Abstract
The emergent activity of biological systems can often be represented as low-dimensional, Langevin-type stochastic differential equations. In certain systems, however, large and abrupt events occur and violate the assumptions of this approach. We address this situation here by providing a novel method that reconstructs a jump-diffusion stochastic process based solely on the statistics of the original data. Our method assumes that these data are stationary, that diffusive noise is additive, and that jumps are Poisson. We use threshold-crossing of the increments to detect jumps in the time series. This is followed by an iterative scheme that compensates for the presence of diffusive fluctuations that are falsely detected as jumps. Our approach is based on probabilistic calculations associated with these fluctuations and on the use of the Fokker–Planck and the differential Chapman–Kolmogorov equations. After some validation cases, we apply this method to recordings of membrane noise in pyramidal neurons of the electrosensory lateral line lobe of weakly electric fish. These recordings display large, jump-like depolarization events that occur at random times, the biophysics of which is unknown. We find that some pyramidal cells increase their jump rate and noise intensity as the membrane potential approaches spike threshold, while their drift function and jump amplitude distribution remain unchanged. As our method is fully data-driven, it provides a valuable means to further investigate the functional role of these jump-like events without relying on unconstrained biophysical models.
Highlights
Complex systems are ubiquitous in many areas of science, including biology, neuroscience, climatology, engineering, as well as in finance and social sciences [1, 2]
3.1 Validation of the false positives (FP) statistics calculations To confirm that the calculations of QA and ΓA are accurate, we start with a simple test case where we consider a time series {Xdiff (t)} obtained from a simulated pure diffusion process
This approach is validated when the jumps are comparable in size to the diffusive fluctuations (Case 1), as well as when they are much larger than diffusive fluctuations (Case 2)
Summary
Complex systems are ubiquitous in many areas of science, including biology, neuroscience, climatology, engineering, as well as in finance and social sciences [1, 2]. The common feature uniting such vastly different systems is the nonlinear interaction between their numerous microscopic constituents This collective activity leads to the emergence of macroscopic order that cannot be reduced to microscopic properties [3]. The resulting model is completely data-driven and captures the core phenomenology of the original data without relying on knowledge or assumptions about the microscopic constituents of the observed system This approach has been successfully applied in a variety of contexts, ranging from neuronal dynamics [8,9,10,11,12], heart rate variability [13, 14], turbulence [15, 16], calibration of optical tweezers [17], and others This approach has been successfully applied in a variety of contexts, ranging from neuronal dynamics [8,9,10,11,12], heart rate variability [13, 14], turbulence [15, 16], calibration of optical tweezers [17], and others (see Ref. [5] for a review)
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