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

Abstract

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...

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

“…Moreover, Eq. (A5) allows the generation of a wide class of stochastic processes with memory which has been applied to other biological and physical systems (Aure et al 2019;Violanda et al 2019;Barredo et al 2018;. With Eq.…”

“…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.…”