow UDPG} \cdot [G1P]} \over {K_m^{G1P \rightarrow UDPG} + [G1P]}} - k_{deg}^{G1P}[G1P] .$$

ADP-Glucose

$${d[ADPG] \over dt} = {{V_{max}^{G1P \rightarrow ADPG} \cdot [G1P]} \over {K_m^{G1P \rightarrow ADPG} + [G1P]}} - {{V_{max}^{ADPG \rightarrow Aml} \cdot [ADPG]} \over {K_m^{ADPG \rightarrow Aml} + [ADPG]}} - k_{deg}^{ADPG}[ADPG] .$$

UDP-Glucose

$${d[UDPG] \over dt} = {{V_{max}^{G1P \rightarrow UDPG} \cdot [G1P]} \over {K_m^{G1P \rightarrow UDPG} + [G1P]}} - {{V_{max}^{UDPG \rightarrow Aml} \cdot [UDPG]} \over {K_m^{UDPG \rightarrow Aml} + [UDPG]}} - k_{deg}^{UDPG}[UDPG] .$$

Amylose

$${d[Aml] \over dt} = {{V_{max} \cdot [ADPG]} \over {K_m + [ADPG]}} + {{V_{max} \cdot [UDPG]} \over {K_m + [UDPG]}} - {{V_{max} \cdot [Aml]} \over {K_m + [Aml}} - K_{deg}[Aml] .$$

Starch

$${d[Starch] \over dt} = {{V_{max}^{Aml \rightarrow Starch} \cdot [Aml]} \over {K_m^{Aml \rightarrow Starch} + [Aml]}} - k_{deg}^{Starch}[Starch] .$$

Parameter search

The kinetic characterization of the reactions must be done through the search of parameters in scientific publications and other databases.

Due to the existence of various information regarding the same constant, an approximation to a single value can be done by assigning them a weight considering the similarity of the corresponding organism and environmental conditions. If you would like to see the criterias, click below.

asd

If you would like to see the used parameters, click below.

