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Autologous chemotaxis at high cell density

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Abstract

Autologous chemotaxis, in which cells secrete and detect molecules to determine the direction of fluid flow, is thwarted at high cell density because molecules from other cells interfere with a given cell's signal. Using a minimal model of autologous chemotaxis, we determine the cell density at which sensing fails, and we find that it agrees with experimental observations of metastatic cancer cells. To understand this agreement, we derive a physical limit to autologous chemotaxis in terms of the cell density, the Péclet number, and the lengthscales of the cell and its environment. Surprisingly, in an environment that is uniformly oversaturated in the signaling molecule, we find that not only can sensing fail, but it can be reversed, causing backwards cell motion. Our results get to the heart of the competition between chemical and mechanical cellular sensing, and they shed light on a sensory strategy employed by cancer cells in dense tumor environments.

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... Computational research has also led to conflicting results. On one hand, Vennettilli et al. (2022) states that autologous chemotaxis fails at high density, and on the other hand, González and Mugler (2023) concludes that there exists a reversal density after which migration of a group of cells occurs collectively at a faster speed than individual migration. Most computational models of flow-induced autologous chemotaxis of multicellular systems assume that the cells are fixed (Khair 2021;Fleury et al. 2006;Fancher et al. 2020;Vennettilli et al. 2022) or that they coexist with the chemoattractant at the same spatial location (González and Mugler 2023;Waldeland and Evje 2018). ...
... On one hand, Vennettilli et al. (2022) states that autologous chemotaxis fails at high density, and on the other hand, González and Mugler (2023) concludes that there exists a reversal density after which migration of a group of cells occurs collectively at a faster speed than individual migration. Most computational models of flow-induced autologous chemotaxis of multicellular systems assume that the cells are fixed (Khair 2021;Fleury et al. 2006;Fancher et al. 2020;Vennettilli et al. 2022) or that they coexist with the chemoattractant at the same spatial location (González and Mugler 2023;Waldeland and Evje 2018). Here, we perform high-fidelity simulations that consider key mechanisms previously ignored in the literature, including that the diffusion of the chemoattractant is restricted to the extracellular space, the displacement of chemokine produced by cell motion (Zigmond 1974), and a realistic representation of the complex fluid flow pattern that occurs in the timeevolving extracellular matrix. ...
... p represents the fluid pressure, K is the permeability of the matrix, and is the dynamic viscosity of the interstitial fluid. We obtain the values of K from Fleury et al. (2006); Vennettilli et al. (2022), and of interstitial fluid from Rydholm et al. (2010); Yao et al. (2012); Chen et al. (1998) which is similar to that of water and ranges in the order 10 −3 − 10 −4 N s μm −2 . ...
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Cell migration via autologous chemotaxis in the presence of interstitial fluid flow is important in cancer metastasis and embryonic development. Despite significant recent progress, our understanding of flow-induced autologous chemotaxis of multicellular systems remains poor. The literature presents inconsistent findings regarding the effectiveness of collective autologous chemotaxis of densely packed cells under interstitial fluid flow. Here, we present a high-fidelity computational model to analyze the migration of multicellular systems performing autologous chemotaxis in the presence of interstitial fluid flow. Our simulations show that the details of the complex transport dynamics of the chemoattractant and fluid flow patterns that occur in the extracellular space, previously overlooked, are essential to understand this cell migration mechanism. We find that, although flow-induced autologous chemotaxis is a robust migration mechanism for individual cells, the cell-cell interactions that occur in multicellular systems render autologous chemotaxis an inefficient mechanism of collective cell migration. Our results offer new perspectives on the potential role of autologous chemotaxis in the tumor microenvironment, where fluid flow is an important modulator of transport.
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... Throughout this work we take precision to be the signal-to-noise ratio for a physical quantity that contains the directional information of the cue. For a chemical gradient, it suffices to consider the difference ∆n = n 2 − n 2 in the number of molecules detected by the two halves of the cell [ Fig. 2(a)] [7,23,24]. For slow flow, the mean of this difference scales as ∆n ∼ ϵνa 2 /D [23], where a is the cell lengthscale, ν is the molecule secretion rate, D is the molecular diffusion coefficient, and the flow speed v enters through the Peclét number ϵ = va/D ≪ 1 (see Table I in the Supplemental Material [25] for a list of all parameters in this work, as well as their experimentally measured values). ...
