The possibility to infer information about hidden degrees of freedom from time series is a key challenge in many disciplines, particularly single-molecule and climate science, as well as epidemiology. Hidden dynamics are often essential, as they reflect the approach to, and mechanism of, critical transitions, e.g. the folding of a protein or RNA, an abrupt shift in climate, an outbreak of a pandemic. Single-molecule experiments in particular probe processes on the level of stochastic trajectories that are typically analyzed by averaging along individual realizations. What makes their interpretation so challenging, is the fact that single-molecule techniques track low-, often one-dimensional projections (see Fig. 1). These also arise on larger scales, e.g. in experiments probing self-assembling meso-structures in living cells. Generally, projections induce memory in the observed dynamics, i.e. transitions depend strongly on the past evolution and not only on the present state. They also hide energy barriers, transition pathways and high-energy intermediate states, and burry dissipative currents in non-equilibrium steady-states, making a driven system appear as if it were in equilibrium. These effects severely impart the analysis and interpretation of projected time series.
Existing approaches to analyzing such time series neglect certain information encoded in the time ordering, which precludes the access to hidden dynamics. HiddenBio proposes a novel concept— to treat time series as “shadows”, resting on the fact that hidden properties of a high-dimensional landscape imprint onto the time-ordering statistics of projected states along individual trajectories. To do so, HiddenBio introduces functionals—path-wise observables—of projected paths that are easily inferred from data, and analyzes their statistics and measure concentration by theory and by inferring them from data.
HiddenBio pursues 3 main objectives:
(1) Developing a theory of fluctuations and non-asymptotic measure concentration.
(2) Mapping the fingerprints of hidden dimensions and currents in projected observables.
(3) Inferring hidden dynamics and buried currents from experiments across the scales.
Objective (1) will provide general insight allowing us to identify and connect easily measurable descriptors to probabilistic properties of the full (including hidden) dynamics. Objective (2) will connect the “library of elementary building blocks” of representative model landscapes and currents to the measured descriptors, and with the results of (1) will provide a deeper understanding and enable a more efficient analysis of dissipative self-assembly (e.g. of microtubules). The experiments in Objective (3) will be performed by our collaborators; the analysis of plasmon ruler and force spectroscopy experiments, as well as Molecular Dynamics simulations will resolve the long-standing debate about high-energy intermediates in folding pathways, the controversial non-ergodicity of folded proteins, and unravel non-equilibrium currents buried in the open-close motion of the molecular chaperon machine Hsp90.
