1)Abstract

We have to optimize combination of recombinant genes and amount of yeast when we apply our salt up taking system to real environment. But these are nontrivial because of cytosolic sodium ions’ inhibition of growth or alteration of intracellular Na⁺’s flux. We tried to make mathematical model that gives initial value corresponding to objective amount of salt decrease. We described yeast cell’s kinetics of salt absorbance. Then, using this model, we looked for best combination of recombinant genes. Through experiments, we calculated yeast’s behavior when the yeast has single protein in this project. We decided kinetic parameter of transporter with our model. Finally, we simulated possible pattern of recombinant yeast in our project.

1)Kinetic Model of Transporter

At first, we have to describe speeds of transportation of HKT1, AVP1, NHX1. HKT1 is Na⁺ Uniporter on yeast cell membrane. AVP1 is PPase on yeast vacuolar membrane. NHX1 is Na⁺/H⁺ Antiporter on yeast vacuoler membrane. We assumed these proteins in transition model. Then we dealt with parameters that can be modeled by rapid equilibirium or approximation of structural symmetry.

1)Four-state Transition Model: HKT1 and NHX1

Uniporter and antiporter (assumed substrates combine with both portal at the same time) can be described with four-state transition model. (Fig 2.1.0.1)

Here, ki ← j, k * i ← j Is the rate constant of the state transition in the i ← j direction and (1), (2), (3) and (4) indicate the enzyme concentration of each state , [So] and [Si] are the concentration of the transport substrate, respectively, and finally it can be considered that it reaches Non-equilibrium steady state, so select 3 from equation (2.1.0.1) and combine conservation law concerning enzyme concentration As a solution to the quaternary linear equation, the Non-equilibrium steady state solution (d [X] / dt = 0 for arbitrary state X) of each enzyme concentration can be completely solved, but as it is, the number of parameters is very large, In the non-equilibrium steady state, the rate-determining step of the state transition is the structural transition of the transporter, and for binding to the substrate, Assume that the equilibrium state holds (Rapid Equilibirium) In other words, we introduce constants Ko d, Ki d for Figure 2.1.0.1 .
Subsequently, assuming that the influence by the membrane potential is neglected, the structural symmetry that sandwiches the cell membrane of the enzyme, that is, the following equation can be assumed.
According to the above assumption, the transport amount can be described by two parameters k, K for one type of transporter: Formula (2.1.0.2) and conservation formula of enzyme amount [1] + [2] + [3] + [4 ] = E 0, Non-equilibrium steady state solution is obtained by simultaneous equations of four equations of the sum of two equations of the expression (2.1.0.1) in the Non-equilibrium steady state, and from right two enzymes right-handed flux of state transition By obtaining Jss 4, the following equation is obtained.
2.2 Three state transition model AVP 1
AVP1 is a transporter that binds to pyrophosphate on the cytoplasmic side, hydrolyzes it with structural transformation, releases hydrogen ions to the vacuolar side, and releases phosphate to the cytoplasmic side. [?] It can be described by the three-state transition model shown in the figure, which can be solved in the same way as the above-described four-state transition model to obtain the next flux Jss3. Here, subscripts of various ion concentrations represent intracellular cytosol and vacuole.
3 salt-absorbing yeast cell model
In addition to HKT1, NHX1, and AVP1 introduced by transformation, the endogenous NHX1-like, AVP 1 -like transporter system and the endogenous cell membrane Na transport system responsible for intracytoplasmic Na + salt concentration were incorporated in this model, In the assay results, the introduction of AVP1 alone influenced the salt absorption performance, so the energy conjugated transport system through H + on the endoplasmic vacuolar membrane was considered to be important and the transportability , But because the yeast cells with added salt tolerance accumulated more salt in the cytoplasm, the importance of the endogenous cell membrane Na transport system in cytoplasmic Na + salt concentration response was suggested. For the former, we used the above-mentioned transporter model, treating the transport mechanism as a Michaelis-Menten system which undergoes competitive inhibition by cytoplasmic Na +, the differential equations of E0If as a threshold response function Parameterized by rewriting using approximately Hill function Kr, it was formulated by the following equation by n.
Here, D is the decomposition rate of the transport system per unit time, after all, the model used this time is a simultaneous differential equation having the same form as the following basic equation.
Here, V c and V vac are the average volume and mean vacuolar volume of yeast cells, Vr is the volume of the system, and f is a function to describe the appropriate cell growth, in which [H + ], [PPi], and [Pi] were supposed to have no time variation as the intrinsic compensation mechanism was assumed.
4 Determination of model parameters
From the assay results of the present study, k was determined for Jss4HKT, Jss4NHX, E0 for Jss3AV P, and other parameters were obtained and estimated as shown in Table 1 as parameters to be used for later hobbies.