Wei Wang

Eukaryotic cells generally sense chemical gradients using the binding of chemical ligands to membrane receptors. To perform chemotaxis effectively in different environments, cells need to adapt to different concentrations. We present a model of gradient sensing where the affinity of receptor-ligand binding is increased when a protein binds to the receptor's cytosolic side. This interior protein (allosteric factor) alters the sensitivity of the cell, allowing the cell to adapt to different ligand concentrations. We propose a reaction scheme where the cell alters the allosteric factor's availability to adapt the average fraction of bound receptors to 1/2. We calculate bounds on the chemotactic accuracy of the cell and find that the cell can reach near-optimal chemotaxis over a broad range of concentrations. We find that the accuracy of chemotaxis depends strongly on the diffusion of the allosteric compound relative to other reaction rates. From this, we also find a tradeoff between adaptation time and gradient sensing accuracy.

Groups of cells, including clusters of cancerous cells, multicellular organisms, and developing organs, may both grow and break apart. What physical factors control these fractures? In these processes, what sets the eventual size of clusters? We first develop a one-dimensional framework for understanding cell clusters that can fragment due to cell motility using an active particle model. We compute analytically how the break rate of cell-cell junctions depends on cell speed, cell persistence, and cell-cell junction properties. Next, we find the cluster size distributions, which differ depending on whether all cells can divide or only the cells on the edge of the cluster divide. Cluster size distributions depend solely on the ratio of the break rate to the growth rate-allowing us to predict how cluster size and variability depend on cell motility and cell-cell mechanics. Our results suggest that organisms can achieve better size control when cell division is restricted to the cluster boundaries or when fracture can be localized to the cluster center. Additionally, we derive a universal survival probability for an intact cluster S(t)=e^{-k_{d}t} at steady state if all cells can divide, which is independent of the rupture kinetics and depends solely on the cell division rate k_{d}. Finally, we further corroborate the one-dimensional analytics with two-dimensional simulations, finding quantitative agreement with some-but not all-elements of the theory across a wide range of cell motility. Our results link the general physics problem of a collective active escape over a barrier to size control, providing a quantitative measure of how motility can regulate organ or organism size.

When cells in a primary tumor work together to invade into nearby tissue, this can lead to cell dissociations—cancer cells breaking off from the invading front—leading to metastasis. What controls the dissociation of cells and whether they break off singly or in small groups? Can this be determined by cell-cell adhesion or chemotactic cues given to cells? We develop a physical model for this question, based on experiments that mimic aspects of cancer cell invasion using microfluidic devices with microchannels of different widths. Experimentally, most dissociation events (“ruptures”) involve single cells breaking off, but we observe some ruptures of large groups ( ∼ 20 cells) in wider channels. The rupture probability is nearly independent of channel width. We recapitulate the experimental results with a phase-field cell motility model by introducing three different cell states (follower, guided, and high-motility “leader” cells) based on their spatial position. These leader cells may explain why single-cell rupture is the universal most probable outcome. Our simulation results show that cell-channel adhesion is necessary for cells in narrow channels to invade, and strong cell-cell adhesion leads to fewer but larger ruptures. Chemotaxis also influences the rupture behavior: Strong chemotaxis strength leads to larger and faster ruptures. Finally, we study the relationship between biological jamming transitions and cell dissociations. Our results suggest unjamming is necessary but not sufficient to create ruptures.

When cells in a primary tumor work together to invade into nearby tissue, this can lead to cell dissociations—cancer cells breaking off from the invading front—leading to metastasis. What controls the dissociation of cells, and whether they break off singly or in small groups? Can this be determined by cell-cell adhesion or chemotactic cues given to cells? We develop a physical model for this question, based on experiments that mimic aspects of cancer cell invasion using microfluidic devices with microchannels of different widths. Experimentally, most dissociation events (“ruptures”) involve single cells breaking off, but we observe some ruptures of large groups ( ∼ 20 cells) in wider channels. The rupture probability is nearly independent of channel width. We recapitulate the experimental results with a phase field cell motility model by introducing three different cell states (follower, guided, and high-motility metabolically active leader cells) based on their spatial position. These leader cells may explain why single-cell rupture is the universal most probable outcome. Our simulation results show that cell-channel adhesion is necessary for cells in narrow channels to invade, and strong cell-cell adhesion leads to fewer but larger ruptures. Chemotaxis also influences the rupture behavior: Strong chemotaxis strength leads to larger and faster ruptures. Finally, we study the relationship between biological jamming transitions and cell dissociations. Our results suggest unjamming is necessary but not sufficient to create ruptures.

Cells that collide with each other repolarize away from contact, in a process called contact inhibition of locomotion (CIL), which is necessary for correct development of the embryo. CIL can occur even when cells make a micron-scale contact with a neighbor-much smaller than their size. How precisely can a cell sense cell-cell contact and repolarize in the correct direction? What factors control whether a cell recognizes it has contacted a neighbor? We propose a theoretical model for the limits of CIL where cells recognize the presence of another cell by binding the protein ephrin with the Eph receptor. This recognition is made difficult by the presence of interfering ligands that bind nonspecifically. Both theoretical predictions and simulation results show that it becomes more difficult to sense cell-cell contact when it is difficult to distinguish ephrin from the interfering ligands, or when there are more interfering ligands, or when the contact width decreases. However, the error of estimating contact position remains almost constant when the contact width changes. This happens because the cell gains spatial information largely from the boundaries of cell-cell contact. We study using statistical decision theory the likelihood of a false-positive CIL event in the absence of cell-cell contact, and the likelihood of a false negative where CIL does not occur when another cell is present. Our results suggest that the cell is more likely to make incorrect decisions when the contact width is very small or so large that it nears the cell's perimeter. However, in general, we find that cells have the ability to make reasonably reliable CIL decisions even for very narrow (micron-scale) contacts, even if the concentration of interfering ligands is ten times that of the correct ligands.