Structural Prediction and Inverse Design by a Strongly Correlated Neural Network

Macromolecules contain molecular units as the coding information for their correlated structures in physical dimensions. The relationship between these two features is governed by the interaction energies of the involved molecular units and their encoded sequences. We present a neural network algorithm that treats molecular units themselves as neural networks, which has the flexibility to allow each unit to respond to its own environment and to influence others in the system. Through a deep neural network and a self-consistent procedure, molecular units in the network establish a strong correlation to produce the desirable features in the physical world. The proposed framework is applied to the HP model. Both the forward problem of predicting folded structures from given sequences and the inverse problem of predicting required sequences for a given structure are examined.

Figure 1

(a) Sketch of the strongly correlated network (SCN) and (b) the physical example used for demonstration (HP model). SCN represents entities in physical feature 1 by neural networks and sends their output to a deep neural network for processing. Two output channels are designed: one for feeding back to the input of the identity layer and the other for the calculated physical feature 2. In the folding example of the HP model, feature 1 is the encoding sequence and feature 2 is the coordinates of the folded structure. In inverse design, feature 1 is the desired fold and feature 2 is the predicted sequence that in turn produces the fold. The network mimics the physical process that connects features 1 and 2.

Figure 2

Accuracy of SCN to produce the correct native structures in the independent test data of the 19mer HP model, as a function of the supervised-training epoch (solid black curve). Other deep NNs, such as vector (VEC), scalar (SCL), and fully connected (FNN) models have prediction accuracies represented by the solid gray, red, and blue curves. The efficiencies of the supervised training are monitored by the dashed black, gray, red, and blue curves, representing the accuracies measured on the training dataset itself, for SCN, VEC, SCL and FNN, respectively. [33].

Figure 3

(a) Designability $D$ and recoverability $R$ of the trained SCN in making inverse-design predictions on the independent test dataset and (b) recoverability $R$ further categorized by the degrees of degeneracy $g$ [33]. These measures are plotted as functions of $M$, the number of designing trials made on the trained SCN. In plot (b), the six colors on the bar graph represent $M=50$, 100, 200, 500, 1000, and 2000, from bottom to top, respectively. The rotated labels associated with vertical bars in (b) indicate the fraction of structures in the testing dataset that have the corresponding $g$.