Team:HIT-Harbin/Application

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<h5 class="hashed"><span>Overview for our application</span></h5>
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<h5 class="hashed"><span>1 lactobacillus: from lactose to lactic acid</span></h5>
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<p>In applications, we plan to enhance Bio-electric Interface, the device designed by 2012 Edinburg iGEM team. If the input is biochemical signal molecules and the output become electrons, B-POM can be coupled with Bio-electric Interface, that ephemeral processes in cells will be precisely measurable by simple electronic methods and analyzable by computer. B-POM is also helpful in yoghurt producing, where the control of pH is inaccurate. When B-POM is transplanted into yoghurt-producing bacteria, let hydrogen ions be the input and lacR be the output, and select the proper B-POM parameters, then the pH will be steady around 5.5. In short, our inspired and reliable device is promising in various fields.</p>
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  1 lactobacillus: from lactose to lactic acid
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<p>Reaction 1: endocytosis transportation of lactose
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Reaction 1: endocytosis transportation of lactose
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<p>Table 1 the definition variables
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Table 1 the definition variables
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<p>The unit of concentration is mmol/L.
-
Name Definition
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<p>LS+Lout <=> temp1 : R1（lactose combines with transporting enzyme）
-
LS Concentration of transporting enzyme
+
<p>vf = k1*Lout*LS（the reaction rate is proportional to reactants’ concentrations）
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Lout Concentration of lactose outside cells
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<p>vr =k_1*temp1（the reverse reaction rate is proportional to product’s concentration）
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L Concentration of lactose in cells
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<p>temp1 => L+LS : R2（lactose is transported into the cell）
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temp Concentration of lactose combined with transporting enzyme
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<p>vf = k2*temp1（the reaction rate is proportional to reactants’ concentrations）
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vf Reaction rate
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vr Reverse reaction rate
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k1 Rate constant of combination of lactose and transporting enzyme
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k_1 Decomposition rate constant
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k2 Transport rate constant of lactose
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The unit of concentration is mmol/L.
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LS+Lout <=> temp1 : R1（lactose combines with transporting enzyme）
+
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vf = k1*Lout*LS（the reaction rate is proportional to reactants’ concentrations）
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vr =k_1*temp1（the reverse reaction rate is proportional to product’s concentration）
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temp1 => L+LS : R2（lactose is transported into the cell）
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vf = k2*temp1（the reaction rate is proportional to reactants’ concentrations）
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Lout is known as 136mmol/L. We estimate that the time for the overall transportation of lactose into cells is 400s and assume that k1=0.1，k_1=0.05，k2=0.1，LS=5，temp1=0，L=0。Then the simulation result is as below:
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<p>Lout is known as 136mmol/L. We estimate that the time for the overall transportation of lactose into cells is 400s and assume that k1=0.1，k_1=0.05，k2=0.1，LS=5，temp1=0，L=0。Then the simulation result is as below:
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<img src="https://static.igem.org/mediawiki/2013/1/1d/0001.png" alt=""/>
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Fig 1. Simulation of lactose transportation
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<p>Fig 1. Simulation of lactose transportation
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We can get from the simulation that the transportation is completed when time is 300s.
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<p>We can get from the simulation that the transportation is completed when time is 300s.
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Reaction 2: from lactose to lactic acid
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<p>Reaction 2: from lactose to lactic acid
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Table 2 the definition variables
 
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Name Definition Value
 
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LZ Concentration of galactosidase 5
 
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L Concentration of lactose in cells 136
 
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Glu Concentration of glucose 0
 
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gala Concentration of galactose 0
 
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PA Concentration of pyruvic acid 0
 
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LA Concentration of lactic acid 0
 
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k3 Rate constant of combination of lactose and galactosidase 0.1
 
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k_3 Decomposition rate constant of lactose-galactosidase complex 0.05
 
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k4 Decomposition rate constant of lactose 0.1
 
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k5 Rate constant from glucose to pyruvic acid 0.1
 
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rm1 Maximum rate of pyruvic acid producing 35
 
