Receptor Concentration
Receptor concentration, notated \(C_{SS,R}\) in Assess, is the concentration of the receptor of interest in a model compartment. Receptor concentration can be defined as a concentration (nM) or as an average expression level (#/cell), which when multiplied with the cell density, notated \(Density_{cells}\) in Assess, equals the receptor concentration. Only receptors accessible to the drug are considered, i.e. cell-surface receptors in the case of cell-impermeable drugs.
Tumor associated antigen (TAA) and T-cell receptor (TCR) are specific types of receptors that can be estimated using the same methods.
Calculating Receptor Concentration
To determine the receptor concentration for a given compartment, the total number of cell surface receptor molecules is first identified by determining:
- The cell types within the compartment that express the receptor
- How many of these cells are present within the compartment; this may also include what proportion of the identified cell types express the receptor
- The density of receptors on each cell
The receptor concentration within the compartment is then calculated based on the total number of receptors (number of expressing cells × receptors per cell) and the compartmental volume.
Receptor Expressing Cell Types
An efficient way to identify which cell types express a target receptor is to first assess receptor expression in large-scale databases of mRNA and protein expression such as the Human Protein Atlas (Uhlén et al. 2015). While mRNA expression does not always correlate closely with protein levels, transcript-level data can be a useful way to eliminate non-expressing cells when mRNA expression is not detected. For multi-compartmental models, the receptor-expressing cells within each compartment will be identified.
For the central compartment, the "immune cell" tab available at the Human Protein Atlas is helpful for determining which circulating immune cells are likely to express the receptor of interest. This information can then be used to perform more targeted literature searches for protein-level evidence of expression for specific cell types. Whether the receptor is expressed by red blood cells or not will have a major effect on the receptor concentration estimate within the central compartment. Proteomic analyses of human red blood cells can be used to qualitatively assess whether the receptor is expressed by RBCs or not (Bryk and Wiśniewski 2017), and similarly, for platelets (Huang et al. 2021).
For the peripheral compartment, the "tissue" tab at the Human Protein Atlas is a useful resource to assess levels of receptor expression within peripheral tissues including distinguishing between cell types within a given tissue. Identification of cell types expressing the receptor of interest may be further identified or corroborated by studies that have examined receptor expression at the protein level. In the absence of species-specific receptor expression information, it is reasonable to assume expression patterns are conserved across species for respective cell-types.
Number of Expressing Cells
The number of cells that express the receptor of interest must be identified for each compartment.
For the central compartment, this can be informed by resources documenting the typical numbers of circulating cells in human or mouse blood and typical blood volumes for a given species (Davies and Morris 1993). Numbers of specific cell types within the peripheral tissues can be derived from studies that have compiled cell estimates such as (Bianconi et al. 2013). If a tumor compartment exists in the model structure and the receptor is expected to be expressed within the tumor, the number of receptor expressing tumor cells will be based on the size of the tumor and the number of tumor cells per volume (Del Monte 2009).
The proportion of a given cell type that expresses the receptor should also be considered. In cases where the receptor is a defining marker for the cell type, such as CD3 for T cells, then the proportion of expressing cells will be 1.0. In a tumor compartment, however, only a proportion of tumor cells may express the target receptor, in which case the appropriate proportion will be applied to the total number of tumor cells to give the number of receptor-expressing tumor cells. An estimate of the proportion of receptor-positive cells of a given cell type is typically made based on flow cytometry or IHC data.
Receptors Per Cell
For each cell type that expresses the receptor of interest, an estimate of the number of receptors per cell (receptor density) is required. A receptor density estimate can be made using studies of cell surface binding sites using receptor-specific antibodies or ligands. Assays that make these measurements include Scatchard analysis and quantitative flow cytometry (for instance, Quantibrite based analyses).
In the absence of such quantitative data, receptor density may be estimated arbitrarily from flow cytometry mean fluorescence intensity (MFI) values relative to the IgG control where the IgG control is assigned 500-1000 receptors per cell, or based on IHC staining where it is assumed that a minimum of 15,000 receptors per cell is required for positive staining.
Example: Total number of Human CD3 Receptors in Central Compartment
The central compartment comprises the circulating blood plasma. We estimate the total number of circulating T cells and the number of CD3 receptors per cell, divided by the central compartment volume.