... For a chemical gradient, it suffices to consider the difference ∆n = n 2 − n 2 in the number of molecules detected by the two halves of the cell [ Fig. 2(a)] [7,23,24]. For slow flow, the mean of this difference scales as ∆n ∼ ϵνa 2 /D [23], where a is the cell lengthscale, ν is the molecule secretion rate, D is the molecular diffusion coefficient, and the flow speed v enters through the Peclét number ϵ = va/D ≪ 1 (see Table I in the Supplemental Material [25] for a list of all parameters in this work, as well as their experimentally measured values). This expression for ∆n follows from taking, in each half of the cell, the ratio of the rates of molecule gain due to secretion, and of loss due to diffusion and flow [23]. ...
Preprint
A cell routinely responds to one of many competing environmental cues. Does the cell have an intrinsic preference for that cue, or does that cue have the highest extrinsic information content? We introduce a theoretical framework to answer this fundamental question. We derive extrinsic detection limits for four types of directional cues -- external and self-generated chemical gradients, fluid flow, and contact inhibition of locomotion -- and thus predict extrinsic decision boundaries when these cues compete as pairs. Comparing the boundaries to published data from cell migration experiments quantitatively determines the degree to which cell decisions are intrinsic vs. extrinsic, revealing the extent of cells' autonomy and providing interpretation of their response networks.
... Experiments have found that autologous chemotaxis fails at high cell density and is overpowered by a competing, density-independent mechanosensing mechanism [3,6]. Theory [7] and simulations [3,7] suggest that the reason for the failure is that, at high cell density, molecules secreted by other cells interfere with a given cell's autologous gradient. Essentially, the signal from all cells produces a background concentration which reduces the relative gradient experienced by any cell. ...
... Experiments have found that autologous chemotaxis fails at high cell density and is overpowered by a competing, density-independent mechanosensing mechanism [3,6]. Theory [7] and simulations [3,7] suggest that the reason for the failure is that, at high cell density, molecules secreted by other cells interfere with a given cell's autologous gradient. Essentially, the signal from all cells produces a background concentration which reduces the relative gradient experienced by any cell. ...
... Essentially, the signal from all cells produces a background concentration which reduces the relative gradient experienced by any cell. A mean-field calculation based on this argument correctly predicts the cell density at which autologous chemotaxis fails [7]. ...
Preprint
Autologous chemotaxis is the process in which cells secrete and detect molecules to determine the direction of fluid flow. Experiments and theory suggest that autologous chemotaxis fails at high cell densities because molecules from other cells interfere with a given cell's signal. Based on observations of collective cell migration in diverse biological contexts, we propose a mechanism for cells to avoid this failure by forming a collective sensory unit. Formulating a simple physical model of collective autologous chemotaxis, we find that a cluster of cells can outperform single cells in terms of the detected anisotropy of the signal. We validate our results with a Monte-Carlo-based motility simulation, demonstrating that clusters chemotax faster than individual cells. Our simulation couples spatial and temporal gradient sensing with cell-cell repulsion, suggesting that our proposed mechanism requires only known, ubiquitous cell capabilities.
... We suspect that hydrodynamic effects may be less relevant to the case of folic acid but might be interesting for sensing concentrations of larger bodies such as extracellular vesicles (49). Applied largerscale fluid flow may also create interesting interactions between secreting and degrading cells (50). Our model describes Dictyostelium more in a test tube than in its natural environment of soil (39)-which we expect to be much more variable. ...
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Light-mediated release of signalling ligands, such as chemoattractants, growth factors and cytokines is an attractive strategy for investigation and therapeutic targeting of leukocyte communication and immune responses. We introduce a versatile optogenetic method to control ligand secretion, combining UV-conditioned ER-to-Golgi trafficking and a furin-processing step. As proof of principle, we achieved light-triggered chemokine secretion and demonstrated that a brief pulse of chemokine release can mediate a rapid flux of leukocyte contacts with target cells in vitro and in vivo. This approach opens new possibilities for dynamic investigation of leukocyte communication in vivo and may confer the potential to control the local release of soluble mediators in the context of immune cell therapies.
