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Evaluation of monoclonality of cell lines from sequential dilution assays
Journal of Immunological Methods, 107 (1988) 151-152 Elsevier
151
JIM04728
Short communication
Evaluation of monoclonality of cell lines from sequential dilution assays * Part II J a m e s A. K o z i o l Department of Basic and Clinical Research, Research Institute of Scrzpps Clinic, 10666 North Torrey Pines Road, La Jolla, CA 92037, U.S.A. (Received 29 October 1987, revised received 24 November 1987, accepted 30 November 1987)
We extend the analysis in Koziol et al. (J. Immunol. Methods (1987) 105,139) for the determination of the probability of achieving monoclonality in limiting dilution assays to three or more cloning stages. We also provide a computer program which will carry out this analysis for an arbitrary number of stages.
Key words: T cell cloning; Limiting dilution method; Poisson analysis; Computer program
In a previous paper (Koziol et al., 1987), we described a two-stage cloning procedure for dilution assays that is designed to achieve a high probability of monoclonality of derived cell lines. We also presented a statistical algorithm appropriate for the calculation of the probability of monoclonality at the second stage, and gave a simple table which could be used in place of the oftentimes tedious calculations. The purpose of this note is two-fold: (i) to extend the analysis formally to three or more stages; and (ii) to announce the availability of a computer program for the determination of the probability of monoclonality at any stage. For simplicity, we shall
Correspondence to: J.A. Koziol, Department of Basic and Clinical Research, Research Institute of Scripps Clinic, 10666 North Torrey Pines Road, La Jolla, CA 92037, U.S.A. * This paper is supported in part by Grants CA41582 and RR00833 from the National Institutes of Health. This is Publication no. 5094BCR from the Research Institute of Scripps Clinic, La Jolla, CA, U.S.A.
adhere to the notational conventions introduced in Koziol et al. (1987), and shall assume the reader is familiar with its content. Suppose that an investigator has used the twostage design described in our previous paper, but finds the calculated probability of monoclonality to be insufficiently high to conclude with confidence that he can select a monoclonal cell line for further experimentation. In this instance, he could readily invoke a third stage, by randomly selecting a positive well from stage 2, and again replating at a low cell density. Thereafter, in order to implement the computational algorithm previously described for determining the likelihood of monoclonality, we first need to derive the probabilities of numbers of clones present in any positive well at stage 2. This derivation has already been carried out for the monoclonal case, and the polyclonal cases follow the same paradigm. The key fact needed for this derivation in general devolves from the recognition that, under the sampling assumptions in our previous paper, to
0022-1759/88/$03.50 © 1988 Elsevier Science Publishers B.V. (Biomedical Division)
152 TABLE VI PROBABILITIESOF NUMBERS OF CLONES PRESENT IN ANY POSITIVEWELL AT STAGE 2 Number of clones, k 1
Probability, PK(k)
2
3
_>4
0.953 0.0476 0.001 0.0002
realize, say, k clones by plating j cells from a well in which i clonal lines are present is equivalent to the scenario addressed in the classical occupancy problem (Feller, 1958); therefore, the probability of this event is given by pk(j,i)=
(i i k
y~ ( - 1)" m=O
rn/~
i
/ '
k
Note in particular that P1(J, i ) = i l - / , as was used previously. Hence P K ( k ) , the probability of k clones present in any positive well at stage 2, is the convolution
The efficacy of the second stage in promoting monoclonality is readily apparent upon comparing Table II in our previous paper with Table VI. Clearly, the induction of a third stage in our particular experimental regimen would yield a probability of monoclonality approaching one. Equation (1) is immediately applicable to this calculation mutatis mutandis and is incorporated into our computer program. The computer program, then, provides the probabilities of numbers of clones present in any positive well, the analogues of Tables II and VL for an arbitrary number of stages. The program is self-contained and written in standard Fortran, and the source code listing is freely available upon request. Alternatively, an executable version which will run under MS-DOS on IBM-PC type personal computers is also available; those interested in obtaining a copy should send a blank diskette and mailer to the author.
References
PK(k)= E
Z Pl(i)PJ(J)pk(J,i)
(1)
i>_l j ~ l
With the particular experimental data presented before, we thereby establish Table VI.
Feller, W. (1958) An Introduction to Probability Theory and Its Applications, Vol. 1. John Wiley, New York, p. 102. Koziol, J.A., Ferrari, C. and Chisari, F.V. (1987) Evaluation ot monoclonality of cell lines from sequential dilution assays. J. Immunol. Methods 105, 139.