Parameters collected from the literature:
| Parameter | Value | Reference |
|---|---|---|
| Number of T cells (low) | 5.40E+05 (cells/mL) | Frequencies of cell types in hPBMC |
| Number of T cells (high) | 1.79E+06 (cells/mL) | Frequencies of cell types in hPBMC |
| Nominal T cells /ml peripheral blood | 1.17E+06 | Mid range of high/low |
| Total blood volume | 5.2 L | Davies and Morris 1993 |
| Central compartment volume (plasma volume) | 3.0 L | Davies and Morris 1993 |
| Proportion of T cells positive for CD3 | 1.0 (100%) | - |
| CD3 receptor density for T cells (receptors/cell) | 57,000 | Bikoue et al. 1996 |
- Total number of CD3+ cells in central compartment: \(1.17*10^6 \frac{cells}{mL}* (5.2 L * 1000 \frac{mL}{L}) = 6.08*10^9 cells\)
- Total number of receptors in central compartment: \(6.08*10^9 cells * 57,000 \frac{receptors}{cell} = 3.47*10^{14} receptors\)
- Concentration of receptors in central compartment: \(3.47*10^{14} receptors * \frac{mole}{6.02 * 10^{23} receptors} * \frac{1}{3 L} = 0.192 nM\)
- Average expression level of receptors in central compartment: \((3.47*10^{14} receptors)/(6.08*10^9 cells) = 57,000 \frac{receptors}{cell}\)
Example: Total number of HER2 Receptors in a Human Tumor Compartment
| Parameter | Value | Reference |
|---|---|---|
| Nominal tumor volume | 10 \(cm^3\) | Nominal value |
| Total tumor cells / mL | 1E+08 (cells/mL) | Del Monte 2009 |
| Proportion of tumor cells that express HER2 | 0.1 | Minimum proportion to be scored IHC2+ or IHC3+ for breast cancer (Ahn et al. 2020) |
| HER2 receptor density for tumor cells (receptors/cell) | 1,500,000 | Nominal value for a high-expressing tumor based on ranges of HER2 density observed across different human cancer cell lines (Li et al. 2016; Shankaran et al. 2013; Mukherjee et al. 2011) |
| Tumor Interstitial Volume | 0.002 L | Nominal value assuming 80% cellularity |
- Total number of HER2+ cells within the tumor compartment: \(1.0*10^8 \frac{cells}{mL}* (10 mL * 0.1) = 1.0*10^8 cells\)
- Total number of receptors in the tumor compartment: \(1.0*10^8 cells * 1,500,000 \frac{receptors}{cell} = 1.50*10^{14} receptors\)
- Concentration of HER2 receptors in the tumor compartment: \(1.50*10^{14} receptors * \frac{mole}{6.02 * 10^{23} receptors} * \frac{1}{0.002 L} = 125 nM\)
- Average expression level of receptors in central compartment: \((1.50*10^{14} receptors)/(1.0*10^8 cells) = 1,500,000 \frac{receptors}{cell}\)
References
- Ahn, Soomin, Ji Won Woo, Kyoungyul Lee, and So Yeon Park. 2020. "HER2 Status in Breast Cancer: Changes in Guidelines and Complicating Factors for Interpretation." Journal of Pathology and Translational Medicine 54 (1): 34–44.
- Bianconi, Eva, Allison Piovesan, Federica Facchin, Alina Beraudi, Raffaella Casadei, Flavia Frabetti, Lorenza Vitale, et al. 2013. "An Estimation of the Number of Cells in the Human Body." Annals of Human Biology 40 (6): 463–71.
- Bikoue, A., F. George, P. Poncelet, M. Mutin, G. Janossy, and J. Sampol. 1996. "Quantitative Analysis of Leukocyte Membrane Antigen Expression: Normal Adult Values." Cytometry 26 (2): 137–47.
- Bryk, Agata H., and Jacek R. Wiśniewski. 2017. "Quantitative Analysis of Human Red Blood Cell Proteome." Journal of Proteome Research 16 (8): 2752–61.
- Davies, B., and T. Morris. 1993. "Physiological Parameters in Laboratory Animals and Humans." Pharmaceutical Research 10 (7): 1093–95.
- Del Monte, Ugo. 2009. "Does the Cell Number 10(9) Still Really Fit One Gram of Tumor Tissue?" Cell Cycle 8 (3): 505–6.
- Huang, Jingnan, Frauke Swieringa, Fiorella A. Solari, Isabella Provenzale, Luigi Grassi, Ilaria De Simone, Constance C. F. M. J. Baaten, et al. 2021. "Assessment of a Complete and Classified Platelet Proteome from Genome-Wide Transcripts of Human Platelets and Megakaryocytes Covering Platelet Functions." Scientific Reports 11 (1): 12358.
- Li, John Y., Samuel R. Perry, Vanessa Muniz-Medina, Xinzhong Wang, Leslie K. Wetzel, Marlon C. Rebelatto, Mary Jane Masson Hinrichs, et al. 2016. "A Biparatopic HER2-Targeting Antibody-Drug Conjugate Induces Tumor Regression in Primary Models Refractory to or Ineligible for HER2-Targeted Therapy." Cancer Cell 29 (1): 117–29.
- Mukherjee, Ali, Youssouf Badal, Xuan-Thao Nguyen, Johanna Miller, Ahmed Chenna, Hasan Tahir, Alicia Newton, Gordon Parry, and Stephen Williams. 2011. "Profiling the HER3/PI3K Pathway in Breast Tumors Using Proximity-Directed Assays Identifies Correlations between Protein Complexes and Phosphoproteins." PloS One 6 (1): e16443.
- Shankaran, Harish, Yi Zhang, Yunbing Tan, and Haluk Resat. 2013. "Model-Based Analysis of HER Activation in Cells Co-Expressing EGFR, HER2 and HER3." PLoS Computational Biology 9 (8): e1003201.
- Uhlén, Mathias, Linn Fagerberg, Björn M. Hallström, Cecilia Lindskog, Per Oksvold, Adil Mardinoglu, Åsa Sivertsson, et al. 2015. "Proteomics. Tissue-Based Map of the Human Proteome." Science 347 (6220): 1260419.