Long-distance intracellular axonal transport is predominantly microtubule-based, and its impairment is linked to neurodegeneration. In this study, we present theoretical arguments that suggest that near the axon boundaries (walls), the effective viscosity can become large enough to impede cargo transport in small (but not large) caliber axons. Our theoretical analysis suggests that this opposition to motion increases rapidly as the cargo approaches the wall. We find that having parallel microtubules close enough together to enable a cargo to simultaneously engage motors on more than one microtubule dramatically enhances motor activity, and thus minimizes the effects of any opposition to transport. Even if microtubules are randomly placed in axons, we find that the higher density of microtubules found in small-caliber axons increases the probability of having parallel microtubules close enough that they can be used simultaneously by motors on a cargo. The boundary effect is not a factor in transport in large-caliber axons where the microtubule density is lower.

While tumor infiltration by CD8+ T cells is now widely accepted to predict outcomes, the clinical significance of intratumoral B cells is less clear. We hypothesized that spatial distribution rather than density of B cells within tumors may provide prognostic significance. We developed statistical techniques (fractal dimension differences and a box-counting method ‘occupancy’) to analyze the spatial distribution of tumor-infiltrating lymphocytes (TILs) in human triple-negative breast cancer (TNBC). Our results indicate that B cells in good outcome tumors (no recurrence within 5 years) are spatially dispersed, while B cells in poor outcome tumors (recurrence within 3 years) are more confined. While most TILs are located within the stroma, increased numbers of spatially dispersed lymphocytes within cancer cell islands are associated with a good prognosis. B cells and T cells often form lymphocyte clusters (LCs) identified via density-based clustering. LCs consist either of T cells only or heterotypic mixtures of B and T cells. Pure B cell LCs were negligible in number. Compared to tertiary lymphoid structures (TLS), LCs have fewer lymphocytes at lower densities. Both types of LCs are more abundant and more spatially dispersed in good outcomes compared to poor outcome tumors. Heterotypic LCs in good outcome tumors are smaller and more numerous compared to poor outcome. Heterotypic LCs are also closer to cancer islands in a good outcome, with LC size decreasing as they get closer to cancer cell islands. These results illuminate the significance of the spatial distribution of B cells and LCs within tumors.

SUMMARY Post-translational modification of tubulin provides differential functions to microtubule networks. Here, we address the role of tubulin acetylation on the penetrative capacity of cells undergoing radial intercalation, which is the process by which cells move apically, insert between outer cells, and join an epithelium. There are opposing forces that regulate intercalation, namely, the restrictive forces of the epithelial barrier versus the penetrative forces of the intercalating cell. Positively and negatively modulating tubulin acetylation in intercalating cells alters the developmental timing such that cells with more acetylation penetrate faster. We find that intercalating cells preferentially penetrate higher-order vertices rather than the more prevalent tricellular vertices. Differential timing in the ability of cells to penetrate different vertices reveals that lower-order vertices represent more restrictive sites of insertion. We shift the accessibility of intercalating cells toward more restrictive junctions by increasing tubulin acetylation, and we provide a geometric-based mathematical model that describes our results.

While the density of tumor-infiltrating lymphocytes (TILs) is now well known to correlate with clinical outcome, the clinical significance of spatial distribution of TILs is not well characterized. We have developed novel statistical techniques (including fractal dimension differences, a hotspot analysis, a box counting method that we call 'occupancy' and a way to normalize cell density that we call 'thinning') to analyze the spatial distribution (at different length scales) of various types of TILs in triple negative breast tumors. Consistent with prior reports, the density of CD20 + B cells within tumors is not correlated with clinical outcome. However, we found that their spatial distribution differs significantly between good clinical outcome (no recurrence within at least 5 years of diagnosis) and poor clinical outcome (recurrence with 3 years of diagnosis). Furthermore, CD20 + B cells are more spatially dispersed in good outcome tumors and are more likely to infiltrate into cancer cell islands. Lastly, we found significant correlation between the spatial distributions of CD20 + B cells and CD8 + (cytotoxic) T cells (as well as CD3 + T cells), regardless of outcome. These results highlight the significance of the spatial distribution of TILs, especially B cells, within tumors. Significance StatementImmune cells can fight cancer. For example, a patient has a good prognosis when a high density of killer T cells, a type of immune cell that can kill cancer cells, infiltrates into a tumor. However, there is no clear association between prognosis and the density of B cells, another type of immune cell, in a tumor. We developed several statistical techniques to go beyond cell density and look at the spatial distribution, i.e., the pattern or arrangement of immune cells, in tumors that have been removed from patients with triple negative breast cancer. We find that B cells and killer T cells tend to be more spread out in the tumors of patients whose cancer did not recur.

In developing tissues, cell polarization and proliferation are regulated by morphogens and signaling pathways. Cells throughout the Drosophila wing primordium typically show subcellular localization of the unconventional myosin Dachs on the distal side of cells (nearest the center of the disc). Dachs localization depends on the spatial distribution of bonds between the protocadherins Fat (Ft) and Dachsous (Ds), which form heterodimers between adjacent cells; and the Golgi kinase Four-jointed (Fj), which affects the binding affinities of Ft and Ds. The Fj concentration forms a linear gradient while the Ds concentration is roughly uniform throughout most of the wing pouch with a steep transition region that propagates from the center to the edge of the pouch during the third larval instar. Although the Fj gradient is an important cue for polarization, it is unclear how the polarization is affected by cell division and the expanding Ds transition region, both of which can alter the distribution of Ft-Ds heterodimers around the cell periphery. We have developed a computational model to address these questions. In our model, the binding affinity of Ft and Ds depends on phosphorylation by Fj. We assume that the asymmetry of the Ft-Ds bond distribution around the cell periphery defines the polarization, with greater asymmetry promoting cell proliferation. Our model predicts that this asymmetry is greatest in the radially-expanding transition region that leaves polarized cells in its wake. These cells naturally retain their bond distribution asymmetry after division by rapidly replenishing Ft-Ds bonds at new cell-cell interfaces. Thus we predict that the distal localization of Dachs in cells throughout the pouch requires the movement of the Ds transition region and the simple presence, rather than any specific spatial pattern, of Fj.