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Membrane Design Group

Membrane as a key element in our devise

A technical highlight of our product is to realize an integral controller for regulating a concentration of a specific DNA strand as an output signal to be a desired level by using a series of DNA strand displacement reactions in combination with a membrane. Therefore we attempted to design of osmosis membrane that DNA strand can move. (Fig.1)
Fig.1 indicates that flow of a single DNA strand and multi-stranded DNA through a membrane. As shown in Fig.1, a specific single-stranded DNA can permeate membrane since the size of single-stranded DNA is enough to move the pore of membrane. However, the multi-stranded DNA can’t permeate membrane since it is much longer than single-stranded DNA. Because of the membrane, we can regulate a concentration of DNA strand.

How to design the membrane

Size of DNA strand
First, we have to inquire into a size of DNA strand that is a solute through the membrane. We suppose that a DNA strand that is used in a series of reactions for realizing the integral controller has 10-40 bases. Here, for the sake of simplicity a DNA strand is approximated by spherical object with a radius of 3 nm as illustrated in Fig.2.
Fig2. Size of DNA we use in this present
Property of membrane
We need some formula to determine the structure of the membrane. Transmission phenomenon of osmosis membrane is described following equations.
where R is a rejection rate of solute, Cb, Cp and Cm are concentrations[M] of solution, permeated liquid, solute in near membrane, respectively. When solute permeates membrane with impurities, Cm increases with pressure. In this present, since we use solution without impurity, we can assume that Cm almost equals to Cb.
where Jv is the flux of solvent [mol/(s•m^3)], Lp is the permeated coefficient, ∆p is the pressure difference of both of membrane [kPa], σ is the reflection coefficient of solute. Where Js is the flux of solute [m^3/(s•m^2)], P is the permeated coefficient.C ̅ is the differences between Cb and Cm. The key elements of the above transmission equation relate to such three transmission coefficients as Lp, σ, and P. We used general model called “pore model” to combine these transmission coefficient. In this model, we assume that DNA strand is hard sphere, pore is cylinder and flow in pore is “Poiseuille flow”.
Fig3. Pore model
The radius of solution is given below expression.
where rs is the radius of solute [nm], rp is the radius of pore [nm], ∆x is the membrane thickness [nm], D is the diffusion coefficient of solute, K is the Boltzmann's constant, T is the absolute temperature [℃], μ is the viscosity of solute. Three transport coefficients are given by following equation.
where q is the ratio of rs to rp, Ak is the value that the unit area of the total area of pores divides the unit area of area of membrane, S_F and S_D are steric hindrance. These are given by following equation.

Determination of the structure

As we mentioned above, we can use formulas as a design theory of membrane. In this present, we designed membrane to satisfy the concentration of a specific DNA strand as an output signal to be a desired level. Therefore, we need to adjust parameters of membrane such as rp, ∆x , and Ak. We define x2 and x4 as concentration of input single, output single, respectively. We assume that Jv is zero in our design. Table 1 shows the each parameter used in our design of membrane.
Figure 4 shows the simulation results by using parameters of Table 1.
Table 1 Parameter and Hypothetical condition
We omit the calculation process, however, we calculated following parameters. rp is 4.97×10^(-9)[m], Js is 4.79×10^(-14)[m^3/(s•m^2)] As Figure 4 shows, we estimated that x4 becomes steady state at approximately 200 second. Therefore, we simulated size of membrane at 200 second.(Fig.5)
Table 1 Parameter and Hypothetical condition
As a result, there are several combinations of rp,∆x and Ak. In other words, we can design membrane of different size.

Future Perspectives

We mentioned design theory of membrane and calculated some pattern of membrane. However, we still have problems to make membrane actually. The problem which we must consider next is below.
・What is the material to make membrane easily and efficiently?
・What is the best size of membrane that DNA strand permeates ?
・How do we make hole in membrane? We are planning to study about membrane engineering and design membrane by experiment to solve the problems.


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