Single-particle tracking (SPT) is of growing importance in the biophysical community. It is used to investigate processes such as drug and gene delivery, viral uptake, intracellular trafficking or membrane-bound protein mobility. Traditionally, SPT is performed in two dimensions (2D) because of its technical simplicity. However, life occurs in three dimensions (3D) and many methods have been recently developed to track particles in 3D. Now, is the third dimension worth the effort? Here we investigate the differences between the 2D and 3D analyses of intracellular transport with the 3D development of a time-resolved mean square displacement (MSD) analysis introduced previously. The 3D trajectories, and the 2D projections, of fluorescent nanoparticles were obtained with an orbital tracking microscope in two different cell types: in Dictyostelium discoideum ameba and in adherent, more flattened HuH-7

Intracellular transport is a complex interplay of ballistic transport along filaments and of diffusive motion, reliably delivering material and allowing for cell differentiation, migration, and proliferation. The diffusive regime, including subdiffusive, Brownian, and superdiffusive motion, is of particular interest for inferring information about the dynamics of the cytoskeleton morphology during intracellular transport. The influence of dynamic cytoskeletal states on intracellular transport are investigated in Dictyostelium discoideum cells by single particle tracking of fluorescent nanoparticles, to relate quantitative motion parameters and intracellular processes before and after cytoskeletal disruption. A local mean-square displacement (MSD) analysis separates ballistic motion phases, which we exclude here, from diffusive nanoparticle motion. In this study, we focus on intracellular subdiffusion and elucidate lag-time dependence, with particular focus on the impact of cytoskeleton compartments like microtubules and actin filaments. This method proves useful for binary motion state distributions. Experimental results are compared to simulations of a data-driven Langevin model with finite velocity correlations that captures essential statistical features of the local MSD algorithm. Specifically, the values of the mean MSD exponent and effective diffusion coefficients can be traced back to negative correlations of the motion's increments. We clearly identify both microtubules and actin filaments as the cause for intracellular subdiffusion and show that actin-microtubule cross talk exerts viscosifying effects at timescales larger than 0.2 s. Our findings might give insights into material transport and information exchange in living cells, which might facilitate gaining control over cell functions.

On flat substrates, several cell types exhibit amoeboid migration, which is characterized by restless stochastic successions of pseudopod protrusions. The orientation and frequency of new membrane protrusions characterize efficient search modes, which can respond to external chemical stimuli as observed during chemotaxis in amoebae. To quantify the influence of mechanical stimuli induced by surface topography on the migration modes of the amoeboid model organism Dictyostelium discoideum, we apply high resolution motion analysis in microfabricated pillar arrays of defined density and geometry. Cell motion is analyzed by a two-state motility-model, distinguishing directed cellular runs from phases of isotropic migration that are characterized by randomly oriented cellular protrusions. Cells lacking myosin II or cells deprived of microtubules show significantly different behavior concerning migration velocities and migrational angle distribution, without pronounced attraction to pillars. We conclude that microtubules enhance cellular ability to react with external 3D structures. Our experiments on wild-type cells show that the switching from randomly formed pseudopods to a stabilized leading pseudopod is triggered by contact with surface structures. These alternating processes guide cells according to the available surface in their 3D environment, which we observed dynamically and in steady-state situations. As a consequence, cells perform ''home-runs'' in low-density pillar arrays, crawling from pillar to pillar, with a characteristic dwell time of $75 s. At the boundary between a flat surface and a 3D structured substrate, cells preferentially localize in contact with micropillars, due to the additionally available surface in the microstructured arrays. Such responses of cell motility to microstructures might open new possibilities for cell sorting in surface structured arrays.