rithm [34], in which the chucker is represented as a point particle and the solute particles are represented as a space and time-dependent density field, the gradient of which provides a force on the chucker. In a mean-field approach, we assume that the density of solute parti- cles can be obtained from the time-dependent analytical solution of the free-space diffusion equation with a point source (the chucker), integrated over the previous trajectory of the chucker. This approach assumes that the thermal fluctuations of the chucker are slower with respect to the solute diffusion, and further neglects thermal fluctuations in the solute density. A similar approach has recently been used to simulate a microorganism performing chemotaxis by Sengupta et al [7]. In our Langevin dynamics simulations, the force f on the “point chucker” depends on the concentration profile c ( r ) of the solute according to [12, 28, 30, 35]: where the prefactor A is determined by the physical process by which an osmotic pressure gradient is converted into colloidal motion. This force produces a drift velocity v which is related to the force f by f = k$_{B}$T v /D$_{1}$ = 6 πηR$_{1}$ v . By tuning the prefactor A , we can tune the drift velocity v . If the solvent-chucker interactions were to be properly taken into account, linearised theory suggests that the drift velocity would be given by Golestanian’s relation v$_{s}$ = − k$_{B}$T λ $^{2}$∇ c/η [11], where (as discussed earlier) λ is related to the lengthscale of solvent-colloid interactions. By combining this relation with Eq.(2), we can obtain an “effective” value of λ for our Langevin dynamics simulations: λ = √ A/ (6 πR$_{1}$k$_{B}$T ) . A full treatment, including solvent, with this value of λ , would give the same drift velocity as our Langevin dynamics simulations with prefactor A . By varying the prefactor A , we can vary the effective λ value. By choosing λ values corresponding to realistic solvent-colloid interaction lengths, we should obtain results closer to those that would be expected for a full treatment including solvent. In contrast, in our Monte Carlo simulations, the value of λ is fixed. Here, the net force on the chucker produced by the imbalance of solute collisions across the colloid surface [13] corresponds to a value A = (4 / 3) πR 3 $_{1}$k$_{B}$ T , or alternatively an effective λ = √$_{2}$$_{R}$$_{1}$$_{/}$$_{3}$$_{.}$ The concentration profile c ( r ) is not represented explicitly in our simulations but is cal- culated analytically from the time history of the position of the point chucker: f = − A ∇ c ( r ) (2) c ( r ) = k$_{c}$ ∫ t 0 dt $^{′}$G ( r − r $^{′}$, t − t $^{′}$) , (3) 7