Model

Introduction

  Our team try to apply a new method of modeling, by analyzing the biology reaction in electronic way.

  Our team notice that many bio-reaction share the same non-linear characteristic just like the semi-conductor component. In the beginning of the beginning, we will introduce some characteristic of the MOSFET.

  U_DS represent the voltage between the Source and Drain port, U_GS represent the voltage between Gate and Source port. I_DS represent the current that go through the Drain and Source. For an Ideal MOSFET the resistance between Gate and Source is infinite, which means the current that go through Gate and Source is always zero. We can notice that when the U_GS is settled, the current that go through Drain and Source steep up rapidly as the U_DS rise. However, as the U_DS keep rising, the saturation will occur. U_GS can determine the saturation current.

  We notice that the curve of MOSFET is very similar to the curve of enzyme activity, when you substitute the U_GS by the concentration of enzyme, and U_DS by the concentration of substrate. Further more, U_GS can be replaced by gene’s active since the enzyme’s concentration is determined by gene active, at least in an ideal model.

  Our team try to use MOSFET to represent genes (PHA degradation genes), by substituting the electric parameter in to biology parameter.

  The model we construct is shown below:

  Capacitor is used to symbolize the accumulation of the PHA degradation product because of it’s unique characteristic: U∝I*T

   The voltage of the capacitor is determined by the product of current and time, which share the same characteristic of the product (SA) accumulation.

   Concentration ∝ V*T

  The value of the capacitor should be carefully settled,Uc ∝1/C

  According to the circuit, U_DS is affected by the voltage of Capacitor, the Geater the capacitor, the slicer U_DS is affected. Set a smaller C is the reaction velocity is affected by the concentration greatly.

   U_DS=VCC-Uc

  The constant g should be considered together with capacitor. The gene active (or you can say the U_GS) is determined by the g and C. Set a greater g/C if gene is very sensitive.

   U_GS ∝ g/C

  Also we add a resistor in parallel with Capacitor to represent the degradation of the product. In electric analysis, a resistor paralleled with a capacitor will form a discharge circuit, the electrons stored in capacitor will be released by the resistor. The resistor’s value should be designed base on the velocity of the product degradation. Theoretically the R can be determined using the following function:

   ln2*R*C=T

  Where T should be the half life of the product(SA).

  For a better simulation, a RLC filter should be set between each step in order to represent the time delay. However, we don’t do so in order to simplify the model.

  Due to time constraints, we were unable to complete the modeling. However, through regression we can conclude that the degradation of phenanthrene generally follows an exponential function. It can be inferred that the primary factor influencing the degradation rate of phenanthrene is its own concentration, with almost no effect from the concentration of products. Therefore, a very small parameter can be assigned to the capacitance in the model, and the on-resistance of the MOSFET can be set as a constant value.