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Collective cell migration is a widespread biological phenomenon, whereby groups of highly coordinated, adherent cells move in a polarized fashion [1, 2]. This migration mode is a hallmark of tissue morphogenesis during development and repair and of solid tumor dissemination [1]. In addition to circulating as solitary cells, lymphoid malignancies can assemble into tissues as multicellular aggregates [3]. Whether malignant lymphocytes are capable of coordinating their motility in the context of chemokine gradients is, however, unknown. Here, we show that, upon exposure to CCL19 or CXCL12 gradients, malignant B and T lymphocytes assemble into clusters that migrate directionally and display a wider chemotactic sensitivity than individual cells. Physical modeling recapitulates cluster motility statistics and shows that intracluster cell cohesion results in noise reduction and enhanced directionality. Quantitative image analysis reveals that cluster migration runs are periodically interrupted by transitory rotation and random phases that favor leader cell turnover. Additionally, internalization of CCR7 in leader cells is accompanied by protrusion retraction, loss of polarity, and the ensuing replacement by new leader cells. These mechanisms ensure sustained forward migration and resistance to chemorepulsion, a behavior of individual cells exposed to steep CCL19 gradients that depends on CCR7 endocytosis. Thus, coordinated cluster dynamics confer distinct chemotactic properties, highlighting unexpected features of lymphoid cell migration. Copyright © 2015 Elsevier Ltd. All rights reserved.
Article
Carcinomas typically invade as a cohesive multicellular unit, a process termed collective invasion. It remains unclear how different subpopulations of cancer cells contribute to this process. We developed three-dimensional (3D) organoid assays to identify the most invasive cancer cells in primary breast tumors. Collective invasion was led by specialized cancer cells that were defined by their expression of basal epithelial genes, such as cytokeratin-14 (K14) and p63. Furthermore, K14+ cells led collective invasion in the major human breast cancer subtypes. Importantly, luminal cancer cells were observed to convert phenotypically to invasive leaders following induction of basal epithelial genes. Although only a minority of cells within luminal tumors expressed basal epithelial genes, knockdown of either K14 or p63 was sufficient to block collective invasion. Our data reveal that heterotypic interactions between epithelial subpopulations are critical to collective invasion. We suggest that targeting the basal invasive program could limit metastatic progression.
Article
The classical problem of heat and mass transfer from single spheres at low values of the Reynolds number, where the velocity field is given by Stokes' formula, is considered. It is shown, by the use of a singular perturbation technique, how an expansion may be derived for the Nusselt number Nu in terms of the Pe´clet number Pe which yields an accurate expression for the rate of transfer of energy or matter in the range 0 &lE; Pe &lE; 1. It is also established, by studying both the Pe ↠ 0 and Pe ↠ ∞ asymptotes, that the functional relation between Nu and Pe as obtained with the Stokes velocity profile is less sensitive to an increase in the Reynolds number than the familiar Stokes law for the drag coefficient.
Article
A calculation is given of the viscous force, exerted by a flowing fluid on a dense swarm of particles. The model underlying these calculations is that of a spherical particle embedded in a porous mass. The flow through this porous mass is decribed by a modification of Darcy's equation. Such a modification was necessary in order to obtain consistent boundary conditions. A relation between permeability and particle size and density is obtained. Our results are compared with an experimental relation due to Carman.
Article
The collective migration of cells as a cohesive group is a hallmark of the tissue remodelling events that underlie embryonic morphogenesis, wound repair and cancer invasion. In such migration, cells move as sheets, strands, clusters or ducts rather than individually, and use similar actin- and myosin-mediated protrusions and guidance by extrinsic chemotactic and mechanical cues as used by single migratory cells. However, cadherin-based junctions between cells additionally maintain 'supracellular' properties, such as collective polarization, force generation, decision making and, eventually, complex tissue organization. Comparing different types of collective migration at the molecular and cellular level reveals a common mechanistic theme between developmental and cancer research.
