Periodic Reporting for period 1 - HiddenBio (Hidden states and currents in biological systems)
Période du rapport: 2023-05-01 au 2025-12-31
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.
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.
Technical aspects of Objective (1) concerned with “fluctuations” are essentially completed. Three papers have been published, two manuscripts are in preparation. The most challenging mathematical aspects of the “concentration-of-measure” in Objective 1 are to ~80% completed, and we will soon proceed towards first publications. We extended the research in the direction of thermophoresis (i.e. particle transport in a temperature gradient), which was not originally planed but was made possible by technical advances achieved in the project group.
The “library” in Objective (2) has been completed for the microscopically reversible setting. We are currently analyzing the database and working on a theory of higher-order statistics of path-wise observables that we anticipate will explain some features we observed which were not foreseen initially. The driven setting will be tackled next. We developed a theory addressing time ordering of meso- and macroscopic composition- and defect-observables in the many-body microtubule dynamics; a major publication on this topic is in preparation. Based on some unexpected technical progress, we further initiated research on path-wise observables in hydrodynamic fluctuations, which we did not anticipate to be feasible within the duration of the ERC project. The first publication on this topic is being prepared.
Within of Objective (3) we fully characterized memory effects in plasmon-ruler data on HSP90 from the Sönnichsen-Hugel (Mainz/Freiburg) Labs (article published) and obtained conclusive evidence of hidden states and (at least one) hidden pathway connecting the open and close states of the chaperone. The Hugel-lab (Freiburg) meanwhile succeeded to measure complementary FRET data with higher temporal resolution, which will be analyzed soon. We also analyzed force-spectroscopy data from the Ritort-lab and begun to analyze experimental data from on driven colloids from labs at the University of Granada (ES) and University of Düsseldorf (GER). These experiments are tailor-made to test the theoretical results in the ERC project and were not anticipated initially but will further enhance the scientific impact of the project.
The “library” in Objective (2) has been completed for the microscopically reversible setting. We are currently analyzing the database and working on a theory of higher-order statistics of path-wise observables that we anticipate will explain some features we observed which were not foreseen initially. The driven setting will be tackled next. We developed a theory addressing time ordering of meso- and macroscopic composition- and defect-observables in the many-body microtubule dynamics; a major publication on this topic is in preparation. Based on some unexpected technical progress, we further initiated research on path-wise observables in hydrodynamic fluctuations, which we did not anticipate to be feasible within the duration of the ERC project. The first publication on this topic is being prepared.
Within of Objective (3) we fully characterized memory effects in plasmon-ruler data on HSP90 from the Sönnichsen-Hugel (Mainz/Freiburg) Labs (article published) and obtained conclusive evidence of hidden states and (at least one) hidden pathway connecting the open and close states of the chaperone. The Hugel-lab (Freiburg) meanwhile succeeded to measure complementary FRET data with higher temporal resolution, which will be analyzed soon. We also analyzed force-spectroscopy data from the Ritort-lab and begun to analyze experimental data from on driven colloids from labs at the University of Granada (ES) and University of Düsseldorf (GER). These experiments are tailor-made to test the theoretical results in the ERC project and were not anticipated initially but will further enhance the scientific impact of the project.
Below we list the most striking achievements of HiddenBio so far:
(a) We proved that the transport of any scalar observable of general high-dimensional dynamics is bounded from above by the total entropy production scaled by how much the observation “stretches” microscopic coordinates. This result reveals an unforeseen thermodynamic limit on nonequilibrium transport of observables and enables to infer a lower bound on dissipation from the transport of any observable. We further proved an inequality for correlation times of observables, explaining how thermodynamics limits the temporal decay of correlations.
(b) We have shown that memory, i.e. the hallmark of hidden degrees of freedom, may emerge under starkly different conditions in dissipative versus reversible (equilibrium) systems.
(c) We developed a model-free method to quantify the duration and magnitude of memory in time series and applied it to HSP90 probed by a plasmon ruler. This result delivers a model-free platform to test for, and quantify, memory in a generic time series.]
(d) We derived higher-order estimators for the energy-dissipation rate in systems observed via low-dimensional projections. These provide improved, guaranteed lower bounds on the entropy-production in a system from the time series of an observable, give insight into the correct form of physical time-reversal in presence of memory, and highlight pitfalls in ignoring memory in thermodynamic inference.
(e) We developed a general method for inferring the presence of hidden states and transition pathways in time series that provides insight about the hidden topology of microscopic paths in a holography-like fashion.
(f) We were invited by the Journal of Chemical Physics to write a perspective article highlighting why in discussing time-reversal symmetry and its violations, the precise assumptions on microscopic dynamics, coarse graining, and further reductions are decisive for drawing physically consistent conclusions. This underscores the timelines and growing relevance of HiddenBio and the corresponding research area.
(a) We proved that the transport of any scalar observable of general high-dimensional dynamics is bounded from above by the total entropy production scaled by how much the observation “stretches” microscopic coordinates. This result reveals an unforeseen thermodynamic limit on nonequilibrium transport of observables and enables to infer a lower bound on dissipation from the transport of any observable. We further proved an inequality for correlation times of observables, explaining how thermodynamics limits the temporal decay of correlations.
(b) We have shown that memory, i.e. the hallmark of hidden degrees of freedom, may emerge under starkly different conditions in dissipative versus reversible (equilibrium) systems.
(c) We developed a model-free method to quantify the duration and magnitude of memory in time series and applied it to HSP90 probed by a plasmon ruler. This result delivers a model-free platform to test for, and quantify, memory in a generic time series.]
(d) We derived higher-order estimators for the energy-dissipation rate in systems observed via low-dimensional projections. These provide improved, guaranteed lower bounds on the entropy-production in a system from the time series of an observable, give insight into the correct form of physical time-reversal in presence of memory, and highlight pitfalls in ignoring memory in thermodynamic inference.
(e) We developed a general method for inferring the presence of hidden states and transition pathways in time series that provides insight about the hidden topology of microscopic paths in a holography-like fashion.
(f) We were invited by the Journal of Chemical Physics to write a perspective article highlighting why in discussing time-reversal symmetry and its violations, the precise assumptions on microscopic dynamics, coarse graining, and further reductions are decisive for drawing physically consistent conclusions. This underscores the timelines and growing relevance of HiddenBio and the corresponding research area.