A physics based feature engineering framework for trajectory analysis

Abstract

Trajectory analysis is of great importance for the understanding of dynamical systems and their properties. Trajectories may describe the time evolution of a variable in different contexts, such as the motion of cancer cell , the volatility of a stock in the stock market, the populational growth and so forth. In physical systems, where we are interested in the time evolution of the position of one or a set of bodies, there are systems where the position of these bodies depends on the concentration of matter at different locations. In such context, the movement of bodies tends to be in the direction of an area with high concentration of matter to a region of low concentration. This motion is called Diffusion. As a general way of describing the time evolution of a body in such systems, we use the Mean Squared Displacement. The motion types, sometimes called the Diffusion Classes, are a way of describing the movement of bodies in systems where Diffusion is observed. To classify the diffusion, the literature uses the time dependence of the Mean Squared Displacement. In the present work, we pointed out that using this time dependence as the only quantity to classify the Diffusion will give rise to an immediate problem, where we can have two or more possible Diffusion Classes for the same motion. With that in mind, we proposed a physics-based feature engineering framework for trajectory analysis called TrajPy as a possible solution to this problem. The framework contains three main components. The first allows us to perform trajectory analysis by computing multiple quantities of physical and statistical interest for any trajectory, whether this trajectory is taken from experiments or generated in a computer simulation. The second component is a combination of two graphical-user interfaces. The first allows us to compute the quantities of the first component in a way that we do not need to be familiar with Python programming. The second graphical-user interface was developed to be a first step towards a general solution to the bottleneck present in the drug discovery process. The third component allows us to simulate the four basic motion types with a range of parameters so that we may use these simulations as a connection between trajectory analysis and Machine Learning, where we aim to classify the Diffusion of particles in a more general way so that we avoid the problem involving the overlapping of diffusion classes. As a demonstration of the application of TrajPy, we performed trajectory analysis and diffusion classification for systems that mimic the capability of cells to be deformed. For this, we simulated multiple systems, using Molecular Dynamics, in a combination of values of pressure and the spring constant related to Hooke’s Law, where each system is composed of 400 two-dimensional polymer rings. As a result, we observed that the polymer rings, once the pressure reaches a certain threshold, present a dynamical transition from Normal Diffusion to Confined Diffusion, i.e., as the pressure increases, the polymer rings become trapped inside a region as an effect of the increase in pressure. Then, we classified the Diffusion of each polymer ring for every system and observed the same behavior from the perspective of the Random Forest Classifier algorithm using Machine Learning.