Modelling non-Markovian fluctuations in intracellular biomolecular transport

Barredo, Wilson I.; Bernido, Christopher C.; Carpio-Bernido, M. Victoria; Bornales, Jinky B.

doi:10.1016/j.mbs.2018.01.004

Cited by 13 publications

(8 citation statements)

References 15 publications

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“…Moreover, Eq. (5) obeys the modified diffusion equation (Barredo et al 2018;, Barredo et al 2018). We now proceed to apply this stochastic process with memory to acquire insights into the empirical datasets for the GBR degradation, sea surface temperatures near the GBR, and the rise of atmospheric CO2 levels.…”

Section: Stochastic Framework With Memorymentioning

confidence: 99%

“…Theoretically, there are many forms of stochastic processes with memory widely known as anomalous diffusion as exemplified by fractional Brownian motion (Metzler et al 2014;Biagini et al 2008;Mishura 2004;Sithi and Lim 1995). The stochastic process with memory used in this paper belongs to a larger class of non-Markovian white noise processes which have been successfully applied recently to investigate other systems such as the ageing of fibrin (Aure et al 2019), the DNA distribution in genomes (Violanda et al 2019), diffusion coefficient values for proteins of varying lengths (Barredo et al 2018), and cyclone track fluctuations , among others. We use an analytical stochastic framework with memory Carpio-Bernido 2012, 2015) which allows direct comparison between analytical and empirical results for the mean square deviation (MSD) of observables.…”

Section: Introductionmentioning

confidence: 99%

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Great Barrier Reef degradation, sea surface temperatures, and atmospheric CO2 levels collectively exhibit a stochastic process with memory

et al. 2021

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Quantifying ecological memory could be done at several levels from the rate of physiological changes in an ecosystem all the way down to responses at the genetic level. One way of unlocking the information encoded in a collective environmental memory is to examine the recorded time-series data generated by different components of an ecosystem. In this paper, we probe into the case of the Great Barrier Reef (GBR) which is threatened by elevated sea surface temperatures (SST) and ocean acidification attributed to rising atmospheric CO2 levels. Specifically, we investigate the interrelated dynamics between the degradation of the GBR, SST, and rising atmospheric CO2 levels, by considering three datasets: (a) the mean percentage hard coral cover of the GBR from the archives of the Australian Institute of Marine Science; (b) SST close to the GBR from the National Oceanic and Atmospheric Administration; and (c) the Keeling curve for atmospheric CO2 levels measured by the Mauna Loa Observatory. We show that fluctuating observables in these datasets have the same memory behavior described by a non-Markovian stochastic process. All three datasets show a good match between empirical and analytical mean square deviation. An explicit analytical form for the corresponding probability density function is obtained which obeys a modified diffusion equation with a time dependent diffusion coefficient. This study provides a new perspective on the similarities of and interaction between the GBR's declining hard coral cover, SST, and rising atmospheric CO2 levels by putting all three systems into one unified framework indexed by a memory parameter and a characteristic frequency . The short-time dynamics of CO2 levels and SST fall in the superdiffusive regime, while the GBR exhibits hyperballistic fluctuation in percent coral cover with the highest values for and .

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Section: Stochastic Framework With Memorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Great Barrier Reef degradation, sea surface temperatures, and atmospheric CO2 levels collectively exhibit a stochastic process with memory

et al. 2021

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“…To provide insights on the anomalous diffusion of tracer particles embedded in fibrin, we introduce a damped white noise process with memory for analyzing the modes of diffusive behavior valid for different gelation stages or ageing times. Guided by insights from the use of different memory kernels for stochastic processes in biological systems (29, 30), we parametrize the fluctuating position x ( τ ) of the tracer particle as, …”

Section: Methodsmentioning

confidence: 99%

Damped White Noise Diffusion with Memory for Diffusing Microprobes in Ageing Fibrin Gels