Table X: Parameters

Symbol	Description	Value	Reference
$$K_m^{F6P \rightarrow E4P}$$	Michaelis-Menten constant for conversion of Fructose 6-Phosphate to Erythrose 4-Phosphate.	v1	r1
$$V_{max}^{F6P \rightarrow E4P}$$	Maximun rate for conversion of Fructose 6-Phosphate to Erythrose 4-Phosphate.	v2	r2
$$K_m^{E4P \rightarrow Sed17P2}$$	Michaelis-Menten constant for conversion of Erythrose 4-Phosphate to Sedoheptulose 1,7-Biphosphatase.	v3	r3
$$V_{max}^{E4P \rightarrow Sed17P2}$$	Maximun rate for conversion of Erythrose 4-Phosphate to Sedoheptulose 1,7-Biphosphatase.	v4	r4
$$k_{deg}^{E4P}$$	Degradation rate of Erythrose 4-Phosphate.	v5	r5
$$k_{deg}^{Sed17P2}$$	Degradation rate of Sedoheptulose 1,7-Biphosphatase.	v6	r6
$$K_m^{Sed7P \rightarrow R5P}$$	Michaelis-Menten constant for conversion of Sedoheptulose 7-Phosphate to Ribose 5-Phosphate.	v6	r6
$$V_{max}^{Sed7P \rightarrow R5P}$$	Maximun rate for conversion of Sedoheptulose 7-Phosphate to Ribose 5-Phosphate.	v4	r4
$$k_{deg}^{Sed7P}$$	Degradation rate of Sedoheptulose 7-Phosphate.	v6	r6
$$K_m^{R5P \rightarrow Rul5P}$$	Michaelis-Menten constant for conversion of Ribose 5-Phosphate to Ribulose 5-Phosphate.	v6	r6
$$V_{max}^{R5P \rightarrow Rul5P}$$	Maximun rate for conversion of Ribose 5-Phosphate to Ribulose 5-Phosphate.	v6	r6
$$k_{deg}^{R5P}$$	Degradation rate of Ribose 5-Phosphate.	v6	r6
$$K_m^{Rul5P \rightarrow Rul15P2}$$	Michaelis-Menten constant for conversion of Ribulose 5-Phosphate to Ribulose 1,5-Bisphosphate.	v6	r6
$$V_{max}^{Rul5P \rightarrow Rul15P2}$$	Maximun rate for conversion of Ribulose 5-Phosphate to Ribulose 1,5-Bisphosphate.	v6	r6
$$k_{deg}^{Rul15P2}$$	Degradation rate of Ribulose 1,5-Bisphosphate.	v6	r6
$$K_m^{Rul15P2 \rightarrow Gl3P}$$	Michaelis-Menten constant for conversion of Ribulose 1,5-Bisphosphate to Glycerate 3-Phosphate.	v6	r6
$$V_{max}^{Rul15P2 \rightarrow Gl3P}$$	Maximun rate for conversion of Ribulose 1,5-Bisphosphate to Glycerate 3-Phosphate.	v6	r6
$$k_{deg}^{Rul15P2}$$	Degradation rate of Ribulose 1,5-Bisphosphate.	v6	r6
$$K_m^{Gl3P \rightarrow Gl13P2}$$	Michaelis-Menten constant for conversion of Glycerate 3-Phosphate to Glycerate 1,3-Biphosphate.	v6	r6
$$V_{max}^{Gl3P \rightarrow Gl313P2}$$	Maximun rate for conversion of Glycerate 3-Phosphate to Glycerate 1,3-Biphosphate.	v6	r6
$$k_{deg}^{Gl3P}$$	Degradation rate of Glycerate 3-Phosphate.	v6	r6
$$K_m^{Gl13P2 \rightarrow GlAl3P}$$	Michaelis-Menten constant for conversion of Glycerate 1,3-Biphosphate to Glyceraldehyde 3-Phosphate	v6	r6
$$V_{max}^{Gl13P2 \rightarrow GlAl3P}$$	Maximun rate for conversion of	v6	r6
$$k_{deg}^{Gl13P2}$$	Degradation rate of	v6	r6
$$K_m^{GlAl3P \rightarrow F16P2}$$	Michaelis-Menten constant for conversion of	v6	r6
$$V_{max}^{GlAl3P \rightarrow F16P2}$$	Maximun rate for conversion of	v6	r6
$$k_{deg}^{GlAl3P}$$	Degradation rate of	v6	r6
$$k_{deg}^{F16P2}$$	Degradation rate of	v6	r6
$$K_m^{F6P \rightarrow G6P}$$	Michaelis-Menten constant for conversion of	v6	r6
$$V_{max}^{F6P \rightarrow G6P}$$	Maximun rate for conversion of	v6	r6
$$k_{deg}^{F6P}$$	Degradation rate of	v6	r6
$$K_m^{G6P \rightarrow F6P}$$	Michaelis-Menten constant for conversion of	v6	r6
$$V_{max}^{G6P \rightarrow F6P}$$	Maximun rate for conversion of	v6	r6
$$k_{Transc}^{FBP/SBP}$$	d6	v6	r6
$$k_{deg}^{RNA_{FBP/SBP}}$$	Degradation rate of	v6	r6
