# Synthetic Data Generation for the Development of 2D Gel Electrophoresis Protein Spot Models
## 2 Materials and Methods
### Synthetic Data Evaluation  
The created dataset must be evaluated in order to draw conclusions about its quality and potential for the development of ML models for protein spot reconstruction and parameterization. Some initial subjective evaluations were performed during the process of creating the protein spot image samples. Subjective evaluation refers to the perceptual (visual) evaluation of the image samples' fidelity to real 2 DGE images. Subjective evaluation and domain knowledge were constantly used and exploited during the development of the method for generating synthetic protein spot images. The objective evaluation of the dataset is possible after using the dataset for its intended purpose--to develop a spot modeling algorithm. If the dataset leads to the creation of an ML model that, according to relevant metrics, is appropriate for the protein spot modeling task (better than some previous models), the synthetic dataset can be treated as useful. The machine learning approach is used for the development of the spot modeling algorithm. The autoencoder (AE) is selected to serve as the core part of the protein spot modeling/reconstruction algorithm. The architecture of the autoencoder, together with some of its hyperparameters, is presented in Figure 7. The AE model additionally has a branch for a second output for the prediction of spot parameters from the bottleneck features. This branch is a multilayer perceptron. The AE model is trained using a decreasing learning rate (LR) schedule. LR is linearly reduced from \(10^{-3}\) to \(10^{-5}\) over 60 epochs. The initial neural network's architecture and hyperparameters are selected and tuned heuristically based on NN's performance on validation data. For the algorithm comparison, two models frequently used in the literature, namely the Gaussian [41; 42; 43; 44; 46] and diffusion [45; 46] models for spot modeling, serve as baseline algorithms. Additionally, several other mathematical spot models [46] are used as baseline algorithms. For the evaluation of the created spot reconstruction algorithm (autoencoder model), several comparative experiments are designed. There are two major groups of experiments: one comparison of the algorithms uses synthetic data that are similar to the training data, and the other is based on real 2 DGE data. The advantage of synthetic data is the availability of precise ground-truth labels. Real data show algorithm performance in real-world scenarios. The performance results may differ from the synthetic data if not all variations of the real spots are represented in the synthetic data. The results of evaluations using the real data may be inaccurate due to the unknown real ground-truth data. The other classes of experiments are the evaluation of the reconstruction accuracy and the evaluation of spot parameter estimation accuracy. The reconstruction accuracy reveals how similar the reconstructed spot is to the ground-truth spot. Parameter estimation accuracy shows how well the essential spot parameters--spot intensity (excluding background intensity) and spot volume--can be computed. Ground-truth spot parameters are computed directly from the synthetic target image. For the baseline algorithms (fitting mathematical model), the predicted spot parameters are computed from the estimated \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Parameter Range**} \\ \hline
**Function** & **Parameter \#1** & **Min** & **Max** & **Parameter \#2** & **Min** & **Max** \\ \hline
**1. Gaussian** & \(\sigma\) & 2 & 15 & \(d\) & 0 & 5 \\
**2. Diffusion** & \(a\) & 3.5 & 8 & \(D\) & 0.2 & 10 \\
**3. Spline** & \(a\) & 0 & 5 & \(b\) & 5 & 35 \\
**4. FL Bell-shaped** & \(a\) & 2 & 20 & \(b\) & 1.2 & 8 \\
**5. Sigmoid** & \(a\) & 0.5 & 1 & \(d\) & 1 & 20 \\
**6. Cosine** & \(a\) & 2 & 20 & \(d\) & 0 & 10 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of the parameter ranges of the functions used to generate 1D edge templates of protein spots.