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Km1 Michaelis constant 100
 
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L+LZ <=> temp2 : R3（lactose combines with galactosidase）
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<p>L+LZ <=> temp2 : R3（lactose combines with galactosidase）
-
vf = k3*L*LZ（the reaction rate is proportional to reactants’ concentrations）
+
<p>vf = k3*L*LZ（the reaction rate is proportional to reactants’ concentrations）
-
vr = k_3*temp2（the reverse reaction rate is proportional to product’s concentration）
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<p>vr = k_3*temp2（the reverse reaction rate is proportional to product’s concentration）
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temp2 => Glu+LZ+gala : R4（lactose decomposes into glucose and galactose）
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<p>temp2 => Glu+LZ+gala : R4（lactose decomposes into glucose and galactose）
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vf = k4*temp2（the reaction rate is proportional to reactants’ concentrations）
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<p>vf = k4*temp2（the reaction rate is proportional to reactants’ concentrations）
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Glu => 2*PA : R5（glucose decomposes into pyruvic acid, multi-step reaction）
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<p>Glu => 2*PA : R5（glucose decomposes into pyruvic acid, multi-step reaction）
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vf = k5*Glu（decomposition rate is proportional to glucose concentration）
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<p>vf = k5*Glu（decomposition rate is proportional to glucose concentration）
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PA => LA : R6（from pyruvic acid to lactic acid）
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<p>PA => LA : R6（from pyruvic acid to lactic acid）
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vf = rm1*PA/(Km1+PA)（Michealis equation, the reactant is adequate）
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<p>vf = rm1*PA/(Km1+PA)（Michealis equation, the reactant is adequate）
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the simulation result is as below:
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<p>the simulation result is as below:
　
　
   
   
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Fig 2. Simulation of lactic acid produciton
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<p>Fig 2. Simulation of lactic acid produciton
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We can get from the simulation that all lactose becomes lactic acid. The final concentration of lactic acid is 272 mmol/L.  
+
<p>We can get from the simulation that all lactose becomes lactic acid. The final concentration of lactic acid is 272 mmol/L.  
-
Then we consider reaction1 and reaction2 together, the simulation result is as below:
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<p>Then we consider reaction1 and reaction2 together, the simulation result is as below:
   
   
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Fig 3. Considering reacton1 and 2 together
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<p>Fig 3. Considering reacton1 and 2 together
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We can see that once lactose enters cells, it is consumed, and the transportation of lactose is faster than the production of lactic acid, which ensure that the production of lactic acid is continuing.
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<p>We can see that once lactose enters cells, it is consumed, and the transportation of lactose is faster than the production of lactic acid, which ensure that the production of lactic acid is continuing.
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The cells are assumed in normal condition.
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<p>The cells are assumed in normal condition.
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Now we are going to analyze the pH switching function f(p)=1-tanh(n*(p-p*)). The curve of f(x)=1-tanh(x) is as below:
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<p>Now we are going to analyze the pH switching function f(p)=1-tanh(n*(p-p*)). The curve of f(x)=1-tanh(x) is as below:
   
   
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Fig 4. Curve of f(x)=1-tanh(x)
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<p>Fig 4. Curve of f(x)=1-tanh(x)
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When x=1, f(x) is nearly 0, the switch is off. That is, when n=1, the difference between pH in cell and pH threshold should be smaller than 1 that the switch can be on.  
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<p>When x=1, f(x) is nearly 0, the switch is off. That is, when n=1, the difference between pH in cell and pH threshold should be smaller than 1 that the switch can be on.  
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The curve of f(x)=1-tanh(30*x) is as below:
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<p>The curve of f(x)=1-tanh(30*x) is as below:
   
   
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Fig 5. Curve of f(x)=1-tanh(30*x)
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<p>Fig 5. Curve of f(x)=1-tanh(30*x)
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When x=0.1, f(x) is nearly 0, the switch is off. That is, when n=30, the difference between pH in cell and pH threshold should be smaller than 0.1 that the switch can be on.  
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<p>When x=0.1, f(x) is nearly 0, the switch is off. That is, when n=30, the difference between pH in cell and pH threshold should be smaller than 0.1 that the switch can be on.  
-
Besides, we get the relationship between pH and lactic acid concentration from experiments:  
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<p>Besides, we get the relationship between pH and lactic acid concentration from experiments:  
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pH=6.32311-0.02168*[LA]+0.0000426042*[LA]^2（0<[LA]<250）
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<p>pH=6.32311-0.02168*[LA]+0.0000426042*[LA]^2（0<[LA]<250）
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its curve is as below:
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<p>its curve is as below:
   
