that D$_{eff}$/D$_{1}$ should be given by: where we have substituted the Stokes-Einstein relation ( D$_{1}$ = k$_{B}$T 6 πR 1 $_{η}$) and the relation µ = k$_{B}$Tλ $^{2}$/η into the expression given in Eq.(7) of Ref [11]. In our MC simulations, the imbalance of solute collisions across the chucker surface is expected to produce a net force which corresponds to a prefactor A = (4 / 3) πR 3 $_{1}$k$_{B}$ T in Eq.(2). This will produce a drift velocity v = f / (6 πηR$_{1}$ ) . Linearized theory, which accounts for solvent-colloid surface interactions, predicts a colloid velocity v$_{s}$ = − k$_{B}$Tλ $^{2}$∇ c/η [11]. Matching these two rela- tions, we find that our MC simulations have an effective λ value λ $_{=}$√$_{2}$$_{R}$$_{1}$$_{/}$$_{3}$$_{. Substituting}$ this into Eq.(7), we obtain a prediction for D$_{eff}$ in our MC simulations. The inset to Figure 5 shows a comparison between this prediction and our MC data, for small chucking rates. For R$_{1}$/R$_{2}$ = 100 , we obtain an excellent fit, whereas for the larger solute particles, R$_{1}$/R$_{2}$ = 10 , the fit is much less convincing. We will revisit the effect of solute size in Figure 7. We note that Golestanian [11] also predicts a regime in which the mean square displacement 〈 r $^{2}$〉 is proportional to t 3 / $^{2}$, for timescales between the inertial and diffusive regimes, for an isotropic chucker. We do not observe this regime in our simulations: for ratios of R$_{1}$/R$_{2}$ ≥ 5 the mean square displacement is linear in time. To further investigate the relationship between chucker diffusion and solute concentration gradient, we performed additional MC simulations for a passive colloid, of radius R$_{1}$ , in a constant density gradient of Asakura-Oosawa solute particles (Fig.6). In order to maintain a constant density in steady state, we introduced a planar source of solute particles (of radius R$_{2}$ ) at the top of the simulation box, and a planar absorbing sink at the bottom. Solute particles are randomly seeded on the source plane at a constant rate k$_{c}$ . The analysis in Ref. [12] can be generalised to yield the following prediction for the steady state velocity of a colloidal particle in a constant concentration gradient (neglecting hydrodynamic effects): where the top and bottom planes have a surface area of L $^{2}$, and we have again used the expectation that λ $_{= (}$√$_{2}$$_{/}$$_{3)}$$_{R}$$_{1}$ in our simulations. Figure 7 shows a comparison between the analytical prediction (8) and our simulation results, for R$_{1}$/R$_{2}$ = 10 (panel a) and R$_{1}$/R$_{2}$ = 100 (panel b). As in the inset to Figure 5, D$_{eff}$ D$_{1}$ = 1 + [ 1 . 17810 ( λ R$_{1}$ ) $^{4}$( 3 π ) ] ( k$_{c}$R 2 D$_{1}$ ) (7) v = 4 πR$_{2}$R 2 $_{1}$k$_{c}$ 3 L 2 (8) 11