מכל מלמדײ השכלתי (duchifat) wrote,
מכל מלמדײ השכלתי
duchifat

Аномальнaя диффузия / аномальный транспорт как результат макромолекулярного столпотворения

Хороший обзор касательно аномальной диффузии (то есть не подчиняющейся стандартным моделям броуновского движения Эйнштейна и фон Смолуховского), связанной со столпотворением макромолекул (macromolecular crowding).

Felix Hofling and Thomas Franosch. Anomalous transport in the crowded world of biological cells. Rep. Prog. Phys. 76 (2013) 046602 (50pp) doi:10.1088/0034-4885/76/4/046602

Пара цитат. Про замедление при аномальной диффузии, выражающееся эквивалентной инерцией и гидродинамической памятью:

"For unsteady motion, the particle excites incessantly new vortices diffusing slowly through the fluid. As a consequence the friction force depends on the entire history of the particle’s trajectory, an effect known as hydrodynamic memory. The theoretical description is achieved most conveniently in the frequency domain. The drag force for a sphere performing small-amplitude oscillations of angular frequency ω has already been calculated by Stokes [39] and leads to a frequency-dependent friction coefficient. For steady motion, ω = 0, the formula reduces to the Stokes drag. The last term appears as an acceleration force for half of the displaced fluid mass, mf = 4πρfa3/3, and it is natural to absorb this contribution by introducing an effective mass for the particle, meff = m + mf/2"

Про связь с перколяцией и разбиением Вороного:

"For a given obstacle configuration, the network may be constructed rigorously from a Voronoi tessellation [84, 85, 106, 107]. Increasing the obstacle densities corresponds to diluting the conductive bonds of the network, precisely as in the bond percolation problem [50, 108].... Directly at the percolation transition, the incipient infinite cluster is a fractal in a statistical sense. It is of inextensive weight and occupies a volume s∞(L) ∼ Ldf within a ball of radius L, defining the fractal dimension, df < d. A self-similar hierarchy of finite clusters coexists with the infinite cluster, whereby the distribution of cluster sizes s follows a power law, s−1−d/df . Away from the transition, the medium is no longer scale-free and self-similarity holds only on length scales below the correlation length, ξ. In particular, the probability to encounter finite clusters of linear extent larger than ξ is at least exponentially suppressed. On the percolating side of the transition, the infinite cluster looks homogeneous at scales larger than ξ ."

Собственно, определение аномальной диффузии или аномального транспорта. Замедление имеет место на средних масштабах времени:

"The probabilistic reasoning presented in the previous subsection suggests that normal diffusion emerges as a statistical law essentially by the central-limit theorem. In particular, the MSD is expected to increase linearly in time for time scales much larger than microscopic. In simple systems such as normal liquids [11, 12] one observes diffusion already at time scales exceeding the picosecond scale. The phenomena of anomalous or complex transport deal with dynamics where this diffusive regime is not visible even on time scales that are by many orders of magnitude larger than picoseconds. Conventionally, non-linear growth of the MSD is taken as an indicator of such unusual behaviour. Typically, the MSD is proportional to a power law, δr2(t) ∝ tα, with an exponent 0 <α< 1. Hence the MSD increases slower than for normal diffusion, formally the diffusion coefficient becomes zero, nevertheless the tracer is not localized. This kind of behaviour is referred to as subdiffusion or anomalous transport"


Зачем я это изучаю и к чему это можно привинтить, пока не знаю сам. :)

Собственно, я попал на эту статью вот по этой ссылке:
"Blood is a prominent example of a non-ergodic, complex fluid for which today’s standards for coagulation tests in vivo are chemically induced offline assays.... In biology, prominent examples [ of non-ergodic phenomena] include intracellular transport in the cytoplasm, cellular transport in the extracellular matrix and in plasma membranes, and the dynamics of blood [16–24]. In such complex media, non-ergodicity results from the transitory localization of scattering centres and from the system’s globally slow structural dynamics"
Guzman-Sepulveda, J. et al. Real-time intraoperative monitoring of blood coagulability via coherence-gated light scattering. Nat Biomed Eng 1, 0028 (2017) doi:10.1038/s41551-017-0028

Слова "кровь" в этой статье нет (хотя есть слово "лейкоциты"). Авторы заявляют, будто всем известно, что кровь не эргодична. Но ссылки нет и вообще ни одной статьи про эргодичность именно крови я пока не нашел почему-то. Кстати, PDF этой статьи в моей библиотеке, которая им. Голды Меир, не было (дожили - журнала группы Nature нет!), пришлось заказать по межбиблиотечному обмену, прислали быстро (часа через три).

PS. One more:
"In this original paper, we specifically address the question of discriminating between spatial and temporal randomness that both lead to anomalous, subdiffusive motion of single molecules in living cells and their compartments like the nucleus or in body fluids like blood and its components. We quantitatively describe the network of molecular interactions of single molecules by the product γ∼ = α⋅γ⋅α accounts for the molecular crowding and γ for the temporal heterogeneity. The paramete γ controls the dynamics of the interaction network...." (То есть шеф моей танцподруги Шерри - не единственный, кто пытается квантифицировать неэргодичность, и совсем не таким как они способом)
Földes-Papp, Z., & Baumann, G. (2011). Fluorescence molecule counting for single-molecule studies in crowded environment of living cells without and with broken ergodicity. Current pharmaceutical biotechnology, 12(5), 824–833. doi:10.2174/138920111795470949
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