Quantification of total T-cell receptor diversity by flow cytometry and spectratyping
- Stanca M Ciupe^{1}Email author,
- Blythe H Devlin^{2},
- Mary Louise Markert^{2, 3} and
- Thomas B Kepler^{4}
https://doi.org/10.1186/1471-2172-14-35
© Ciupe et al.; licensee BioMed Central Ltd. 2013
Received: 19 April 2013
Accepted: 26 July 2013
Published: 6 August 2013
Abstract
Background
T-cell receptor diversity correlates with immune competency and is of particular interest in patients undergoing immune reconstitution. Spectratyping generates data about T-cell receptor CDR3 length distribution for each BV gene but is technically complex. Flow cytometry can also be used to generate data about T-cell receptor BV gene usage, but its utility has not been compared to or tested in combination with spectratyping.
Results
Using flow cytometry and spectratype data, we have defined a divergence metric that quantifies the deviation from normal of T-cell receptor repertoire. We have shown that the sample size is a sensitive parameter in the predicted flow divergence values, but not in the spectratype divergence values. We have derived two ways to correct for the measurement bias using mathematical and statistical approaches and have predicted a lower bound in the number of lymphocytes needed when using the divergence as a substitute for diversity.
Conclusions
Using both flow cytometry and spectratyping of T-cells, we have defined the divergence measure as an indirect measure of T-cell receptor diversity. We have shown the dependence of the divergence measure on the sample size before it can be used to make predictions regarding the diversity of the T-cell receptor repertoire.
Background
The immune system’s ability to fight a large array of foreign particles is facilitated by the diversity of the T-cell receptor (TCR) repertoire [1]. This diversity is generated during thymocyte development by a process of somatic recombination. Inside the thymus, the constant (C) and variable (V) domains of the α and β chains of the TCR are assembled via random genetic rearrangements of the variable (V), diversity (D) and joining (J) gene segments [2]. Additional diversity is added through imprecise joining of the V and J regions along with random nucleotide additions and deletions at the V(D)J junctions [2, 3]. Consequently, most of the variability lies in the third complementary determining region (CDR3) which is encoded by the V(D)J junction and comes in contact with the antigenic peptide on the surface of peptide/major histocompatibility complex (pMHC) molecules [4, 5]. While the total number of lymphocytes in the blood can be directly measured, assessment of the diversity of the TCR repertoire requires more complex and indirect assays in a research setting. Such assays include flow cytometry, spectratyping and nucleotide sequencing.
Different T-cell clones use different V gene families in the rearrangement of their β chains. Through the use of commercially available monoclonal antibodies (named TCR V β), one can use standard flow cytometry on whole blood samples to determine the percentage of CD4 T-cells that use a given TCR BV family in subjects or controls. Measures of heterogeneity of TCR BV family usage in these CD4 T-cells can be used as a substitute for TCR repertoire diversity [6]. Flow cytometry is not only faster, cheaper, and technically simpler to use; the data reflects real population percentages.
Spectratyping uses messenger RNA (mRNA) from T-cells to amplify, by PCR, the complementary DNA (cDNA) across the CDR3 region. This generates information about the heterogeneity of the relative frequencies of different CDR3 length products within a functional TCR BV family. Because different T-cell clones have different sequences or lengths of CDR3, analysis of the CDR3 length distributions can be used to determine the overall TCR repertoire diversity [7–11]. Spectratyping has the advantage of providing a finer level of resolution than just analyzing BV gene family expression on the T-cells of flow cytometry. Although spectratyping provides the total number of CDR3 sizes and their pattern of distribution, the investigator cannot determine the frequency of cells used by a particular BV family. Amplifications of variations from a background distribution of each individual BV family may lead to over-representation of immunodominant clonotypes and therefore yield results that are not representative of the contribution of those cells in the entire T-cell repertoire.
TCR diversity can also be assessed by nucleotide sequencing of DNA CDR3 regions, but this is labor-intensive and generates an even lower level of resolution of the whole T-cell repertoire compared to spectratyping [12].
This paper focuses on the role of flow cytometry in measuring T-cell population diversity and compares it to T-cell population diversity as given by spectratyping. Traditionally, spectratyping data is quantified using a wide range of methods from visual [13, 14] to quantitative scoring [15–17]. Our group previously described the use of a likelihood method for measuring deviation from a normal TCR repertoire [9, 11]. For each observed CDR3 length distribution by spectratyping, we compute the Kullback-Leibler divergences between the patient CDR3 length distribution and a known reference distribution [9, 11]. We have modified the Kullback-Leibler divergence to measure the deviation of T-cell receptor diversity from normal. This was done by accounting for both the TCR BV family usage as measured by flow cytometry and by comparing the utility of this method to CDR3 length distribution as measured by spectratyping [11].
