Width Scaling of an Interface Constrained by a Membrane

Abstract

We investigate the shape of a growing interface in the presence of an impenetrable moving membrane. The two distinct geometrical arrangements of the interface and membrane, obtained by placing the membrane behind or ahead of the interface, are not symmetrically related. On the basis of numerical results and an exact calculation, we argue that these two arrangements represent two distinct universality classes for interfacial growth: while the well-established Kardar-Parisi-Zhang (KPZ) growth is obtained in the "ahead" arrangement, we find an arrested KPZ growth with a smaller roughness exponent in the "behind" arrangement. This suggests that the surface properties of growing cell membranes and expanding bacterial colonies, for example, are fundamentally distinct.

Solvable model of a many-filament Brownian ratchet

“…We define B as a κ-independent constant. We repeat this method to extract the κ-dependence from the (N − 1)dimensional integrals in (9) to give an overall scaling for the membrane velocity…”

“…In mathematical terms, the standard Brownian ratchet may be formulated as a drift-diffusive problem for a single spatial co-ordinate [5]. More recently many-filament systems involving several spatial co-ordinates have been introduced and studied [6][7][8][9][10][11][12][13][14][15][16][17][18].…”

“…The model that we set out here falls into a class that we refer to as pure ratchets [14]. The defining property of these ratchets is that the membrane moves under thermal fluctuations, and the network grows quickly to occupy any space left vacant (see [5][6][7][8][9] for examples). The key phenomenon that can arise from these pure ratchets, then, is that a membrane that has a natural drift in one direction, may have a net movement in the opposite direction, arising exclusively from steric interactions and thermal fluctuations.…”

Undulation of a moving fluid membrane pushed by filament growth

“…However, membrane fluctuations have not yet been studied. In most studies reported in the literature [16][17][18][19][20][21][22][23], the membrane is modeled as a flat rigid surface; thus, no fluctuations are accounted for. Although the membrane fluctuations are assumed to be a Gaussian distribution of the membrane height in Ref.…”

“…For example, actin filaments grow at the front side of crawling cells and push the membrane forward. This membrane motion has been intensively studied by Brownian ratchet theories and simulations [15][16][17][18][19][20][21][22][23][24][25][26][27].…”