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Generalizing HMMs to Continuous Time for Fast Kinetics: Hidden Markov Jump Processes.

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Area of Science:

  • Physical Chemistry
  • Biophysics
  • Statistical Mechanics

Background:

  • Hidden Markov Models (HMMs) are standard for time series analysis in single-molecule experiments.
  • HMMs assume discrete time steps, which conflicts with the continuous-time evolution of physical systems.
  • Current HMM applications are limited to slow kinetic processes relative to data acquisition rates.

Purpose of the Study:

  • To generalize the HMM framework for physical systems that evolve in continuous time.
  • To develop a model capable of analyzing fast molecular kinetics in single-molecule experiments.
  • To overcome the limitations of discrete-time assumptions in HMMs for real-world physical processes.

Main Methods:

  • Exploited mathematical tools for inferring Markov jump processes.
  • Developed the hidden Markov jump process (HMJP).
  • Demonstrated the mathematical limit where HMJP reduces to HMM.

Main Results:

  • The hidden Markov jump process accurately models systems with fast transition rates.
  • The HMJP removes the assumption that physical processes must be slower than data acquisition.
  • Transition rates can be learned even when they occur on the same timescale as data acquisition.

Conclusions:

  • The hidden Markov jump process provides a more accurate framework for analyzing single-molecule dynamics.
  • This generalization enables the study of faster molecular events previously inaccessible to HMMs.
  • The HMJP resolves the discrete-time discrepancy inherent in traditional HMMs for physical systems.