Estimator bias is a concern when using this method of divergence scoring. In particular, it is desirable to determine how much deviation in the computation of the divergence occurs when the initial number of lymphocytes used in generating the data is varied. We have addressed this question in the context of divergence measures generated individually by flow cytometry and spectratyping. The results are especially useful when using the techniques for limited numbers of cells.
Results
We used the Kullback-Leibler divergence to quantify similarities between different frequency distributions in the T-cell repertoire diversity when measured by either flow cytometry or spectratyping. We started with two assumptions: 1) the reference distribution corresponds to a polyclonal TCR repertoire and 2) in individual subjects, a positive divergence determines the deviation from the normal TCR repertoire. The flow divergence, D_{ f }, is the distance between the individual and the perfectly sampled reference control distributions of all TCR BV family usage measured by flow cytometry. The spectratype divergence, D_{ s }, is the distance between the individual and the perfectly sampled reference control distributions of the CDR3 lengths of each TCR BV family and averaged over all TCR BV families as measured by spectratyping (see section Kullback-Leibler divergence and [9]).
where i = f,s for flow cytometry and spectratyping, respectively. L_{ f } is the number of BV families used in the flow cytometry assay (in our case 18) and L_{ s } is the number of CDR3 lengths used in the spectratype assay (in our case 14).
Therefore, only the number of measured events, n, and the dimension of the measured space, L_{ i } are needed to correct the divergence measures. We used this formula to assess the performance of D_{ f } and D_{ s } measures in an athymic DiGeorge subject (Figure 1) during a period of limited numbers of peripheral blood T-cells as the patient underwent immune reconstitution following thymus transplantation.
Flow cytometry results
Average CD4 T-cell sample size, measured flow divergence D _{ f } , and corrected flow divergence D _{ f , corr } in a DiGeorge subject
Days after | Average CD4 nr | Measured flow | Corrected flow |
---|---|---|---|
transplant | in gate (n) | D_{ f } value | D_{f, corr} value |
70 | 341 | 0.47 | 0.44 |
88 | 103 | 1.02 | 0.94 |
117 | 174 | 0.39 | 0.34 |
145 | 581 | 0.129 | 0.11 |
181 | 737 | 0.103 | 0.091 |
398 | 1569 | 0.063 | 0.057 |
868 | 4514 | 0.06 | 0.058 |
Summary of T-cell sample size and the corresponding flow divergence values D _{ f }
Subject | Average CD4 T-cell nr | Measured flow |
---|---|---|
in gate n | divergence D_{ f } | |
Control 1 | 66 | 0.252 |
340 | 0.135 | |
675 | 0.132 | |
10051 | 0.098 | |
Control 2 | 58 | 0.260 |
290 | 0.135 | |
603 | 0.079 | |
4438 | 0.070 | |
29438 | 0.053 | |
Control 3 | 60 | 0.214 |
290 | 0.084 | |
585 | 0.366 | |
5965 | 0.021 | |
11889 | 0.022 | |
Control 4 | 136 | 0.112 |
282 | 0.083 | |
425 | 0.045 | |
4354 | 0.018 | |
Subject 1 | 89 | 0.679 |
445 | 0.379 | |
756 | 0.445 | |
887 | 0.466 | |
Subject 2 | 59 | 0.678 |
194 | 0.403 | |
299 | 0.399 | |
605 | 0.355 | |
Subject 3 | 19 | 0.479 |
95 | 0.366 | |
207 | 0.191 | |
2013 | 0.182 | |
3946 | 0.183 | |
Subject 4 | 103 | 0.158 |
213 | 0.229 | |
329 | 0.115 | |
3367 | 0.087 |
where, y(n) is the observed D_{ f } and n is the number of CD4 T-cells in the sample. The intercept α is the true divergence, D_{f,corr}, and the slope C quantifies the rate at which the diversity is dependent on the sample size. In equation (1), slope C corresponds to the (L_{ f } - 1)/2 value, which for an assay that uses 18 BV families, reduces to 8.5. The errors, ε, are independent and normally distributed.
