Identifying non-equilibrium fluctuations in Intracellular Motion Using Recurrent Neural Networks

TL;DR

The study tackles distinguishing active, non-equilibrium fluctuations from passive Brownian motion in intracellular trajectories and identifying the underlying active-noise mechanism. It couples physics-based stochastic models (AOUP and RBP) with a recurrent neural network trained on synthetic data to classify trajectories and infer the active-diffusion coefficient $D_a$. Applied to intracellular tracer motion, the LSTM achieves near-optimal classification performance and consistently identifies AOUP as the best-fit model, with $D_a$ estimates aligning with independent correlation-based fits. The approach provides a data-efficient, generalizable route to quantify non-equilibrium fluctuations in living systems and can be extended to other active-matter contexts.

Abstract

Distinguishing active from passive dynamics is a fundamental challenge in understanding the motion of living cells and other active matter systems. Here, we introduce a framework that combines physical modeling, analytical theory, and machine learning to identify and characterize active fluctuations from trajectory data. We train a long short-term memory (LSTM) neural network on synthetic trajectories generated from well-defined stochastic models of active particles, enabling it to classify motion as passive or active and to infer the underlying active process. Applied to experimental trajectories of a tracer in the cytoplasm of a living cell, the method robustly identifies actively driven motion and selects an Ornstein-Uhlenbeck active noise model as the best description. Crucially, the classifier's performance on simulated data approaches the theoretical optimum that we derive, and it also yields accurate estimates of the active diffusion coefficient. This integrated approach opens a powerful route to quantify non-equilibrium fluctuations in complex biological systems from limited data.

Figures (5)

• Figure 1: (A) Schematic of the experimental setup. (B) Example of simulated trajectories of a particle evolving according to the AOUP model, shown on the top for the passive case (that is, with $D_a = 0$) and on the bottom for the active case. (C) Schematic of the machine learning classification workflow: a given trajectory is first processed by an LSTM unit, followed by two fully connected layers of a feedforward network, which outputs a single value between $0$ and $1$, representing the predicted probability that the trajectory has active noise. (D) Position histogram for the cellular trajectory studied in this paper.
• Figure 2: The LSTM classifier was trained on simulated data to distinguish between passive and active trajectories based on their time series. The model assigns a low probability of having active noise to passive trajectories (blue, "No Active Noise") and a high probability to trajectories generated with Ornstein-Uhlenbeck active noise (red, "AOUP"). The classifier successfully differentiates passive from active cases, with minimal overlap between distributions. The rightmost plot (green, "RBP") shows the results of applying a separate LSTM trained to distinguish between rotational brownian noise (labeled with a 1) and Ornstein-Uhlenbeck noise (labeled with a 0) to simulated data with rotational brownian noise. The result shows that it correctly distinguishes the different active noises and classifies the rotational brownian trajectories with values close to 1.
• Figure 3: Classifier performance nears the theoretical optimum. Log-loss of the binary classification of trajectories with and without Ornstein-Uhlenbeck active noise, as a function of total trajectory length. The LSTM and analytical model show strong improvement in classification accuracy as trajectory length increases, whereas the feedforward model exhibits only limited improvement.
• Figure 4: Results of LSTMs in predicting $D$ and $D_a$ on the test set, compared to their real values.
• Figure 5: Result of calculating the correlation $\langle x(t) x(t+t')\rangle$ as a function of $t'$ for the experimental cell trajectory (in blue). Also shown is the result of fitting Eq. \ref{['eq:corr']} (or Eq. \ref{['eq:corr_BAM']}, since it has the same shape) to the data (in orange).