Colloidal hydrodynamics of biological cells: A frontier spanning two fields

One of the ultimate goals of science is an understanding of biological cells so complete that one can construct a living cell from its constituent molecules, control its dynamics, and repair its machinery. Advances in experimental and computational biology techniques over the past 30 years have led to landmark progress toward this goal, from atomistic models of proteins to synthesis of entire bacterial genomes. However, the current frontier in operational mastery of cells arguably resides at the interface between biology and fluid physics: cellular processes that operate over colloidal length scales, where continuum fluid mechanics and Brownian motion underlie whole-cell-scale behavior. It is at the colloidal scale that much of cell machinery operates and where reconstitution and manipulation of cells is most challenging. This operational regime is centered between the two well-understood regimes of structural biology and systems biology, where the former focuses on atomistic-scale spatial resolution with little time evolution and the latter on kinetic models that abstract space away. Low-Reynolds-number colloidal hydrodynamics modeling bridges the divide between these regimes by unifying the disparate length scales and timescales of solvent molecule and colloidal dynamics and may hold the key to operational mastery of cells. Bridging the divide between the two disciplines of biology and fluid physics is as much a part of the way forward as are developing new tools and asking new questions. In this paper we highlight the central and nontrivial roles played by low-Reynolds-number hydrodynamics and colloidal-scale motion that appear in common across cell functions, types, and conditions.

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Figure 1

State-of-the-art modeling of biological cells is successful at two distinct spatial and temporal regimes. (a) Structural biology models represent the dynamics and function of individual nanometer-scale macromolecules at atomistic spatial resolution but typically across nanosecond timescales (a ribosome is shown, from [1], with permission). (b) Systems biology models represent cells using kinetic networks, where biological functions span minutes but with limited or no spatial resolution (figure from [2], with permission). (c) A biocolloidal regime bridges microscopic physical forces of individual molecules and whole-cell biological function across the two regimes, but its biological operating principles remain largely a mystery (an illustration of E. coli is shown, adapted from [3], with permission).

Figure 2

Active motion regulates transport in cells. (a) In cells of the plant Chara corallina, an active motor network climbs a chiral network of actin filaments generating flow that (b) enhances the rate of nutrient uptake to the center of the cell $(R$ is the radius of the cylindrical cell and $D$ is the diffusion coefficient of nutrients). (c) In smaller animal cells, structured networks cause randomly directed motor protein motion; thus, active motors lead to fluctuating disturbance flows in the cytoplasm that are stronger than thermal fluctuations. These flows (d) enhance movement of surrounding macromolecules in the cytoplasmic milieu. This is illustrated by measuring diffusive speed (via FRAP) of a fluorescent protein Dendra2 in melanoma cells. Diffusion is faster in fed cells (in the presence of ATP) [figures (a) and (b) are from [52] (Copyright (2008) National Academy of Sciences U.S.A.) and (c) and (d) are from [56], with permission].

Figure 3

Glass transitions can control dynamics in cells. The mobility of plasmid DNA (a circular DNA of colloidal size $\sim 150\text{nm}$ [59]) decreases significantly in starved E. coli due to a glasslike transition. (a) Two-dimensional trajectories of fluorescently labeled plasmids show evidence of cage trapping, hypothesized to result from crowding rather than network trapping. (b) Mean-square displacement from (a), plotted versus lag time, for fed and starved conditions (figure is from [59], with permission).

Figure 4

Phase-separated biomolecular condensates are essential to healthy cell function. (a) Images of condensates in cells. On the left are nucleoli (red) and histone locus bodies (green) in the nucleus of an X. laevis oocyte, and on the right are purinosomes in a HeLa cell (from [92], with permission). (b) Diagram of known condensates in eukaryotic cells (from [89], with permission). (c) The ALS-associated protein FUS forms phase-separated condensates that convert to solid aggregates faster when the protein contains ALS patient-derived mutations (figure is from [91], with permission).

Figure 5

The bacterial cytoplasm can be modeled via Brownian dynamics. Shown is an instantaneous snapshot of a Brownian dynamics simulation of 1008 macromolecules from McGuffee and Elcock. The 50 most abundant macromolecules in the E. coli cytoplasm are represented with experimentally determined shapes and relative abundances (figure is from [103], with permission).

Figure 6

Hydrodynamic flow plays an essential role in the positioning of the mitotic spindle. (a) Dynamic simulations of mitotic spindle positioning using three different putative force transduction mechanisms. (b) Each mechanism leads to distinct cytoplasmic flows within the model cell. (c) However, all three flows result in the same final positioning of the mitotic spindle, suggesting that these flows can be used to differentiate between underlying mechanisms. The simulations include hydrodynamic interactions but not Brownian motion (figure is from [64], with permission).

Figure 7

(a) Active extensile forces within the nucleus can induce fluid disturbances that lead to (b) coherent motion of chromatin, represented here as a confined flexible chain. This work shows that long-ranged hydrodynamic coupling can lead to biologically relevant self-organization critical to gene expression (figure is from [60], with permission).

Figure 8

Long-range hydrodynamic towing may regulate whole-cell physical dynamics. (a) If a particle (black) in a confined suspension is driven in a direction, any other particle in line (red) will be towed in the same direction. The strength of this towing is dependent on proximity between particles as well as volume fraction and confinement of the suspension. (b) Movement of particles that are not in line causes towing that changes direction depending on proximity to the wall: Particles near the center are towed along, but those near the wall are towed backward (figure is from [114], with permission).

Figure 9

Short-time self-diffusion of small particles $\left(D_{0,\mathrm{small}}^s\right)$ in spherically confined suspensions changes with different volume compositions of small and large particles and with distance from the center of confinement. The undulations are a consequence of structural heterogeneity and hydrodynamic interactions, viz., vanishing mobility at the wall [113]. The diffusivity of small particles is increasingly diminished in the direction parallel to the wall in suspensions with greater relative volume fraction of small particles. The horizontal lines are to guide the eye (figure is adapted from [70], with permission).

Figure 10

The Cellular Stokesian dynamics algorithm [70, 112, 113] can be used to model whole-cell processes. As one example, the algorithm can be used to study (a) phase separation at the colloidal scale resulting from interparticle attractions, characterized by (b) an interaction potential, which may comprise variable-distance repulsions and attractions that are uniformly distributed over molecular surfaces or patchy. In Cellular Stokesian dynamics models, (c) hydrodynamic interactions and size polydispersity in a cell coupled with (d) attractive forces can thwart phase separation, instead inducing gelation and formation of fibrous or ropy networks reminiscent of those implicated in ALS and other age-related diseases [figures (a) and (b) are from [124], (c) is from [70], and (d) is from [131], with permission].

Figure 11

Translation elongation in E. coli is an ideal model problem for elucidating the colloidal physics underpinning whole-cell behavior. While the nucleoid is confined to the center (gold region), translation occurs in the nucleoid-excluded perimeter, where tRNA complexes (red or green) search for matching ribosomes (purple). The search is a complex combinatoric and transport process that spans both regions and involves cell-scale changes in spatial organization as growth rates change [123] (figure is adapted from [3], with permission).