Parameter values and confidence intervals for model (2)
Subject | Value | CI | |
---|---|---|---|
Control 1 | α | 0.107 | [0.079,0.135] |
C | 9.7 | [6.1, 13.4] | |
Control 2 | α | 0.07 | [0.02,0.129] |
C | 10.9 | [4.7, 17.2] | |
Control 3 | α | 0.111 | [-0.17,0.373] |
C | 6.9 | [-29, 43] | |
Control 4 | α | 0.02 | [-0.027,0.067] |
C | 13 | [2, 24] | |
Subject 1 | α | 0.39 | [0.214, 0.574] |
C | 25 | [-6.3, 56] | |
Subject 2 | α | 0.32 | [0.253, 0.377] |
C | 21.3 | [14.5, 28.1] | |
Subject 3 | α | 0.205 | [0.087, 0.322] |
C | 5.5 | [0.7, 10.4] | |
Subject 4 | α | 0.113 | [-0.116, 0.342] |
C | 7.9 | [-33, 49] |
where α_{ i } are the corrected divergence values for the patient i, with i = 1,...,8. The rate at which the diversity is dependent on the sample size, C, is considered constant among the subjects. The errors for each of the subjects, ε_{ i }, are independent and normally distributed.
Parameter values and confidence intervals for model (3)
Subject | α | CI |
---|---|---|
Control 1 | 0.117 | [0.033,0.202] |
Control 2 | 0.085 | [0.009,0.161] |
Control 3 | 0.107 | [0.032,0.184] |
Control 4 | 0.039 | [-0.045,0.123] |
Subject 1 | 0.46 | [0.38, 0.55] |
Subject 2 | 0.41 | [0.32, 0.49] |
Subject 3 | 0.175 | [0.089, 0.261] |
Subject 4 | 0.113 | [0.029, 0.2] |
Subject | C | CI |
All | 7.705 | [4.55, 10.85] |
Events estimation
From our estimates C = 7.705 and α = 0.19 (median 0.12). This implies the sample size, n, must be larger than 364 (median 577) cells for an accurate D_{f,corr} estimate. In our case, we gated the flow cytometry on CD4 T-cells, so more than 364 CD4 T-cells, or events, must be captured in the flow analysis.
Spectratype results
CD3 T-cell sample size, measured spectratype divergence D _{ s } , and corrected spectratype divergence D _{ s,,corr } in a DiGeorge subject
Subject | Days after transplant | CD3 T-cells n_{ 0 } | Measured D_{ s } value | Corrected D_{s, corr} value |
---|---|---|---|---|
Subject 1 | 9 | 420,000 | 0.91 | 0.9096 |
34 | 12,220,000 | 0.61 | 0.61 | |
70 | 550,000 | 0.97 | 0.9697 | |
Subject 4 | 540 | 670,000 | 0.039 | 0.0388 |
1540 | 1,260,000 | 0.073 | 0.0729 | |
2017 | 1,140,000 | 0.076 | 0.0759 | |
Subject 5 | 70 | 700,000 | 1.15 | 1.1498 |
88 | 400,000 | 0.83 | 0.8296 | |
117 | 700,000 | 0.41 | 0.4098 | |
145 | 1,000,000 | 0.46 | 0.4599 | |
181 | 1,080,000 | 0.106 | 0.1059 | |
398 | 2,000,000 | 0.116 | 0.1159 | |
Subject 6 | 175 | 1,440,000 | 0.107 | 0.1069 |
209 | 800,000 | 0.168 | 0.1678 | |
286 | 1,480,000 | 0.086 | 0.0859 | |
730 | 1,200,000 | 0.12 | 0.1199 | |
Subject 7 | 102 | 380,000 | 0.43 | 0.4296 |
130 | 460,000 | 0.23 | 0.2297 | |
166 | 500,000 | 0.08 | 0.0797 | |
372 | 1,250,000 | 0.14 | 0.1399 |
The corrected D_{s,corr} is found by subtracting (L_{ s } - 1)/2n, where n = n_{0}/π, from the measured divergence at each time point, where L_{ s } = 14 (Table 5). The measured and corrected divergences as a function of 1/n_{0} are plotted in Figure 1(b). We note that there is no correction in the measured spectratype divergence, D_{ s }, since the number n_{0} of CD3 T-cells that we are starting with is always high.
