Polymer science and biology: structure and dynamics at multiple scales

Abstract

I give a brief, biased survey of some recent problems in molecular and cell biology from the perspective of physical science, with a few answers, but a great many questions, challenges and opportunities.

Fig. 1

Morphology of ordered fibrils. (a) A physical model and a schematic of a two-fibril adherent bundle. Any inherent curvature in the bundle leads to a mismatch in the strains experienced by the two filaments which have different path lengths. This leads to a set of periodic kinks, such as that highlighted in red. The schematic shows that the kink size depends on a characteristic ratio of the length of a subunit and its diameter, L/D. In bundles that are non-planar, the filaments can twist relative to each other and this allows them to further increase their adhesion. (b) In a bundle with 4 filaments which can twist relative to each other, the symmetry of packing leads to three possible states, so that the bundle can switch from one to another even if its central axis is straight. This can lead to a periodic pattern of defects as the filaments switch their relative positions at a cross-section. (c) In a bundle with many filaments, so that n ≫ 1, one may be able to use a continuum theory that accounts for the shear, stretch, twist and bending.

Fig. 2

Mechanics of disordered networks. (a) A two-dimensional network of fibres, with the average coordination number (see text) z < z_c, so that the network is floppy, is subject to a strain at the boundaries. As seen, this leads to the shrinking of the network in one direction and an extension in the direction of the applied strain, coupled to an orientational ordering of the filaments. (b) A plot of the nominal stress (using arbitrary units) as a function of the nominal strain shows that the collective response of the network leads to no stress until the strain reaches a critical value γ*. This is because of the presence of floppy modes that allow for the rotation of parts of the network to accommodate the boundary strains up to a critical threshold. Only beyond this critical threshold does the network deform with a finite resistance. The springs are all assumed to be harmonic, i.e. they are linear, with a spring constant inversely proportional to their rest length. The simulations were carried out using a damped molecular dynamics method.

Fig. 3

(a) A plan view of an animal cell (Wikipedia) stained to show some of the cytoskeletal proteins such as microtubules (green), and actin (red). The characteristic size of the cell is about 10 µm, and clearly shows that it is made of a heterogeneous network similar to that shown in Fig. 2. Water makes up as much as 70–80% of a cell’s volume. (b) A minimal model of the cell that accounts for the fluid and solid phases of the cytoplasm is that of a soft, fluid-infiltrated sponge. Here, to understand the response of such a system, we assume that the cytoplasmic gel is confined to a rigid chamber and compressed by a porous piston, with u(x, t) the displacement of a cross-section at a location x at time t.

Fig. 4

(a) A view of normal (disc-shaped) and sickled (elongated) red blood cells (Wikipedia). The diameter of normal red blood cells is 8 µm, while the length of the sickled cells can be more than twice as large. As a consequence, sickled cells cannot flow through narrow capillaries. This vaso-occlusive process leads to hypoxia in downstream tissues, triggering the main symptoms of the disease. (b) A simple view of the jamming process can be characterized in terms of relation between the flow velocity of the red blood suspension U as a function of the cell volume fraction φ. At low volume fractions the velocity is a constant that is determined by the balance between the driving pressure gradient and the viscous resistance, while as the volume fraction approaches an effective close-packing fraction φ_m, the suspension viscosity increases dramatically and its velocity vanishes. This leads to a jam not unlike those observed in traffic flows.