151
JIM04728
Short communication
Evaluation of monoclonality of cell lines from sequential dilution assays * Part II J a m e s A. K o z i o l Department of Basic and Clinical Research, Research Institute of Scrzpps Clinic, 10666 North Torrey Pines Road, La Jolla, CA 92037, U.S.A. (Received 29 October 1987, revised received 24 November 1987, accepted 30 November 1987)
We extend the analysis in Koziol et al. (J. Immunol. Methods (1987) 105,139) for the determination of the probability of achieving monoclonality in limiting dilution assays to three or more cloning stages. We also provide a computer program which will carry out this analysis for an arbitrary number of stages.
Key words: T cell cloning; Limiting dilution method; Poisson analysis; Computer program
In a previous paper (Koziol et al., 1987), we described a two-stage cloning procedure for dilution assays that is designed to achieve a high probability of monoclonality of derived cell lines. We also presented a statistical algorithm appropriate for the calculation of the probability of monoclonality at the second stage, and gave a simple table which could be used in place of the oftentimes tedious calculations. The purpose of this note is two-fold: (i) to extend the analysis formally to three or more stages; and (ii) to announce the availability of a computer program for the determination of the probability of monoclonality at any stage. For simplicity, we shall
Correspondence to: J.A. Koziol, Department of Basic and Clinical Research, Research Institute of Scripps Clinic, 10666 North Torrey Pines Road, La Jolla, CA 92037, U.S.A. * This paper is supported in part by Grants CA41582 and RR00833 from the National Institutes of Health. This is Publication no. 5094BCR from the Research Institute of Scripps Clinic, La Jolla, CA, U.S.A.
adhere to the notational conventions introduced in Koziol et al. (1987), and shall assume the reader is familiar with its content. Suppose that an investigator has used the twostage design described in our previous paper, but finds the calculated probability of monoclonality to be insufficiently high to conclude with confidence that he can select a monoclonal cell line for further experimentation. In this instance, he could readily invoke a third stage, by randomly selecting a positive well from stage 2, and again replating at a low cell density. Thereafter, in order to implement the computational algorithm previously described for determining the likelihood of monoclonality, we first need to derive the probabilities of numbers of clones present in any positive well at stage 2. This derivation has already been carried out for the monoclonal case, and the polyclonal cases follow the same paradigm. The key fact needed for this derivation in general devolves from the recognition that, under the sampling assumptions in our previous paper, to
0022-1759/88/$03.50 © 1988 Elsevier Science Publishers B.V. (Biomedical Division)
152 TABLE VI PROBABILITIESOF NUMBERS OF CLONES PRESENT IN ANY POSITIVEWELL AT STAGE 2 Number of clones, k 1
Probability, PK(k)
2
3
_>4
0.953 0.0476 0.001 0.0002
realize, say, k clones by plating j cells from a well in which i clonal lines are present is equivalent to the scenario addressed in the classical occupancy problem (Feller, 1958); therefore, the probability of this event is given by pk(j,i)=
(i i k
y~ ( - 1)" m=O
rn/~
i
/ '
k
Note in particular that P1(J, i ) = i l - / , as was used previously. Hence P K ( k ) , the probability of k clones present in any positive well at stage 2, is the convolution
The efficacy of the second stage in promoting monoclonality is readily apparent upon comparing Table II in our previous paper with Table VI. Clearly, the induction of a third stage in our particular experimental regimen would yield a probability of monoclonality approaching one. Equation (1) is immediately applicable to this calculation mutatis mutandis and is incorporated into our computer program. The computer program, then, provides the probabilities of numbers of clones present in any positive well, the analogues of Tables II and VL for an arbitrary number of stages. The program is self-contained and written in standard Fortran, and the source code listing is freely available upon request. Alternatively, an executable version which will run under MS-DOS on IBM-PC type personal computers is also available; those interested in obtaining a copy should send a blank diskette and mailer to the author.
References
PK(k)= E
Z Pl(i)PJ(J)pk(J,i)
(1)
i>_l j ~ l
With the particular experimental data presented before, we thereby establish Table VI.
Feller, W. (1958) An Introduction to Probability Theory and Its Applications, Vol. 1. John Wiley, New York, p. 102. Koziol, J.A., Ferrari, C. and Chisari, F.V. (1987) Evaluation ot monoclonality of cell lines from sequential dilution assays. J. Immunol. Methods 105, 139.