Total divergence
By combining the individual contributions of flow and spectratype divergence, we defined the total divergence, D (see section ‘Kullback-Leibler divergence’). D measures the divergence of the individual from the perfectly sampled reference control and accounts for differences in distributions of CDR3 lengths within each TCR BV family by spectratyping as well as differences in distributions of overall TCR BV families by flow cytometry. Corrections in the flow and spectratype divergences are sufficient to ensure that the total divergence is independent of the sample size.
Discussion
The data used in our study came from flow cytometry and spectratype assays in both DiGeorge subjects after thymus transplantation and healthy adult volunteers. This study presents significant information regarding the utility of flow cytometry, as well as spectratyping, to assess the diversity of the antigen receptor repertoire. Importantly, these data identify a bias in measurement errors which must be corrected. The paper presents the relationships between the number of gated events in the flow cytometry assay, as well as the number of CD3 T-cells in the spectratype assay, and the information-theory measures, D_{ f } and D_{ s }, used as surrogates of TCR diversity.
We addressed a critical issue of estimator bias. Starting with the assumption that such a bias exists, we have derived ways to account for the error in the measured divergences. We show that D_{ f } and D_{ s } can be corrected by substracting a number inversely proportional to the sample size.
Correlation coefficient and p-values as given by a Pearson comparison test, between the inverse average number of CD4 T-cell used in flow cytometry assays and the flow divergence
Subject | Correlation coefficient | p-value |
---|---|---|
Control 1 | 0.99 | 0.0076 |
Control 2 | 0.98 | 0.0031 |
Control 3 | 0.32 | 0.58 |
Control 4 | 0.96 | 0.035 |
Subject 1 | 0.92 | 0.075 |
Subject 2 | 0.99 | 0.005 |
Subject 3 | 0.9 | 0.036 |
Subject 4 | 0.5 | 0.49 |
Our study allows us to predict a lower bound for the number of CD4 T-cells needed in the flow cytometry gated events. We have shown that at least 364 CD4 T-cells have to be counted as gated events for a 90% confidence in the D_{ f } measures. With fewer gated events, the D_{ f } measurement cannot be used as a substitute for diversity. This is particularly important to keep in mind when assessing patients with limited numbers of T-cells, such as those undergoing immune reconstitution following thymus, stem cell or bone marrow transplantation. Each of these is a clinical situation in which the development of the T-cell repertoire correlates to immune competency. Thus, these data provide a quantitative basis by which T-cell repertoire diversity can be assessed by flow cytometry.
Correlation coefficient and p-values as given by a Pearson comparison test, between the inverse total number of CD3 T-cell used in spectratype assays and the spectratye divergence
Subject | Correlation coefficient | p-value |
---|---|---|
Subject 1 | 0.92 | 0.25 |
Subject 4 | -0.98 | 0.11 |
Subject 5 | 0.66 | 0.15 |
Subject 6 | 0.97 | 0.03 |
Subject 7 | 0.64 | 0.35 |
The total divergence actively incorporates the flow divergence. Correction in the flow divergence, D_{ f }, guarantees independence of the total divergence, D, from the sample size.
Conclusions
In conclusion, sample size is a sensitive parameter in the predicted flow divergence values, but not in the spectratype divergence values. Although using flow cytometry to assess T-cell repertoire diversity is a valuable tool, one must have sufficient cells, or events, in the flow cytometry gate before using either the flow or the total divergence as a prediction for the TCR repertoire diversity.
Methods
Human subjects
List of TCR BV families and antibodies used in the flow cytometry assay
Antibody names | Clone | Family name^{∗} |
---|---|---|
V β 1 | BL37.2 | TRBV9 |
V β 2 | MPB2D5 | TRBV20 |
V β 3 | CH92 | TRBV28 |
V β 4 | WJF24 | TRBV29 |
V β 5.1 | IMMU157 | TRBV5 |
V β 5.3 | 3D11 | TRBV5 |
V β 5.2 | 36213 | TRBV5 |
V β 7.1 | ZOE | TRBV4 |
V β 7.2 | Zizou4 | TRBV4 |
V β 8.1 & V β 8.2 | 56C5 | TRBV12 |
V β 9 | FIN9 | TRBV3 |
V β 11 | C21 | TRBV25 |
V β 12 | VER2.32.1 | TRBV10 |
V β 13.2 | H132 | TRBV6 |
V β 13.6 | JU-74 | TRBV6 |
V β 14 | CAS1.1.3 | TRBV27 |
V β 16 | TAMAYA 1.2 | TRBV14 |
V β 17 | E17.5F3 | TRBV19 |
V β 18 | BA62 | TRBV18 |
V β 20 | ELL 1.4 | TRBV30 |
V β 22 | IMMU 546 | TRBV2 |
V β 23 | AF23 | TRBV13 |
List of TCR VB families and antibodies excluded from the flow cytometry studies
Antibody names | Clone | Family name^{∗} |
---|---|---|
V β 13.1 & 13.4 & 13.6 | IMMU 222 | TRBV6-5 & 6-6 & 6-9 |
V β 21.3 | IG125 | TRBV11-2 |
Human subjects
Subjects were enrolled in protocols that were approved by the Duke University Health System Institutional Review Board and were reviewed by the Food and Drug Administration under an Investigational New Drug application. All subjects were children. The parent(s) of each subject provided written informed consent.
