Team:UChile OpenBio-CeBiB/Model/Procedure

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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

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

  • Amylose

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

  • Amylose

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

  • Amylose

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

  • ARN \Delta STA1

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



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.

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

Table X: Parameters

s
Symbol Description Value Reference
$$K_m^{F6P \rightarrow E4P}$$ Michaelis-Menten constant for conversion of Fructose 6-Phosphate to Erythrose 4-Phosphate. 3.05 r1
$$V_{max}^{F6P \rightarrow E4P}$$ Maximun rate for conversion of Fructose 6-Phosphate to Erythrose 4-Phosphate. 165.24 r2
$$K_m^{E4P \rightarrow Sed17P2}$$ Michaelis-Menten constant for conversion of Erythrose 4-Phosphate to Sedoheptulose 1,7-Biphosphatase. 0.33 r3
$$V_{max}^{E4P \rightarrow Sed17P2}$$ Maximun rate for conversion of Erythrose 4-Phosphate to Sedoheptulose 1,7-Biphosphatase. 26.27 r4
$$k_{deg}^{E4P}$$ Degradation rate of Erythrose 4-Phosphate. 5.5e-6 r5
$$k_{deg}^{Sed17P2}$$ Degradation rate of Sedoheptulose 1,7-Biphosphatase. 5.5e-6 r6
$$K_m^{Sed7P \rightarrow R5P}$$ Michaelis-Menten constant for conversion of Sedoheptulose 7-Phosphate to Ribose 5-Phosphate. 4 r6
$$V_{max}^{Sed7P \rightarrow R5P}$$ Maximun rate for conversion of Sedoheptulose 7-Phosphate to Ribose 5-Phosphate. 10 r4
$$k_{deg}^{Sed7P}$$ Degradation rate of Sedoheptulose 7-Phosphate. 5.5e-6 r6
$$K_m^{R5P \rightarrow Rul5P}$$ Michaelis-Menten constant for conversion of Ribose 5-Phosphate to Ribulose 5-Phosphate. 0.72 r6
$$V_{max}^{R5P \rightarrow Rul5P}$$ Maximun rate for conversion of Ribose 5-Phosphate to Ribulose 5-Phosphate. 2.76e3 r6
$$k_{deg}^{R5P}$$ Degradation rate of Ribose 5-Phosphate. 5.5e-6 r6
$$K_m^{Rul5P \rightarrow Rul15P2}$$ Michaelis-Menten constant for conversion of Ribulose 5-Phosphate to Ribulose 1,5-Bisphosphate. 0.06 r6
$$V_{max}^{Rul5P \rightarrow Rul15P2}$$ Maximun rate for conversion of Ribulose 5-Phosphate to Ribulose 1,5-Bisphosphate. 5.35 r6
$$k_{deg}^{Rul15P2}$$ Degradation rate of Ribulose 1,5-Bisphosphate. 5.5e-6 r6
$$K_m^{Rul15P2 \rightarrow Gl3P}$$ Michaelis-Menten constant for conversion of Ribulose 1,5-Bisphosphate to Glycerate 3-Phosphate. 0.03 r6
$$V_{max}^{Rul15P2 \rightarrow Gl3P}$$ Maximun rate for conversion of Ribulose 1,5-Bisphosphate to Glycerate 3-Phosphate. 9.01 r6
$$k_{deg}^{Rul15P2}$$ Degradation rate of Ribulose 1,5-Bisphosphate. 5.5e-6 r6
$$K_m^{Gl3P \rightarrow Gl13P2}$$ Michaelis-Menten constant for conversion of Glycerate 3-Phosphate to Glycerate 1,3-Biphosphate. 0.40 r6
