Modelling Active Non-Markovian Oscillations

Abstract

Modelling noisy oscillations of active systems is one of the current challenges in physics and biology. Because the physical mechanisms of such processes are often difficult to identify, we propose a linear stochastic model driven by a non-Markovian bistable noise that is capable of generating self-sustained periodic oscillation. We derive analytical predictions for most relevant dynamical and thermodynamic properties of the model. This minimal model turns out to describe accurately bistable-like oscillatory motion of hair bundles in bullfrog sacculus, extracted from experimental data. Based on and in agreement with these data, we estimate the power required to sustain such active oscillations to be of the order of one hundred kBT per oscillation cycle.

Violation of the fluctuation-response relation from a linear model of hair bundle oscillations

“…We estimated that an oscillating hair bundle generates at least 5 aW or 146 k B T /cycle. This value is in good agreement with a recent estimate of 100 k B T /cycle, based on a model fitted to bi-stable oscillations of hair bundles [24]. Furthermore, we derived a scaling behavior, indicating that the energy dissipation per cycle scaled by k B T • s is of the same order of magnitude as the characteristic frequency.…”

“…Although these studies answered the question of whether these spontaneous movements were active or passive, they did not investigate the nonequilibrium energetics of the driving. Investigators have subsequently used a combination of modeling and single-cell data analysis to estimate the energy that is dissipated during an oscillatory cycle [23, 24]. These studies relied on the observed displacement of the bundle without perturbing it.…”

The impact of memory on learning sequence-to-sequence tasks

“…On the contrary, when the distribution p(x t ) is unimodal (corresponding to the case of fast relaxation times t κ ) the learning performance worsens as the data is not su ciently informative about the latent state C. Interestingly, we observe that along the "phase boundary" between unimodal and bimodal the error is roughly homogeneous and approximately equal to 25%. The presence of two "phases" in terms of the bimodality/unimodality of the distribution p(x t ) is rationalised using recent analytical results [33] for the loci of the phase boundary in the the case k = 1, which is given by…”

“…We rst describe a latent variable model for seq2seq tasks, which we call the Stochastic Switching-Ornstein-Uhlenbeck (SSOU) model. This model was introduced recently in biophysics [33] to describe the spontaneous oscillations of the tip of hair-cell bundles in the ear of the bullfrog. We consider observable sequences X = (X t ) which are described by a one-dimensional stochastic process whose dynamics is driven by an autonomous latent stochastic process C = (C t ) and a Gaussian white noise that is independent to C t .…”

“…al. [33] to show that statistical properties of the model such as its correlation functions, can be computed exactly even in the non-Markovian case and give important insights into the performance of various students trained on the reconstruction task.…”