Article
Many types of cells are able to accurately sense shallow gradients of chemicals across their diameters, allowing the cells to move toward or away from chemical sources. This chemotactic ability relies on the remarkable capacity of cells to infer gradients from particles randomly arriving at cell-surface receptors by diffusion. Whereas the physical limits of concentration sensing by cells have been explored, there is no theory for the physical limits of gradient sensing. Here, we derive such a theory, using as models a perfectly absorbing sphere and a perfectly monitoring sphere, which, respectively, infer gradients from the absorbed surface particle density or the positions of freely diffusing particles inside a spherical volume. We find that the perfectly absorbing sphere is superior to the perfectly monitoring sphere, both for concentration and gradient sensing, because previously observed particles are never remeasured. The superiority of the absorbing sphere helps explain the presence at the surfaces of cells of signal-degrading enzymes, such as PDE for cAMP in Dictyostelium discoideum (Dicty) and BAR1 for mating factor α in Saccharomyces cerevisiae (budding yeast). Quantitatively, our theory compares favorably with recent measurements of Dicty moving up a cAMP gradient, suggesting these cells operate near the physical limits of gradient detection. • chemotaxis • receptors • noise
Article
Statistical fluctuations limit the precision with which a microorganism can, in a given time T, determine the concentration of a chemoattractant in the surrounding medium. The best a cell can do is to monitor continually the state of occupation of receptors distributed over its surface. For nearly optimum performance only a small fraction of the surface need be specifically adsorbing. The probability that a molecule that has collided with the cell will find a receptor is Ns/(Ns + pi a), if N receptors, each with a binding site of radius s, are evenly distributed over a cell of radius a. There is ample room for many indenpendent systems of specific receptors. The adsorption rate for molecules of moderate size cannot be significantly enhanced by motion of the cell or by stirring of the medium by the cell. The least fractional error attainable in the determination of a concentration c is approximately (TcaD) - 1/2, where D is diffusion constant of the attractant. The number of specific receptors needed to attain such precision is about a/s. Data on bacteriophage absorption, bacterial chemotaxis, and chemotaxis in a cellular slime mold are evaluated. The chemotactic sensitivity of Escherichia coli approaches that of the cell of optimum design.
Article
Aggregation of attachment-dependent animal cells represents a series of motility, collision, and adhesion events applicable to such diverse fields as tissue engineering, bioseparations, and drug testing. Aggregation of human prostate cancer cells in liquid-overlay culture was modeled using Smoluchowski's collision theory. Using well (LNCaP) and poorly differentiated (DU 145 and PC 3) cell lines, the biological relevance of the model was assessed by comparing aggregation rates with diffusive and adhesive properties. Diffusion coefficients ranged from 5 to 90 microm(2)/min for single LNCaP and PC 3 cells, respectively. Similar diffusivities were predicted by the persistent random walk model and Einstein relation, indicating random motion. LNCaP cells were the most adhesive in our study with reduced cell shedding, 100% adhesion probability, and enhanced expression of E-cadherin. There was an increase in DU 145 cells staining positive for E-cadherin from nearly 20% of single cells to uniform staining across the surface of all aggregates; under 30% of PC 3 aggregates stained positive. Aggregation rates were more consistent with adhesive properties than with motilities, suggesting that aggregation in our study was reaction-controlled. Relative to other assays employed here, aggregation rates were more sensitive to phenotypic differences in cell lines and described size-dependent changes in aggregation at a finer resolution. In particular, model results suggest similar aggregation rates for two-dimensional DU 145 and PC 3 aggregates and upwards of 4-fold higher rates for larger three-dimensional DU 145 spheroids, consistent with expression of E-cadherin. The kinetic model has application to spheroid production, to cell flocculation and as an adhesion assay.
Article
Cell response to extracellular cues is often driven by gradients of morphogenetic and chemotactic proteins, and therefore descriptions of how such gradients arise are critical to understanding and manipulating these processes. Many of these proteins are secreted in matrix-binding form to be subsequently released proteolytically, and here we explore how this feature, along with small dynamic forces that are present in all tissues, can affect pericellular protein gradients. We demonstrate that 1), pericellular gradients of cell-secreted proteins can be greatly amplified when secreted by the cell in matrix-binding form as compared to a nonmatrix-interacting form; and 2), subtle flows can drive significant asymmetry in pericellular protein concentrations and create transcellular gradients that increase in the direction of flow. This study thus demonstrates how convection and matrix-binding, both physiological characteristics, combine to allow cells to create their own autologous chemotactic gradients that may drive, for example, tumor cells and immune cells into draining lymphatic capillaries.
Article
CCR7 is implicated in lymph node metastasis of cancer, but its role is obscure. We report a mechanism explaining how interstitial flow caused by lymphatic drainage directs tumor cell migration by autocrine CCR7 signaling. Under static conditions, lymphatic endothelium induced CCR7-dependent chemotaxis of tumor cells through 3D matrices. However, interstitial flow induced strong increases in tumor cell migration that were also CCR7 dependent, but lymphatic independent. This autologous chemotaxis correlated with metastatic potential in four cell lines and was verified by visualizing directional polarization of cells in the flow direction. Computational modeling revealed that transcellular gradients of CCR7 ligand were created under flow to drive this response. This illustrates how tumor cells may be guided to lymphatics during metastasis.