Circuit Design Features of a Stable Two-Cell System

Abstract

Cell communication within tissues is mediated by multiple paracrine signals including growth factors, which control cell survival and proliferation. Cells and the growth factors they produce and receive constitute a circuit with specific properties that ensure homeostasis. Here, we used computational and experimental approaches to characterize the features of cell circuits based on growth factor exchange between macrophages and fibroblasts, two cell types found in most mammalian tissues. We found that the macrophage-fibroblast cell circuit is stable and robust to perturbations. Analytical screening of all possible two-cell circuit topologies revealed the circuit features sufficient for stability, including environmental constraint and negative-feedback regulation. Moreover, we found that cell-cell contact is essential for the stability of the macrophage-fibroblast circuit. These findings illustrate principles of cell circuit design and provide a quantitative perspective on cell interactions.

Keywords: CSF1; PDGF; carrying capacity; cell circuits; cell-cell contact; fibroblasts; growth factors; macrophages; stability; tissue homeostasis.

Figure 1.. Reciprocal expression of growth factors and their receptors results in proliferation of macrophages and fibroblasts.

A. Illustration of growth factor (GF)-dependent cell circuits. B. Growth factor-dependent proliferation of macrophages (MP) and fibroblasts (FB). MP or FB were fed daily with 50 ng/ml recombinant Csf1, Pdgfb, Pdgfd, or Hbegf. Cell numbers were determined each day starting 6 hr after plating (Day 0) for 3 total days (data representative of three independent experiments, n=7). C. Expression of growth factors and growth factor receptors in MP and FB. RNA expression in MP and FB was quantified by qPCR and normalized to Hprt1 expression, “nd” = not detected (data representative of two independent experiments, n=3). Data are represented as Mean ± SEM (B) or Mean ± SD (C). See also Figure S1.

Figure 2.. Co-cultures of macrophages and fibroblasts reach stable cell ratios.

A. Time course of population ratios for MP and FB in co-culture. MP and FB were plated with starting ratios spanning a range of up to 100-fold. Ratios over time were calculated using flow cytometry (data representative of five independent experiments, n=2). B. Simulated population ratios of a growth factor-dependent cell circuit. ΔFB and ΔMP are net changes in population size (Proliferation - removal). Data are represented as Mean ± SD. See also Figure S2.

Figure 3.. Analytical screening identifies negative feedback as a necessary feature of a stable two-cell circuit.

A. Illustration of analytical screening of a growth factor-dependent circuit. X₁ is cell 1; X₂ is cell 2; C₁₂ is the growth factor made by X₁ for X₂; C₂₁ is the growth factor made by X₂ for X_1. Red and blue arrows indicate different forms of regulation on growth factors. B. Enumeration of all possible circuit interactions in the analytical screen resulted in 144 different circuit topologies. C. Examples of both stable and unstable two-cell circuits identified by the screen. D. Two minimal circuits that generate circuit stability. Both circuits show negative feedback on cell X₂, in which cell X₂ effectively downregulates its own growth factor, either by auto-regulation (top) or by cross-regulation (bottom). See also Figure S3.

Figure 4.. Circuit stability is maintained through auto-regulation.

A. Mathematical definition of carrying capacity. The growth curve of cell number N is modeled with maximum proliferation rate β, carrying capacity K, and cell removal rate μ. B. Measurement of carrying capacity for MP and FB. Proliferation rate was approximated using the percentage of EdU⁺ cells after overnight culture and 2 hr of EdU labeling. MP and FB were plated at different cell densities range from 10,000 to 500,000 in 6-well plates. Actual cell numbers at the time of assay are depicted. Carrying capacity (K) and proliferation rate (β) were determined as the intercepts of the x- and y-axes with linear fit (data representative of three independent experiments, n=3). C. Relative surface expression of Csf1 receptor on MP and Pdgf receptors on FB after growth factor stimulation with 50 ng/ml Csf1 or 50 ng/ml Pdgfb as measured by flow cytometry. (data representative of two independent experiments, n=3) D. Expression of Pdgfb in MP and Csf1 in FB after addition of 50 ng/ml Csf1 and 50 ng/ml Pdgfb for 24 hr. RNA expression was quantified by qPCR and normalized to Hprt1 expression. (data representative of two independent experiments, n=3). E. Model depicting the MP-FB circuit, including carrying capacity, reciprocal growth factor expression, negative feedback through growth factor receptor internalization and transcriptional suppression, and autocrine growth factor production by FB. Data are represented as Mean ± SEM (B, C) or Mean ± SD (D). See also Figure S4.

