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A unified approach for sparse dynamical system inference from temporal measurements.

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We introduce Unified Sparse Dynamics Learning (USDL), a novel method to simultaneously learn the structure and parameters of diverse dynamical systems. This approach handles various system types, outperforming existing methods on simulated and real biological data.

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Area of Science:

  • Computational Biology
  • Systems Biology
  • Data Science

Background:

  • Dynamical systems in natural sciences are often modeled using differential or difference equations.
  • Existing algorithms struggle to handle diverse dynamical system types (discrete/continuous time, deterministic/stochastic, time-series/time-course data) simultaneously.
  • There is a need for a unified approach to infer dynamical system structure and parameters across different data types.

Purpose of the Study:

  • To present a unified approach for inferring the structure and parameters of non-linear dynamical systems.
  • To develop a method capable of handling various types of dynamical systems, including those with stochasticity and multiple interventions.
  • To enable robust analysis of biological signaling pathways from complex datasets.

Main Methods:

  • Introduced Unified Sparse Dynamics Learning (USDL), a two-step approach for dynamical system inference.
  • Utilized the weak formulation to derive an atemporal system of equations.
  • Framed the inference problem as sparse signal recovery, leveraging existing algorithms and theory.
  • Applied the method to both simulated and real single-cell mass cytometry data.

Main Results:

  • USDL effectively infers structure and parameters for diverse dynamical systems, provided they are linear with respect to parameters.
  • Demonstrated superior performance over existing methods on simulated data, especially under interventions and stochasticity.
  • Showed strong correlation between USDL accuracy and theoretical metrics like the exact recovery coefficient.
  • Successfully identified high-confidence subgraphs of signaling pathways from real single-cell data.

Conclusions:

  • USDL offers a unified and powerful framework for dynamical systems inference.
  • The approach is robust and accurate, outperforming existing methods in complex scenarios.
  • USDL has practical applications in uncovering biological pathway structures from experimental data.
  • The algorithm is accessible via source code and integrated into the SCENERY online tool.