Three-dimensional cell migration does not follow a random walk

Abstract

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...

Intratumoral oxygen gradients mediate sarcoma cell invasion

“…The images were analyzed using Imaris spot analysis software (Imaris 8.1; Bitplane) to track the time-dependent mobility. The 3D migration analysis was performed following the strategy developed by Wirtz and coworkers (29,30). A minimum of 100 individual cells at each point were tracked to generate x, y, and z coordinates at each time point.…”

“…By choosing the time frame with the most visible cells we could maximize the sample size of cells that could be analyzed. Finally, velocity and speed profiles, MSDs, and trajectory plots were calculated using code adapted from Wirtz and coworkers (29,30) for triplicate tracking trials (n = 3). The statistical analysis was performed using MATLAB (Mathworks, Inc.) to calculate the mean, SD, and SE of the mean.…”

“…Graphed data are presented as average ± SD. Significance levels were set at *P < 0.05,^P < 0.01, and # P < 0.001 (29,30).…”

Simulating tissue mechanics with agent-based models: concepts, perspectives and some novel results

“…Some authors use the inertia term m i dv i /dt to mimic the effect of persistence [28] while in principle it can be directly simulated using a memory term. In this case, Γ cx i j v k (x ∈ {c, s}, k ∈ {i, j}) has to be replaced by…”

“…During metastasis in cancer, cells detach from the tumor and migrate through the stroma. Studies have revealed that cells remodel the matrix around them [26,27], thereby possibly creating trails for other cells [28,29].…”