Autologous morphogen gradients by subtle interstitial flow and matrix interactions

Abstract

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.

FIGURE 1

Physiological ranges of flow velocities and diffusion coefficients result in biased cell-secreted morphogen gradients. Typical concentration contours show the trend toward biased gradients as either velocity is increased or the diffusion coefficient of the secreted protein is decreased. This biasing occurs for low Peclet numbers (Pe < 1).

FIGURE 2

Creation and amplification of autologous morphogen gradients by subtle physiological flows and matrix-binding properties of morphogen. (A) Dimensionless concentration gradients of cell-released proteases calculated using a constant surface concentration are increasingly skewed in the direction of flow with increasing flow velocities. Red, 1 (maximum concentration); dark blue, 0. (B) Dimensionless concentration gradients of liberated morphogen are released from the ECM through the action of the cell-secreted protease whose profiles are shown in A. (C) Distributions of cell-released morphogen demonstrate, when compared with the corresponding profiles in B, the marked gradient amplification effect in matrix-released versus cell-secreted morphogen properties under otherwise identical conditions. (D) Cell-secreted morphogen concentrations as calculated along a line parallel to flow and passing through the cell midlines. All flow conditions result in cell concentrations that decrease with increasing distance from the cell. (E) ECM-released morphogen concentrations show greater asymmetry compared to those of cell-secreted morphogens for the same flow conditions. Interestingly, the higher Peclet numbers (0.25 and 0.5) show increasing concentration gradients with increasing distance downstream from the cell. (F) Calculated transcellular gradients (percentage difference between the downstream and upstream sides of the cell) reveal the degree of gradient amplification that is achieved when morphogen is secreted into matrix-binding form and demonstrate the potential for autologous chemotaxis gradients.

FIGURE 3

Effect of protein decay on protease and morphogen gradients for Pe = 0.25. Pericellular distributions of cell-secreted protease (top row) and resulting ECM-released morphogen (bottom row) with (A) no decay, (B) morphogen decay of k_m= 0.2 s⁻¹, (C) protease decay of k_p = 0.2 s⁻¹, and (D) both protease and morphogen decay k_p and k_m = 0.2 s⁻¹. In all cases the ECM-released morphogen concentrations were normalized: dark red, 1 (maximum concentration); dark blue, 0. (E) Concentrations of ECM-released morphogen as measured along a line passing through the cell midline parallel to flow in each of the conditions (A–D), each with and without inclusion of a cell consumption term. k_eff was varied between 0 s⁻¹ (solid lines), 0.4 s⁻¹ (thick dotted lines), and 1.0 s⁻¹ (thin dotted lines). (F) Calculated transcellular gradients were reduced in magnitude by the decay considerations, and cell consumption affected the gradients by negligible amounts; however, in all cases the transcellular gradients still increased in the direction of flow, and remained well above physiologically detectable levels of 1–10%.

FIGURE 4

Effects of boundary and initial conditions on morphogen gradients for Pe = 0.25. (A) Cell-secreted protease distribution assuming a constant surface concentration (top row) and corresponding ECM-released morphogen distribution (bottom row) serve as a control for evaluating effects of changing boundary conditions. Dark red, 1 (maximum concentration); dark blue, 0. (B) The constant surface flux protease condition resulted in a slightly altered cell-released protease distribution (top row) when compared to the constant concentration boundary case (A); however, the dimensionless ECM-released morphogen profiles shown on the bottom row appear nearly identical. (C) Protease distribution of A, with the resulting ECM-released morphogen profile calculated assuming that the ECM-bound morphogen was nonuniformly distributed. The ECM-released morphogen gradient (bottom row) shares the same qualitative shape as for the previous two conditions. (D) Dimensionless ECM-released concentration profiles along the bisecting midline of the three cases shown in A–C are similar.