$$k_{Trad}^{FBP/SBP}$$	d6	v6	r6
$$k_{deg}^{FBP/SBP}$$	Degradation rate of	v6	r6
$$K_m^{F6P \rightarrow G6P2}$$	Michaelis-Menten constant for conversion of	v6	r6
$$V_{max}^{F6P \rightarrow G6P2}$$	Maximun rate for conversion of	v6	r6
$$K_m^{G6P \rightarrow G1P}$$	Michaelis-Menten constant for conversion of	v6	r6
$$V_{max}^{G6P \rightarrow G1P}$$	Maximun rate for conversion of	v6	r6
$$k_{deg}^{G6P}$$	Degradation rate of	v6	r6
$$K_m^{G6P \rightarrow UDPG}$$	Michaelis-Menten constant for conversion of	v6	r6
$$V_{max}^{G6P \rightarrow UDPG}$$	Maximun rate for conversion of	v6	r6
$$k_{deg}^{G1P}$$	Degradation rate of	v6	r6
$$K_m^{ADPG \rightarrow Aml}$$	Michaelis-Menten constant for conversion of	v6	r6
$$V_{max}^{ADPG \rightarrow Aml}$$	Maximun rate for conversion of	v6	r6
$$k_{deg}^{ADPG}$$	Degradation rate of	v6	r6
$$K_m^{Aml \rightarrow Starch}$$	Michaelis-Menten constant for conversion of	v6	r6
$$V_{max}^{Aml \rightarrow Starch}$$	Maximun rate for conversion of	v6	r6
$$k_{deg}^{ADPG}$$	Degradation rate of	v6	r6
$$k_{deg}^{Aml}$$	Degradation rate of	v6	r6
$$k_{deg}^{UDPG}$$	Degradation rate of	v6	r6
$$k_{deg}^{Starch}$$	Degradation rate of	v6	r6
$$k_{Transc}^{\Delta STA1}$$	d6	v6	r6
$$K_{met}$$	d6	v6	r6
$$k_{link}^{STA1}$$	d6	v6	r6
$$k_{deg}^{RNA_{\Delta STA1}}$$	Degradation rate of	v6	r6
$$k_{deg}^{dsSTA1}$$	Degradation rate of	v6	r6
$$k_{Transl}^{STA1}$$	d6	v6	r6
$$k_{deg}^{STA1}$$	Degradation rate of	v6	r6
$$k_{Transc}^{\Delta STA6}$$	d6	v6	r6
$$k_{link}^{STA6}$$	d6	v6	r6
$$k_{deg}^{RNA_{\Delta STA6}}$$	Degradation rate of	v6	r6
$$k_{deg}^{dsSTA6}$$	Degradation rate of	v6	r6
$$k_{Transl}^{STA6}$$	d6	v6	r6
$$k_{deg}^{STA6}$$	Degradation rate of	v6	r6
$$k_{Transc}^{\Delta GBS2}$$	d6	v6	r6
$$k_{link}^{GBS2}$$	d6	v6	r6
$$k_{deg}^{RNA_{\Delta GBS2}}$$	Degradation rate of	v6	r6
$$k_{deg}^{dsGBS2}$$	Degradation rate of	v6	r6
$$k_{Transl}^{GBS2}$$	d6	v6	r6
$$k_{deg}^{GBS2}$$	Degradation rate of	v6	r6
$$K_o$$	d6	v6	r6
$$K_c$$	d6	v6	r6
$$k_{cat,C}$$	d6	v6	r6
$$K_{aa}$$	d6	v6	r6
$$K_m^{F16P2 \rightarrow F6P}$$	Michaelis-Menten constant for conversion of	v6	r6
$$V_{max}^{F16P2 \rightarrow F6P}$$	Michaelis-Menten constant for conversion of	v6	r6
$$K_m^{F16P2 \rightarrow F6P}$$	Michaelis-Menten constant for conversion of	v6	r6
$$V_{max}^{F16P2 \rightarrow F6P}$$	Michaelis-Menten constant for conversion of	v6	r6
$$K_m^{Sed17P2 \rightarrow Sed7P}$$	Michaelis-Menten constant for conversion of	v6	r6
$$V_{max}^{Sed17P2 \rightarrow Sed7P}$$	Michaelis-Menten constant for conversion of	v6	r6
$$K_{STA}$$	d6	v6	r6
$$K_{GBS2}$$	d6	v6	r6

Matlab simulation

Afterwards, all the collected data will be entered into Matlab and a contrast between the wild-type metabolism and the modified version will be studied.

If you would like to see the Matlab code, click the link below.

MATLAB code

Model fitting

Once the interesting questions are answered (selection between B12-sensitive promoter and light-sensitive promoter, quantity of B12 necessary to keep a sustainable amount of starch while glucose availability is increased, light level required to maximize carbon fixation), measurements of various physical and chemical magnitudes must be made to adjust the model, and establish a probability of a parameter to belong in a certain range. The fitting will be made by the least- square method.

After the model