A Mathematical Model for Neutrophil Gradient Sensing and Polarization

Directed cell migration in response to chemical cues, also known as chemotaxis, is an important physiological process involved in wound healing, foraging, and the immune response. Cell migration requires the simultaneous formation of actin polymers at the leading edge and actomyosin complexes at the sides and back of the cell. An unresolved question in eukaryotic chemotaxis is how the same chemoattractant signal determines both the cell's front and back. Recent experimental studies have begun to reveal the biochemical mechanisms necessary for this polarized cellular response. We propose a mathematical model of neutrophil gradient sensing and polarization based on experimentally characterized biochemical mechanisms. The model demonstrates that the known dynamics for Rho GTPase and phosphatidylinositol-3-kinase (PI3K) activation are sufficient for both gradient sensing and polarization. In particular, the model demonstrates that these mechanisms can correctly localize the “front” and “rear” pathways in response to both uniform concentrations and gradients of chemical attractants, including in actin-inhibited cells. Furthermore, the model predictions are robust to the values of many parameters. A key result of the model is the proposed coincidence circuit involving PI3K and Ras that obviates the need for the “global inhibitors” proposed, though never experimentally verified, in many previous mathematical models of eukaryotic chemotaxis. Finally, experiments are proposed to (in)validate this model and further our understanding of neutrophil chemotaxis

HER2+ Cancer Cell Dependence on PI3K <i>vs</i>. MAPK Signaling Axes Is Determined by Expression of EGFR, ERBB3 and CDKN1B

<div><p>Understanding the molecular pathways by which oncogenes drive cancerous cell growth, and how dependence on such pathways varies between tumors could be highly valuable for the design of anti-cancer treatment strategies. In this work we study how dependence upon the canonical PI3K and MAPK cascades varies across HER2+ cancers, and define biomarkers predictive of pathway dependencies. A panel of 18 HER2+ (<i>ERBB2</i>-amplified) cell lines representing a variety of indications was used to characterize the functional and molecular diversity within this oncogene-defined cancer. PI3K and MAPK-pathway dependencies were quantified by measuring <i>in vitro</i> cell growth responses to combinations of AKT (MK2206) and MEK (GSK1120212; trametinib) inhibitors, in the presence and absence of the ERBB3 ligand heregulin (NRG1). A combination of three protein measurements comprising the receptors EGFR, ERBB3 (HER3), and the cyclin-dependent kinase inhibitor p27 (CDKN1B) was found to accurately predict dependence on PI3K/AKT vs. MAPK/ERK signaling axes. Notably, this multivariate classifier outperformed the more intuitive and clinically employed metrics, such as expression of phospho-AKT and phospho-ERK, and PI3K pathway mutations (<i>PIK3CA</i>, <i>PTEN</i>, and <i>PIK3R1</i>). In both cell lines and primary patient samples, we observed consistent expression patterns of these biomarkers varies by cancer indication, such that ERBB3 and CDKN1B expression are relatively high in breast tumors while EGFR expression is relatively high in other indications. The predictability of the three protein biomarkers for differentiating PI3K/AKT vs. MAPK dependence in HER2+ cancers was confirmed using external datasets (Project Achilles and GDSC), again out-performing clinically used genetic markers. Measurement of this minimal set of three protein biomarkers could thus inform treatment, and predict mechanisms of drug resistance in HER2+ cancers. More generally, our results show a single oncogenic transformation can have differing effects on cell signaling and growth, contingent upon the molecular and cellular context.</p></div

Multivariate protein biomarkers predict pathway dependence.

<p><b>(A)</b> Rank correlation coefficients between protein expression and four model parameters, hierarchically clustered by Pearson correlations. <b>(B)</b> Accuracy of Pathway Bias predictions from Logistic regression models built on all input features (FULL), all protein measurements (PROT), PI3K pathway genetic status (GENE), cellular phenotype (tissue source and proliferation rate; PHEN), or 3 protein biomarkers EGFR, ERBB3, and CDKN1B (3BM). Results (filled circles) are overlaid on cumulative distributions from 10,000 randomized models (lines), thus relating predictive accuracies to statistical significance. <b>(C)</b> Normalized regression coefficients (BETA × median signal) for the three protein biomarker model. <b>(D)</b> Model-predicted Pathway Bias using the three protein biomarkers, separated by PI3K, SWITCH, and MAPK sub-groups.</p

Canonical PI3K/AKT and MAPK/ERK signaling nodes and their statistical association with biomarker-defined cell line subsets represented in Project Achilles.

<p>Canonical PI3K/AKT and MAPK/ERK signaling nodes and their statistical association with biomarker-defined cell line subsets represented in Project Achilles.</p

TCGA Analysis of biomarker expression in HER2+ cancers.

<p>(A) Protein expression of CDKN1B, ERBB3, and EGFR across the 18 cell lines +/- heregulin treatments, scaled by row and organized as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004827#pcbi.1004827.g001" target="_blank">Fig 1</a>, categorized as breast vs. non-breast. (B) mRNA Expression of the same three biomarkers (<i>EGFR</i>, <i>ERBB3</i>, and <i>CDKN1B</i>) in 10 HER2+ cancer indications as compared to breast cancer, expressed as signed <i>P</i>-values (rank-sum test).</p

HER2+ cancer models vary by their dependence on PI3K <i>vs</i>. MAPK pathways and cellular properties.

<p><b>(A)</b> Relative PI3K/AKT vs. MAPK/ERK dependence (Pathway Bias) across 18 HER2+ cell lines in the presence and absence of exogenous Heregulin (HRG) stimulation. Error bars represent 95% CI. Tissue, genetic status of PI3K-pathway components, and <i>in vitro</i> proliferation rates (96 hr population doublings; PD) are indicated below for each cell line. <b>(B)</b> Representative surface responses to AKT and MEK inhibitor combinations in the absence (top) and presence (below) of exogenous HRG for PI3K-dependent, MAPK-dependent, and switching class cells.</p

Differential signaling networks, cellular features, and drug responsiveness between PI3K and MAPK-biomarker stratified HER2+ cancer cell lines.

<p><b>(A)</b> Differences in drug sensitivity (log₁₀(IC₅₀)) between PI3K vs. MAPK biomarker-enriched cell lines, based on protein measurements of EGFR and ERBB3, and filtered by Rank-sum <i>P</i>-value < 0.1. Bars are color-coded accordingly by predicted PI3K (blue) vs. MAPK (red) dependence. <b>(B)</b> Frequency of PI3K mutations (<i>PIK3CA</i>, <i>PIK3R1</i>,and <i>PTEN</i>) and tissue source (Breast vs. Non-breast cancers) in the two groups of cell lines. <b>(C)</b> Genes identified as differentially sensitive between the biomarker-defined cell line subsets (<i>EGFR</i>^HI<i>ERBB3</i>^LO<i>CDKNIB</i>^LO vs. <i>EGFR</i>^LO<i>ERBB3</i>^HI<i>CDKNIB</i>^HI) were mapped onto oncogenic signaling networks in NCI-PID and color-coded by differential association.</p