Figure 5.. The observed stable circuit is density-dependent.

A. Stable two-cell phase portrait showing ON, OFF, and ON-OFF states. B. Theoretical phase portrait depicting population kinetics. C. Phase portrait depicting MP-FB system kinetics measured in vitro. Each arrow-tail represents one measurement 2 days after co-culture at a given starting cell number and each arrow-head represents the cell numbers from this same condition 2–5 days later (54 separate conditions, n=2). The separatrix represents the switch between the ‘ON’ (blue circle) and ‘OFF’ (red circle) states. The base of the separatrix is the unstable point (empty circle) where FB culture alone will either flow to the ‘ON-OFF’ (green circle) or ‘OFF’ state. D. Theoretical phase portraits using density-independent (left) and density-dependent (right) models, with identical model parameters (Table S2). E. Estimated values of the unstable points, empty circles in (D), from experimental observations (black bar) and density-dependent models (empty and gray bar). F. Theoretical phase portraits of cell circuits with variations on the observed circuit (i): (ii) the observed circuit missing autocrine signaling for FB (X₁); (iii) Circuit with stability provided through cross-repression of growth factor produced from X₁ instead of X₂; (iv) negative feedback through receptor internalization removed from the observed circuit. Data are represented as Mean ± SD. See also Figure S5.

Figure 6.. The macrophage-fibroblast circuit is resilient to perturbations.

A. Perturbation of MP-FB co-culture with the addition of recombinant Csf1, Pdgfb, or MP. The population ratios (left), number of MP (middle) and number of FB (right) are shown for day 4, 7 and 21 of co-culture. On Day 0, 100,000 FB and 200,000 MP were plated for co-culture. On day 4, a single dose of 50 ng/ml Pdgfb, 50 ng/ml Csf1, or 500,000 MP was added to co-culture (data representative of two independent experiments, n=3). B. Dynamics of cell numbers and ratios after modeling the same perturbations performed experimentally in (A), using similar parameters from the phase portrait in Figure 5C (Table S2 and Methods). Data are represented as Mean ± SD.

Figure 7.. Stable growth of macrophages and fibroblasts in co-culture requires contact-dependent mechanisms.

A. A theoretical phase portrait showing the change in FB fate when cultured near the unstable point, with or without MP (left). FB number when cultured with or without MP (right). 20,000 FB were cultured with 40,000 MPs and cell numbers were evaluated on day 4 using flow cytometry (data representative of two independent experiments, n=3) B. Co-cultures of FB with Pdgfb WT or Pdgfb KO MP. Cas9-knock-in MP transduced with lentivirus carrying empty vector (control) or vector carrying Pdgfb guides (Pdgfb KO) were plated together with FB. On day 0, 20,000 FB and 40,000 MP were plated and the co-cultures were examined after 6 and 12 days (data representative of two independent experiments, n=3). C. Co-cultures of MP with control or Csf1 KO FB. Csf1^fl/fl FB transduced with lentivirus carrying GFP (control) or Cre-GFP (Csf1 KO) were plated together with MP. On day 0, 20,000 FB and 40,000 MP were plated, and the co-cultures were examined after 4, 7, and 11 days (data representative of two independent experiments, n=3). D. Immunofluorescent images of MP cultured with control or Csf1 KO FB after 7 days. Two representative fields of each condition are shown. FB are transduced with lentivirus carrying GFP and MP are stained with anti-CD11b (red). Scale bar indicates 50 μm. E. Time-lapse imaging of interactions between MP and FB. TdTomato⁺ FB (red) and Csf1r-GFP (green) MP were imaged 3 hr after plating. Arrows and arrowheads denote MP. Arrows mark the daughter cells from a dividing MP. Scale bar indicates 50 μm. F. Ratios between GFP⁺ (control or Csf1 KO) FB and TdTomato⁺ WT FB in co-culture with MP. 10,000 GFP⁺ FB and 10,000 TdTomato⁺ FB were combined and plated together with 40,000 MPs (data representative of two independent experiments, n=3). G. Schematic of the “Spring-and-Ceiling model” of the MP-FB circuit. MP and FB maintain a stable circuit due to carrying capacity preventing FB from expanding (“ceiling”) and negative regulation controlling MP cell numbers relative to fibroblasts (arrows, “spring”). Data are represented as Mean ± SD. See also Figure S6.