   
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Fig 5. Relationship between pH and lactic acid concentration
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<p>Fig 5. Relationship between pH and lactic acid concentration
 +
 
 +
<p>In experiments, the maximum of pH is 6.3, the minimum is 3.6. We assume that the threshold of pH is 5.5.
 +
 
 +
<h5 class="hashed"><span>2 the expression of LacR through pH-induced promoter</span></h5>
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In experiments, the maximum of pH is 6.3, the minimum is 3.6. We assume that the threshold of pH is 5.5.
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<p>=> LA
 +
<p>vf = 0
 +
<p>=> mRNA1
 +
<p>vf = v0+v1*f(LA)-dm1*mRNA1
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2 the expression of LacR through pH-induced promoter
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<p>=> LR
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=> LA
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<p>vf = km*mRNA1-dn1*LR
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vf = 0
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=> mRNA1
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vf = v0+v1*f(LA)-dm1*mRNA1
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  => LR
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  <p>=> mRNA2
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vf = km*mRNA1-dn1*LR
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<p>vf = vm-dm2*mRNA2-c*a*LR/(1+a*LR)
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  => mRNA2
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  <p>=> LS
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vf = vm-dm2*mRNA2-c*a*LR/(1+a*LR)
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<p>vf = ks*mRNA2-ds*LS
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  => LS
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  <p>=> LZ
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vf = ks*mRNA2-ds*LS
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<p>vf = kz*mRNA2-dz*LZ
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=> LZ
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<p>Table 3 the value of variables
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vf = kz*mRNA2-dz*LZ
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Table 3 the value of variables
 
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NAME VALUE
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<p>the simulation result is as below:
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LA(0) 272
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LR(0) 10
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LS(0) 5
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LZ(0) 5
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mRNA1(0) 1
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mRNA2(0) 1
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v0 1
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v1 30
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dm1 0.5
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km 1
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dn1 0.5
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vm 1
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c 1.2
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a 1
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dm2 0.2
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ks 1
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ds 0.5
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kz 1
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dz 0.5
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the simulation result is as below:
+
   
   
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Fig 6. Simulation of pH induction
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<p>Fig 6. Simulation of pH induction
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Form the figure we can see that in 20s (far from 400s) the concentration of transporting enzyme and galactosidase is very small, which means the inhibition resulted from pH induction is transitory for production of lactic acid. In other word, the inhibition can respond to the fast change of pH.
+
<p>Form the figure we can see that in 20s (far from 400s) the concentration of transporting enzyme and galactosidase is very small, which means the inhibition resulted from pH induction is transitory for production of lactic acid. In other word, the inhibition can respond to the fast change of pH.
-
Finally, we put pH induction and lactic acid production together.
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<p>Finally, we put pH induction and lactic acid production together.
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When n=1, the simulation is as below:
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<p>When n=1, the simulation is as below:
   
   
-
Fig 7. Taking pH induction and lactic acid production together (n=1)
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<p>Fig 7. Taking pH induction and lactic acid production together (n=1)
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We can see that the concentration of lactic acid doesn’t decline but only slow down (the inhibition). Time to achieve platform phase increases to 800s.
+
<p>We can see that the concentration of lactic acid doesn’t decline but only slow down (the inhibition). Time to achieve platform phase increases to 800s.
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When n=30, the simulation is as below:
+
<p>When n=30, the simulation is as below:
   
   
-
Fig 8. Taking pH induction and lactic acid production together (n=30)
+
<p>Fig 8. Taking pH induction and lactic acid production together (n=30)
-
The time to achieve platform phase decreases to 100s.
+
<p>The time to achieve platform phase decreases to 100s.

Latest revision as of 04:14, 28 September 2013

HIT-Harbin

Application

1 lactobacillus: from lactose to lactic acid

Reaction 1: endocytosis transportation of lactose

Table 1 the definition variables

The unit of concentration is mmol/L.