$$V_{max}^{Gl3P \rightarrow Gl313P2}$$ Maximun rate for conversion of Glycerate 3-Phosphate to Glycerate 1,3-Biphosphate. 113.77 r6
$$k_{deg}^{Gl3P}$$ Degradation rate of Glycerate 3-Phosphate. 5.5e-6 r6
$$K_m^{Gl13P2 \rightarrow GlAl3P}$$ Michaelis-Menten constant for conversion of Glycerate 1,3-Biphosphate to Glyceraldehyde 3-Phosphate 0.40 r6
$$V_{max}^{Gl13P2 \rightarrow GlAl3P}$$ Maximun rate for conversion of Glycerate 1,3-Biphosphate to Glyceraldehyde 3-Phosphate. 113.77 r6
$$k_{deg}^{Gl13P2}$$ Degradation rate of Glycerate 1,3-Biphosphate. 5.5e-6 r6
$$K_m^{GlAl3P \rightarrow F16P2}$$ Michaelis-Menten constant for conversion of Glyceraldehyde 3-Phosphate to Fructose 1,6-Biphosphate. 9.50 r6
$$V_{max}^{GlAl3P \rightarrow F16P2}$$ Maximun rate for conversion of Glyceraldehyde 3-Phosphate to Fructose 1,6-Biphosphate. 27.93 r6
$$k_{deg}^{GlAl3P}$$ Degradation rate of Glyceraldehyde 3-Phosphate. 5.5e-6 r6
$$k_{deg}^{F16P2}$$ Degradation rate of Fructose 1,6-Biphosphate. 5.5e-6 r6
$$K_m^{F6P \rightarrow G6P}$$ Michaelis-Menten constant for conversion of Fructose 6-Phosphate to Glucose 6-Phosphate. 0.16 r6
$$V_{max}^{F6P \rightarrow G6P}$$ Maximun rate for conversion of Fructose 6-Phosphate to Glucose 6-Phosphate. 86.12 r6
$$k_{deg}^{F6P}$$ Degradation rate of Fructose 6-Phosphate. 5.5e-6 r6
$$K_m^{G6P \rightarrow F6P}$$ Michaelis-Menten constant for conversion of Glucose 6-Phosphate to Fructose 6-Phosphate. 1 r6
$$V_{max}^{G6P \rightarrow F6P}$$ Maximun rate for conversion of Glucose 6-Phosphate to Fructose 6-Phosphate. 1 r6
$$k_{Transc}^{FBP/SBP}$$ Transcription rate of FBP/SBP. 0.032 r6
$$k_{deg}^{RNA_{FBP/SBP}}$$ Degradation rate of RNA_{FBP/SBP} 4.17e-4 r6
$$k_{Transl}^{FBP/SBP}$$ Translation rate of FBP/SBP. 0.032 r6
$$k_{deg}^{FBP/SBP}$$ Degradation rate of FBP/SBP. 6.17e-6 r6
$$K_m^{G6P \rightarrow G1P}$$ Michaelis-Menten constant for conversion of Glucose 6-Phosphate to Glucose 1-Phosphate. 8.64 r6
$$V_{max}^{G6P \rightarrow G1P}$$ Maximun rate for conversion of Glucose 6-Phosphate to Glucose 1-Phosphate. 10 r6
$$k_{deg}^{G6P}$$ Degradation rate of Glucose 6-Phosphate. 5.5e-6 r6
$$K_m^{G1P \rightarrow UDPG}$$ Michaelis-Menten constant for conversion of Glucose 6-Phosphate to UDP-Glucose. 0.21 r6
$$V_{max}^{G6P \rightarrow UDPG}$$ Maximun rate for conversion of Glucose 6-Phosphate to UDP-Glucose. 14.81 r6
$$k_{deg}^{G1P}$$ Degradation rate of Glucose 1-Phosphate. 5.5e-6 r6
$$K_m^{ADPG \rightarrow Aml}$$ Michaelis-Menten constant for conversion of ADP-Glucose to Amylose. 1,36 r6
$$V_{max}^{ADPG \rightarrow Aml}$$ Maximun rate for conversion of ADP-Glucose to Amylose. 53.29 r6
$$k_{deg}^{ADPG}$$ Degradation rate of ADP-Glucose. 5.5e-6 r6
$$K_m^{Aml \rightarrow Starch}$$ Michaelis-Menten constant for conversion of Amylose to Starch. 1.96 r6
