Heterogeneous anomalous transport in cellular and molecular biology

Abstract

It is well established that a wide variety of phenomena in cellular and molecular biology involve anomalous transport e.g. the statistics for the motility of cells and molecules are fractional and do not conform to the archetypes of simple diffusion or ballistic transport. Recent research demonstrates that the anomalous transport is in many cases heterogeneous in both time and space. Thus single anomalous exponents and single generalized diffusion coefficients are unable to satisfactorily describe many crucial phenomena in cellular and molecular biology. We consider advances in the field of heterogeneous anomalous transport (HAT) highlighting: experimental techniques (single molecule methods, microscopy, image analysis, fluorescence correlation spectroscopy, inelastic neutron scattering and NMR), theoretical tools for data analysis (robust statistical methods such as first passage probabilities, survival analysis, different varieties of mean square displacements etc), analytic theory and generative theoretical models based on simulations. Special emphasis is made on high throughput analysis techniques based on machine learning and neural networks. Furthermore, we consider anomalous transport in the context of microrheology and the heterogeneous viscoelasticity of complex fluids. HAT in the wavefronts of reaction-diffusion systems is also considered, since it plays an important role in morphogenesis and signalling. In addition we present specific examples from cellular biology including: embryonic cells, leukocytes, cancer cells, bacterial cells, bacterial biofilms and eukaryotic microorganisms. Case studies from molecular biology include: DNA, membranes, endosomal transport, endoplasmic reticulum, mucins, globular proteins and amyloids.

Electrical Signalling in Three Dimensional Bacterial Biofilms Using an Agent Based Fire-Diffuse-Fire Model

“…Anomalous diffusion of wavefronts in reaction-diffusion systems has not been studied extensively in the literature from the perspective of simulations [16] or experiments [6]. Analytic solutions to classical reaction-diffusion equations tend to predict diffusive (R 2 ∼ t) or ballistic (R 2 ∼ t 2 ) scaling of wavefront transport, but it is an inconvenient truth that the majority of real systems probably have intermediate scaling of wavefront position with time [27]. For the anomalous motion of single particles, standard models invoke non-Markovian effects (e.g.…”

“…For the anomalous motion of single particles, standard models invoke non-Markovian effects (e.g. continuous time random walks or fractional Brownian motion) [27]. No non-Markovian effects were explicitly included in our simulations (classical diffusion was modelled for the ions and ion release from bacteria is assumed fast on the time scale of the simulations e.g.…”

“…The mean square displacement of the wavefront position (R 2 ) is a useful method to describe how transport occurs in a reaction-diffusion system [27]. R 2 is analogous to the mean square displacement (M SD) of particles used to define the anomalous transport of particles [28] i.e.…”

“…where D α is the generalized diffusion coefficient and α is the scaling exponent. The wavefront of the K + ion concentration field can be described using [27],…”

“…To understand the propagation of ion channel signalling in a 3D biofilm, the K + wavefront was analysed by fitting equation I.4 to the mean square displacement of the K + wavefront position and the equation provides an empirical definition of the anomalous wavefront dynamics [27]. The hyperpolarisation and depolarization wavefronts are denoted as the centripetal and centrifugal wavefronts respectively.…”