Untangling cause and correlation in molecular simulations

Distinguishing cause and correlation is a difficult yet important task across many fields of study. Many areas from epidemiology to sociology have developed rigorous statistical frameworks to make this distinction. Yet how causality emerges remains an unanswered question in molecular dynamics simulations where time can be inverted without changing the results.

Del Tatto et al. developed a framework for determining causal links in molecular simulations. The framework uses two independent computational methods that infer causality with the language of information transfer.

“The key was simplifying the problem,” said author Alessandro Laio. “Molecular simulations typically describe systems with hundreds of thousands of degrees of freedom, but we found that causality can be observed even on systems with two degrees of freedom, in which what happens can be clearly interpreted.”

To demonstrate their framework, the authors simulated a single tryptophan molecule in water. Using discrete Markov-state and Langevin dynamics on a 2D free energy surface, they showed that even in a simple system, there can be asymmetries which portray unidirectional information transfer in the molecular system.

“What also excites us is that our work not only shows how to measure causality in equilibrium systems, but also offers a conceptual understanding of how causal relations emerge at the mesoscopic scale, which appears to be deeply connected to fundamental principles in statistical mechanics and thermodynamics,” Laio said.

The authors hope the work will strengthen ties between experimentalists and experts in computer simulations. They intend to extend their work into the experimental realm next with studies of specific molecular phenomena, such as allosteric transitions in proteins.

Source: “Towards a robust approach to infer causality from molecular dynamics simulations,” by Vittorio Del Tatto, Debarshi Banerjee, Ali Hassanali, and Alessandro Laio, Journal of Chemical Physics (2025). The article can be accessed at https://doi.org/10.1063/5.0267926 .

This paper is part of the Michele Parrinello Festschrift Collection, learn more here .