$$V_{max}^{Aml \rightarrow Starch}$$ Maximun rate for conversion of Amylose to Starch. 99.01 r6
$$k_{deg}^{ADPG}$$ Degradation rate of ADP-Glucose. 5.5e-6 r6
$$k_{deg}^{Aml}$$ Degradation rate of Amylose. 5.5e-6 r6
$$k_{deg}^{UDPG}$$ Degradation rate of UDP-Glucose. 5.5e-6 r6
$$k_{deg}^{Starch}$$ Degradation rate of Starch. 5.5e-6 r6
$$k_{Transc}^{\Delta STA1}$$ Transcription rate of anti STA1. 0.04 r6
$$K_{met}$$ metE promoter constant. 1 r6
$$k_{link}^{STA1}$$ Link rate of 1e8 r6
$$k_{deg}^{RNA_{\Delta STA1}}$$ Degradation rate of RNA anti STA1. 4.17e-4 r6
$$k_{deg}^{dsSTA1}$$ Degradation rate of dsSTA1. 4.17e-4 r6
$$k_{Transl}^{STA1}$$ Translation rate of STA1. 0.04 r6
$$k_{deg}^{STA1}$$ Degradation rate of STA1. 6.17e-6 r6
$$k_{Transc}^{\Delta STA6}$$ Transcription rate of anti STA6. 0.04 r6
$$k_{link}^{STA6}$$ Link rate of complementary RNA regarding STA6. 1e20 r6
$$k_{deg}^{RNA_{\Delta STA6}}$$ Degradation rate of anti STA6 4.17e-4 r6
$$k_{deg}^{dsSTA6}$$ Degradation rate of dsSTA6. 4.17e-4 r6
$$k_{Transl}^{STA6}$$ Translation rate of STA6. 0.04 r6
$$k_{deg}^{STA6}$$ Degradation rate of STA6. 6.17e-6 r6
$$k_{Transc}^{\Delta GBS2}$$ Transcription rate of anti GBS2. 0.038 r6
$$k_{link}^{GBS2}$$ Link rate of complementary RNA regarding GBS2. 1e20 r6
$$k_{deg}^{RNA_{\Delta GBS2}}$$ Degradation rate of RNA anti GBS2. 4.17e-4 r6
$$k_{deg}^{dsGBS2}$$ Degradation rate of dsGBS2. 4.17e-4 r6
$$k_{Transl}^{GBS2}$$ Translation rate of GBS2. 0.04 r6
$$k_{deg}^{GBS2}$$ Degradation rate of GBS2. 4.17e-4 r6
$$K_o$$ ------------ 0.48 r6
$$K_c$$ ------------- 0.014 r6
$$k_{cat,C}$$ ------------------- 1.5r6
$$K_{aa}$$ --------------------- 0.025 r6
$$K_m^{F16P2 \rightarrow F6P}$$ Michaelis-Menten constant for conversion of Fructose 1,6-Biphosphatase to Fructose 6-Phosphate. 0.16 r6
$$V_{max}^{F16P2 \rightarrow F6P}$$ Michaelis-Menten constant for conversion of Fructose 1,6-Biphosphatase to Fructose 6-Phosphate. 0.16 r6
$$K_m^{F16P2 \rightarrow F6P}$$ Michaelis-Menten constant for conversion of Fructose 1,6-Biphosphatase to Fructose 6-Phosphate. 0.16 r6
$$V_{max}^{F16P2 \rightarrow F6P}$$ Maximun rate for conversion of Fructose 1,6-Biphosphatase to Fructose 6-Phosphate. 7.35 r6
$$K_m^{Sed17P2 \rightarrow Sed7P}$$ Michaelis-Menten constant for conversion of Sedoheptulose 1,7-Biphosphate to Sedoheptulose 7-Phosphate. 0.16 r6
$$V_{max}^{Sed17P2 \rightarrow Sed7P}$$ Maximun rate for conversion of Sedoheptulose 1,7-Biphosphate to Sedoheptulose 7-Phosphate. 7.35 r6
$$K_m^{STA}$$ Michaelis-Menten constant for STA1 and STA6. 0.17 r6
$$K_m^{GBS2}$$ Michaelis-Menten constant for GBS2. 15.67 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

    Maximize glucose availability by carbon fixation through adjustment of environmental conditions.