# A Microbial Screening in Silico Method for the Fitness Step Evaluation in Evolutionary Algorithms
## 2 Materials and Methods
### Microbial Screening Methods in Silico: Procedures and Implementation
#### 2.1.1 Method for Obtaining the Evaluation Function in the 0/1 Knapsack Problem  
Let \(x\) be the value of a knapsack, \(x_{i}\) the value of a set of items selected for the knapsack and \(y_{i}\) the fitness value for \(x_{i}\), the value for which is estimated by applying a method of screening in silico. The procedure involves increasing \(x\) to a pre-set increase, \(\Delta x\). Once an initial value of \(x\) has been set, for instance equal to 2.0 (Figure 7), the size of the synthetic bacteria colony grows according to an exponential or Malthusian growth model [26]. As the number of bacteria increases, so do the levels of a synthesized reporter protein, i.e., the green fluorescent protein (GFP). As the colony grows, in a given time, \(t\), the procedure records the average value of GFP/volume. The fitness value, \(y_{i}\), for each value of \(x_{i}\) is calculated by multiplying the colony size, i.e., the number of bacteria, by the average GFP/volume. As a result, a scatter plot of the points \((x_{1},y_{1})\), \((x_{2},y_{2})\),..., \((x_{n},y_{n})\) is obtained, and the fitness regression line \(y=a+bx\) is fitted by the least squares method (Appendix A, Figure A4). Figure 4: In our simulation experiments, when a bacterium satisfies a condition, it is equivalent in synthetic biology to a bacterium carrying a gene of interest (GOI). This means that the protein it synthesizes is useful in industry, clinics, etc. When GOI is expressed by synthesizing a protein, then the antibiotic resistance gene is also expressed, for example, tetracycline resistance (TetR). As a result, bacteria that do not meet the condition will not express the resistance gene and will die in the presence of the antibiotic. The genome of the bacterium shows the promoter (P) and terminator (T). Figure 5: In simulation experiments, when a bacterium satisfies a given condition, then the bacterium will bear the lactose (Lac) operon, being able to metabolize sugar and lactose. The figure displays an elementary model of the Lac operon: The lacZ gene synthesizes an enzyme named galactosidase, i.e., a protein with catalytic ability, transforming lactose into glucose and galactose. If the medium in which the bacteria is present has enough levels of glucose, then the Lac operon is inhibited by the action of a repressor known as LacI. Other genes in the operon are lacY involved in the entrance of lactose into the bacterium, and lacA. The genome of the bacterium shows the promoter (P) and terminator (T). The described procedure was carried out twice, obtaining two regression lines. In one case, we will obtain the fitness function (regression line) for those instances that meet the knapsack weight restriction, i.e., the weight is less than the maximum capacity set (w \(<\) W), whereas in the other, we obtain the fitness function (regression line) for those instances that do not fulfill the constraint, and therefore, w \(>\) W. In order to obtain the first regression line, we will select in the register of the script in Gro (Figure 7; Appendix A, Figure A5) any desired value of q.w (total value of a set of items) that complies  
Figure 6: Bacterial chemotaxis. (**A**) When the S signal is present in the medium, S binds to the MCP (methyl-accepting chemotaxis proteins) receptor leading to CheY phosphorylation (CheY-P). Following, CheY-P will bind with the engine’s FliM protein, resulting in the clockwise (CW) motor rotation, which causes a random movement of the bacteria or bacterial ‘tumbling’. (**B**) On the other hand, in the absence of the S signal, CheY is defoghorylated, leading to the counterclockwise (CCW) motor rotation and therefore, the bacterium moves in a straight direction or ‘swimming’. Figure 7: Flowchart of 0/1 knapsack problem implemented in Gro language. The routine records three variables of the optimization problem: weight (\(q.w\)), value (\(q.v\)) and maximum capacity or weight (\(q.W\)) of the knapsack.