Aure¹,

Bernido²,

Carpio-Bernido³

et al. 2019

Preprint

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1From observations of colloidal tracer particles in fibrin undergoing gelation, we introduce an 2 analytical framework that allows determination of the probability density function (PDF) for 3 a stochastic process beyond fractional Brownian motion. Using passive microrheology via 4 videomicroscopy, mean square displacements (MSD) of tracer particles suspended in fibrin at 5 different ageing times are obtained. The anomalous diffusion is then described by a damped 6 white noise process with memory, with analytical results closely matching experimental plots 7 of MSD and PDF. We further show that the white noise functional stochastic approach 8 applied to passive microrheology reveals the existence of a gelation parameter µ which 9 elucidates the dynamics of constrained tracer particles embedded in a time dependent soft 10 material. This study offers experimental insights on the ageing of fibrin gels while presenting 11 a white noise functional stochastic approach that could be applied to other systems exhibiting 12 non-Markovian diffusive behavior. 13 14 15 16 17 18 19 20 21 22 23 24 25 1Fibrin is a protein polymer network that plays a crucial role in blood clotting, wound healing, 2 and other biological processes such as blood vessel formation and cell growth (1-6). Aside 3 from its importance in clinical applications, fibrin also finds an increasing role in tissue 4 regeneration and engineering (5,(7)(8). Thus, it is important to have a quantitative description 5 of the mechanics and complex structural formation of fibrin as a viscoelastic biomaterial (3, 6 9-11). Since not much is known about the diffusive behavior of probe particles in fibrin as its 7 structure evolves in time, we use passive microrheology via video microscopy to reveal the 8 gelation dynamics of fibrin by tracking the movement of probe particles suspended in its 9 network of protein polymers (12)(13)(14). Moreover, to elucidate how the structure of fibrin is 10 affected at different ageing times, we present a theoretical framework for the stochastic 11 fluctuations exhibited by the experimental observations. 12The diffusion of colloidal tracer particles in complex fluids is usually analyzed by 13 measuring the mean square displacement (MSD), < Δ 2 ( ) >, where brackets represent an 14 ensemble average and τ is the lag time between two positions taken by the particle in its 15 trajectory. Numerous studies have interestingly revealed anomalous diffusion or deviations 16 from purely Brownian motion (15-26) thus making studies of probe particles in many 17 biophysical systems an active area of research. Examples of systems where anomalous 18 diffusion occurs include entangled F-Actin networks (17-19), living cells (20, 21), cytoplasm 19(22, 23), colloidal liquids (24, 25), and lipid membranes (26), among others. Anomalous 20 diffusion, is often characterized analytically using fractional Brownian motion (fBm), which 21 follows power law scaling of the form (13, 15), < Δ 2 ( ) >~ . In particular, the motion of 22 the probe particles suspended in t...

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“…(10) is expressed in its Fourier representation so that one could apply the definition of the white noise characteristic functional, (11) for a regular test function . The procedure yields the diffusion propagator which is still Gaussian in the displacement variable, while having time dependence in the transport coefficient: ,…”

Section: Other Classes Of Stochastic Processes With Memory: Propagatomentioning

confidence: 99%

On time-dependent diffusion coefficients arising from stochastic processes with memory

Carpio-Bernido

Barredo

Bernido

2017

AIP Conference Proceedings

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Abstract. Time-dependent diffusion coefficients arise from anomalous diffusion encountered in many physical systems such as protein transport in cells. We compare these coefficients with those arising from analysis of stochastic processes with memory that go beyond fractional Brownian motion. Facilitated by the Hida white noise functional integral approach, diffusion propagators or probability density functions (pdf) are obtained and shown to be solutions of modified diffusion equations with time-dependent diffusion coefficients. This should be useful in the study of complex transport processes.

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Modelling non-Markovian fluctuations in intracellular biomolecular transport

Cited by 13 publications

References 15 publications

Great Barrier Reef degradation, sea surface temperatures, and atmospheric CO2 levels collectively exhibit a stochastic process with memory

Great Barrier Reef degradation, sea surface temperatures, and atmospheric CO2 levels collectively exhibit a stochastic process with memory

Damped White Noise Diffusion with Memory for Diffusing Microprobes in Ageing Fibrin Gels

On time-dependent diffusion coefficients arising from stochastic processes with memory

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