This trend is due to the increased mass of the larger particle, which gives rise to a (a function of and (a function of and refers to the track length in seconds in this contextthe settling displacement will eventually overtake the random Brownian displacement. of each particle. It was found that the aggregates were highly porous with density decreasing from 1.080 g/cm3 to 1 1.028 g/cm3 as the size increased from 1.37 m to 4.9 m. aggregate9964 Open in a separate window Track Analysis a. Determination of hydrodynamic diameter from Brownian motion The analysis to determine particle size is similar to what is used in nanoparticle tracking analysis (NTA); the main difference is that the particles coordinates are based on the particle image, rather than the light scattering distribution. Tracks were analyzed using a mean-square-displacement (MSD) algorithm to calculate a hydrodynamic diameter23-25 and a settling velocity. The program is supplied in the Supplementary Information. For each particle, the MSD was calculated over the first time intervals between measurements25. For this work, was chosen as 10, which DB04760 gave good results for particle diameters ranging from 1 m to 10 m. For a two-dimensional diffusion process, the MSD scales according to: is the two-dimensional position of the particle and is the timestamp for the position measurement. A linear fit to the results from Equation 2 is used to extract the diffusion coefficient, using the Stokes-Einstein equation is DB04760 the difference in density between the particle and buffer, is the viscosity, is the gravitation constant 9.8 m/s2, is obtained from Equation (3), and the velocity was obtained from a linear fit of the vertical position as a function of time. Deviations from Stokes Law due to wall effects and non-sphericity can be accounted for by generalizing Equations 3 and 4 cases to: (in Equation 6) represents the diameter of an Rabbit polyclonal to EPHA4 equivalent volume sphere, is the wall factor 13,26 approximated by a model in which particles are falling midway between two semi-infinite walls separated by a distance is the dynamic shape factor27 which can be approximated as, and the equivalent circular diameter of the particles projection normal to its motion and the equivalent diameter of a sphere with the same surface area as the particle, respectively. The wall factor was included in our calculations, and found to have a 10 percent effect for particles with 5 m, with reduced effect as decreases. The value of was estimated for a variety of nonspherical shapes. For prolate/oblate spheroids with a 0.5 aspect ratio, = 0.96 if the long axis is parallel to the flow, and = 1.07 if the long axis is perpendicular to the flow. Particles were observed to tumble during sedimentation, so is effectively averaged over the path. Because the vast majority of particles had an aspect ratio 0.5, we did not include corrections for shape in the analysis. RESULTS & DISCUSSION Figure 2 shows examples of tracks obtained for the 1 m to 5 m diameter microspheres (Figure 2 a-d) and for the protein aggregates (Figure 2 e). For the 1 m diameter microspheres in Figure 2 a, a selection of tracks longer than 4000 s is shown. These tracks exhibit substantial diffusive motion in combination with a net vertical displacement resulting from sedimentation. As the microsphere size increases, the net diffusive motion is reduced compared to the net vertical motion. For the 5 m diameter microspheres in Figure 2 dwhere tracks longer than 300 s are DB04760 shownthe motion is primarily settling with a small amount of diffusive motion still evident in the track. This trend is due to the increased mass of the larger particle, which gives rise to a (a function of and (a function of and refers to the track length in seconds in this contextthe settling displacement will eventually overtake the random Brownian displacement. Nevertheless, the medians of these distributions are meaningful and yield the average settling velocity for the 1 m diameter microspheres. For the 5 m diameter microspheres, the increased mass and settling velocity reduces the time that a particular microsphere is in the field of view. In addition, the Brownian motion component is smaller in each time step, so there is less information to calculate the MSD diameter. This reduced information results in a larger MSD diameter spread, compared to the 1 m diameter microspheres DB04760 (Figure 4 a) and set a diameter value of 5 m as an upper limit for MSD analysis of size in this experimental arrangement. We note that NTA and dynamic light scattering (DLS) face similar difficulties at larger sizes. Brownian motion has little effect on the net vertical displacement, resulting.