Flow cytometry
Mean % of CD4 T-cells that use a TCR BV family as predicted by the flow cytometry assay
Antibody names | Mean % of CD4 T-cells |
---|---|
V β 1 | 3.21 |
V β 2 | 9.79 |
V β 3 | 4.80 |
V β 4 | 2.58 |
V β 5.1 | 6.78 |
V β 5.3 | 0.97 |
V β 5.2 | 0.70 |
V β 7.1 | 1.89 |
V β 7.2 | 1.12 |
V β 8.1 & V β 8.2 | 4.71 |
V β 9 | 3.48 |
V β 11 | 0.73 |
V β 12 | 1.85 |
V β 13.2 | 2.66 |
V β 13.6 | 1.84 |
V β 14 | 3.03 |
V β 16 | 0.91 |
V β 17 | 5.79 |
V β 18 | 1.96 |
V β 20 | 2.35 |
V β 22 | 4.12 |
V β 23 | 0.45 |
Spectratyping
Kullback-Leibler divergence
Flow Kullback-Leibler divergence
The flow Kullback-Leibler divergence is a measure of the distance between the two frequency distributions or, equivalently, it is the inefficiency of assuming that the distribution of BV family usage is p_{ i }, i = 1,...,n_{ F }, when the true frequency usage is P_{ i },i = 1,...,n_{ F }.
Spectratype Kullback-Leibler divergence
Total Kullback-Leibler divergence
Sampling bias - theoretical derivation
The distribution of BV family usage (CDR3 length within a BV family) of a perfectly sampled reference control can be described by a L_{ f } (L_{ s })-dimensional multinomial distribution with the parameter vector P, where p_{ i } is the relative numbers of T-cells that use the BV family (CDR3 length) i. The distribution of the actual, but not yet observed, BV family (CDR3 length) usage in individual patient/controls are subsamples q of the ideal distribution, where q_{ i } are the relative numbers of T-cells that use the BV family (CDR3 length) i. The distance between these two distributions is given by the parameter d^{-1}, with a large d accounting for a closer similarity between P and q. Finally, the observed distribution of BV family usage (CDR3 length), p, are samples of n measured events for every individual patient/control, where p_{ i } are the relative numbers of T-cells that use the BV family (CDR3 length) i. Here L_{ f } (L_{ s }) is the dimension of the measured space, i.e. the number of BV families used in the flow cytometry assay, in our case 18 (the number of CDR3 lengths used in spectratyping assay, in our case 14).
is the Kullback-Leibler divergence between p and q.
which relaxes the concern of variability due to sampling error.
Declarations
Acknowledgements
This work was supported by National Institute of Health grants R01 AI 54843, R01 AI 47040, M03 RR60 (Duke General Clinical Research Center, National Center for Research Resources, National Institute of Health), and Office of Orphan Products Development, Food and Drug Administration, grant FD-R-002606. MLM and TBK are members of the Duke Comprehensive Cancer Center. We acknowledge the technical assistance of Marilyn Alexieff, Jie Li, Chia-San Hsieh, Jennifer Lonon and Julie E. Smith, the clinical research assistance of Stephanie Gupton and Alice Jackson, and the regulatory affairs assistance of Elizabeth McCarthy and Michele Cox are appreciated as is the clinical care by the faculty and fellows of the Duke Pediatric Allergy and Immunology Division. We acknowledge the collaboration of surgeons James Jaggers, Andrew Lodge, Henry Rice, Micheal Skinner, and Jeffrey Hoehner. We appreciate the assistance of Drs. Michael Cook and Scott Langdon in the Duke Comprehensive Cancer Center flow cytometry and sequencing facilities.
Authors’ Affiliations
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