Cell migration through 3D extracellular matrices is critical to the normal development of tissues and organs and in disease processes, yet adequate analytical tools to characterize 3D migration are lacking. Here, we quantified the migration patterns of individual fibrosarcoma cells on 2D substrates and in 3D collagen matrices and found that 3D migration does not follow a random walk. Both 2D and 3D migration features a non-Gaussian, exponential mean cell velocity distribution, which we show is primarily a result of cellto-cell variations. Unlike in the 2D case, 3D cell migration is anisotropic: velocity profiles display different speed and selfcorrelation processes in different directions, rendering the classical persistent random walk (PRW) model of cell migration inadequate. By incorporating cell heterogeneity and local anisotropy to the PRW model, we predict 3D cell motility over a wide range of matrix densities, which identifies density-independent emerging migratory properties. This analysis also reveals the unexpected robust relation between cell speed and persistence of migration over a wide range of matrix densities.theory | 3D motility | cancer R andom walks are ubiquitous in biology (1). In particular, the motility of bacteria and eukaryotic cells in the absence of symmetry-breaking gradients has long been described in terms of random walk statistics. Eukaryotic cell migration is a complex process that is a tightly regulated and critical to the normal development of organs and tissues (2-4). Cell migration is activated in a wide range of human diseases, including cancer metastasis (5, 6), immunological responses (7), and wound healing (8). Most of what we know about eukaryotic cell migration at a mechanistic molecular level has stemmed from well-controlled studies of cell migration on flat dishes (i.e., 2D environment). However, cell migration in vivo often forces cells to remodel, exert pulling forces on, and move through a 3D collagen I-rich matrix. Recent work has demonstrated that mechanisms of 3D migration are often different from their 2D counterparts (9-15). Migration on 2D dishes, which induces a basal-apical polarization of the cell, is driven by actomyosin contractility of stress fibers between large focal adhesions and the formation of a wide lamellipodium terminated by thin filopodial protrusions at the leading cellular edge (4, 16). The same cells in collagen-rich 3D matrix do not display a lamellipodium or filopodia. Instead, they display highly dendritic pseudopodial protrusions controlled by distinct proteins that rely both on acto-myosin contractility and microtubule assembly/disassembly dynamics (11, 17). 3D cell migration depends on the expression of metalloproteinases (MMPs), which are dispensable in 2D migration, and physical properties of the 3D matrix (18), such as pore size (6). Recent work has also shown how cancer cells in 3D can alternate between a mesenchymal and an amoeboid migratory phenotype depending on the physical properties of the matrix (19,20) and MMP inhibition (17...

Cell migration through three-dimensional (3D) extracellular matrices is critical to the normal development of tissues and organs and in disease processes, yet adequate analytical tools to characterize 3D migration are lacking. The motility of eukaryotic cells on 2D substrates in the absence of gradients has long been described using persistent random walks (PRW). Recent work shows that 3D migration is anisotropic and features an exponential mean cell velocity distribution, rendering the PRW model invalid. Here we present a protocol for the analysis of 3D cell motility using the anisotropic persistent random walk model. The software, implemented in MATLAB, enables statistical profiling of experimentally observed 2D and 3D cell trajectories and extracts the persistence and speed of cells along primary and non-primary directions and an anisotropic index of migration. Basic computer skills and experience with MATLAB software are recommended for successful use of the protocol. This protocol is highly automated and fast, taking less than 30 minutes to analyze trajectory data per biological condition.

Cells often migrate in vivo in an extracellular matrix that is intrinsically three-dimensional (3D) and the role of actin filament architecture in 3D cell migration is less well understood. Here we show that, while recently identified linkers of nucleoskeleton to cytoskeleton (LINC) complexes play a minimal role in conventional 2D migration, they play a critical role in regulating the organization of a subset of actin filament bundles – the perinuclear actin cap - connected to the nucleus through Nesprin2giant and Nesprin3 in cells in 3D collagen I matrix. Actin cap fibers prolong the nucleus and mediate the formation of pseudopodial protrusions, which drive matrix traction and 3D cell migration. Disruption of LINC complexes disorganizes the actin cap, which impairs 3D cell migration. A simple mechanical model explains why LINC complexes and the perinuclear actin cap are essential in 3D migration by providing mechanical support to the formation of pseudopodial protrusions.

Spontaneous molecular oscillations are ubiquitous in biology. But to our knowledge, periodic cell migratory patterns have not been observed. Here we report the highly regular, periodic migration of cells along rectilinear tracks generated inside three-dimensional matrices, with each excursion encompassing several cell lengths, a phenotype that does not occur on conventional substrates. Short hairpin RNA depletion shows that these one-dimensional oscillations are uniquely controlled by zyxin and binding partners α-actinin and p130Cas, but not vasodilator-stimulated phosphoprotein and cysteine-rich protein 1. Oscillations are recapitulated for cells migrating along one-dimensional micropatterns, but not on two-dimensional compliant substrates. These results indicate that although two-dimensional motility can be well described by speed and persistence, three-dimensional motility requires two additional parameters, the dimensionality of the cell paths in the matrix and the temporal control of cell movements along these paths. These results also suggest that the zyxin/α-actinin/p130Cas module may ensure that motile cells in a three-dimensional matrix explore the largest space possible in minimum time.

Arp2/3 is a protein complex that nucleates actin filament assembly in the lamellipodium in adherent cells crawling on planar 2-dimensional (2D) substrates. However, in physiopathological situations, cell migration typically occurs within a 3-dimensional (3D) environment, and little is known about the role of Arp2/3 and associated proteins in 3D cell migration. Using time resolved live-cell imaging and HT1080, a fibrosarcoma cell line commonly used to study cell migration, we find that the Arp2/3 complex and associated proteins N-WASP, WAVE1, cortactin, and Cdc42 regulate 3D cell migration. We report that this regulation is caused by formation of multigeneration dendritic protrusions, which mediate traction forces on the surrounding matrix and effective cell migration. The primary protrusions emanating directly from the cell body and prolonging the nucleus forms independent of Arp2/3 and dependent on focal adhesion proteins FAK, talin, and p130Cas. The Arp2/3 complex, N-WASP, WAVE1, cortactin, and Cdc42 regulate the secondary protrusions branching off from the primary protrusions. In 3D matrices, fibrosarcoma cells as well as migrating breast, pancreatic, and prostate cancer cells do not display lamellipodial structures. This study characterizes the unique topology of protrusions made by cells in a 3D matrix and show that these dendritic protrusions play a critical role in 3D cell motility and matrix deformation. The relative contribution of these proteins to 3D migration is significantly different from their role in 2D migration.