Enhanced bacterial swimming speeds in macromolecular polymer solutions

Abstract

The locomotion of swimming bacteria in simple Newtonian fluids can successfully be described within the framework of low Reynolds number hydrodynamics [1]. The presence of polymers in biofluids generally increases the viscosity, which is expected to lead to slower swimming for a constant bacterial motor torque. Surprisingly, however, several experiments have shown that bacterial speeds increase in polymeric fluids [2][3][4][5], and there is no clear understanding why. Therefore we perform extensive coarse-grained simulations of a bacterium swimming in explicitly modeled solutions of macromolecular polymers of different lengths and densities. We observe an increase of up to 60% in swimming speed with polymer density and demonstrate that this is due to a depletion of polymers in the vicinity of the bacterium leading to an effective slip. However this in itself cannot predict the large increase in swimming velocity: coupling to the chirality of the bacterial flagellum is also necessary.Microorganisms typically move through complex biological environments which contain high-molecular weight polymeric material. Prominent examples include the extracellular matrix, mucosal barriers and polymer-aggregated marine snow [6,7]. Many explanations have been proposed to describe the increase in speed of bacteria in such polymeric fluids, including viscoelastic effects [5], local shear thinning [4], local shear-induced viscosity gradients [8], polymer depletion [9] or modelling the polymers as a gel-forming network [3,10] or a porous medium [11]. Experiments do not, however, yet have the resolution to distinguish between the different theories. Therefore there is a vital role for detailed numerical models that will allow us to understand motion through biologically relevant but rheologically complex, fluids. Drawing on ideas from simulations of polymer hydrodynamics [12] and of bacterial locomotion in Newtonian fluids (see for example ) we simulate a bacterium moving in suspensions of different polymer density (Figure 1 and Supplementary Movie 1). Hence we reproduce, and explain, the enhanced swimming speed.Swimming bacteria such as Pseudomponas aeruginosa, Helicobacter pylori or Eschericia coli rotate helical flagella attached to their cell body to create a thrust force which moves them forwards [1]. Inspired by the biological swimmers we employ a model bacterium consisting of an elongated cell body of length 2b and width 2a connected to a stiff helical flagellum of radius R (Fig. 1a). Our swimmer is driven by applying a constant motor torque T to the flagellum and an opposing torque −T to the body (Fig. 1b). This results in the body rotating with angular velocity Ω, and the counter-rotating flagellum with angular velocity ω (Fig. 1a) which drives the model cell to swim forwards at an average speed V .The fluid consists of a Newtonian background fluid at viscosity η 0 and temperature T modelled by multiparticle collision dynamics (MPCD, see Methods). This is coupled to an ensemble of coarse-grained polymers that are modelled as...

Computational models for active matter

“…Experiments of E. coli in concentrated polymer solutions indicate that peculiarities of flagellated locomotion are indeed due to the fast-rotating flagellum, giving rise to a lower local viscosity in its vicinity [103]. A detailed modeling and simulation of bacteria in dense polymer solutions, with explicit polymers, reaches similar conclusions, specifically a depletion of polymers at the flagellum is obtained [104]. An increased swim speed with increasing polymer density is predicted, due to a nonuniform distribution of polymers in the vicinity of the bacterium, leading to an apparent slip, in combination with the chirality of the bacterial flagellum [104].…”

Viscoelastic propulsion of a rotating dumbbell

“…Some changes in the swimming motion can be in part explained by the ability of the cells to push against the microstructure [31][32][33] and by the presence of length scales in the fluid comparable to, or larger than, the cell size [34]. A boost in locomotion is also possible due to polymer depletion near the swimmer and resulting apparent fluid slip [35,36]. A commonly used model for microorganism locomotion is the spherical squirmer [37] whose swimming has been shown to be significantly affected by viscoelasticity [38,39].…”

Mesoscale modelling of polymer aggregate digestion

“…The MPCD implementation used here follows Refs. [28,29], see references therein, in particular the work of Gompper et al [30]. The main difference with the approach from Ref.…”

“…where v cell is the centre-of-mass velocity of the cell, v rand is a random velocity obeying the Maxwell-Boltzmann distribution at temperature T , and the terms v P and v L ensure that linear and angular momentum are conserved [28]. The parameters for the MPCD fluid are the same as in Ref.…”

“…The parameters for the MPCD fluid are the same as in Ref. [28] and correspond to a viscous flow with a low Reynolds number: the number density of the fluid particles is ρ MPCD = 10/σ 3 , the time step is δt = 0.02 mσ 2 /(k B T ), m being the mass of an individual particle. The quantity τ 0 = mσ 2 /(k B T ) has the dimension of time, and throughout the text, it is the implied time unit wherever no other is specified.…”