LS+Lout <=> temp1 : R1（lactose combines with transporting enzyme）

vf = k1*Lout*LS（the reaction rate is proportional to reactants’ concentrations）

vr =k_1*temp1（the reverse reaction rate is proportional to product’s concentration）

temp1 => L+LS : R2（lactose is transported into the cell）

vf = k2*temp1（the reaction rate is proportional to reactants’ concentrations）

Lout is known as 136mmol/L. We estimate that the time for the overall transportation of lactose into cells is 400s and assume that k1=0.1，k_1=0.05，k2=0.1，LS=5，temp1=0，L=0。Then the simulation result is as below:

Fig 1. Simulation of lactose transportation

We can get from the simulation that the transportation is completed when time is 300s.

Reaction 2: from lactose to lactic acid

L+LZ <=> temp2 : R3（lactose combines with galactosidase）

vf = k3*L*LZ（the reaction rate is proportional to reactants’ concentrations）

vr = k_3*temp2（the reverse reaction rate is proportional to product’s concentration）

temp2 => Glu+LZ+gala : R4（lactose decomposes into glucose and galactose）

vf = k4*temp2（the reaction rate is proportional to reactants’ concentrations）

Glu => 2*PA : R5（glucose decomposes into pyruvic acid, multi-step reaction）

vf = k5*Glu（decomposition rate is proportional to glucose concentration）

PA => LA : R6（from pyruvic acid to lactic acid）

vf = rm1*PA/(Km1+PA)（Michealis equation, the reactant is adequate）

the simulation result is as below: 　

Fig 2. Simulation of lactic acid produciton

We can get from the simulation that all lactose becomes lactic acid. The final concentration of lactic acid is 272 mmol/L.

Then we consider reaction1 and reaction2 together, the simulation result is as below:

Fig 3. Considering reacton1 and 2 together

We can see that once lactose enters cells, it is consumed, and the transportation of lactose is faster than the production of lactic acid, which ensure that the production of lactic acid is continuing.

The cells are assumed in normal condition.

Now we are going to analyze the pH switching function f(p)=1-tanh(n*(p-p*)). The curve of f(x)=1-tanh(x) is as below:

Fig 4. Curve of f(x)=1-tanh(x)

When x=1, f(x) is nearly 0, the switch is off. That is, when n=1, the difference between pH in cell and pH threshold should be smaller than 1 that the switch can be on.

The curve of f(x)=1-tanh(30*x) is as below:

Fig 5. Curve of f(x)=1-tanh(30*x)

When x=0.1, f(x) is nearly 0, the switch is off. That is, when n=30, the difference between pH in cell and pH threshold should be smaller than 0.1 that the switch can be on.

Besides, we get the relationship between pH and lactic acid concentration from experiments:

pH=6.32311-0.02168*[LA]+0.0000426042*[LA]^2（0<[LA]<250）

its curve is as below:

Fig 5. Relationship between pH and lactic acid concentration

In experiments, the maximum of pH is 6.3, the minimum is 3.6. We assume that the threshold of pH is 5.5.

2 the expression of LacR through pH-induced promoter

=> LA

vf = 0

=> mRNA1

vf = v0+v1*f(LA)-dm1*mRNA1

=> LR

vf = km*mRNA1-dn1*LR

=> mRNA2

vf = vm-dm2*mRNA2-c*a*LR/(1+a*LR)

=> LS

vf = ks*mRNA2-ds*LS

=> LZ

vf = kz*mRNA2-dz*LZ

Table 3 the value of variables

the simulation result is as below:

Fig 6. Simulation of pH induction

Form the figure we can see that in 20s (far from 400s) the concentration of transporting enzyme and galactosidase is very small, which means the inhibition resulted from pH induction is transitory for production of lactic acid. In other word, the inhibition can respond to the fast change of pH.

Finally, we put pH induction and lactic acid production together.

When n=1, the simulation is as below:

Fig 7. Taking pH induction and lactic acid production together (n=1)

We can see that the concentration of lactic acid doesn’t decline but only slow down (the inhibition). Time to achieve platform phase increases to 800s.

When n=30, the simulation is as below:

Fig 8. Taking pH induction and lactic acid production together (n=30)

The time to achieve platform phase decreases to 100s.

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