Dose response curve fitting

Ramnik J Xavier

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Dose response curve fitting

RX Ramnik J Xavier

Last updated date: Oct 21, 2020 Views: 974 Forks: 0

An abbreviated version of this protocol was published in eLife in May, 2015

The kinase DYRK1A reciprocally regulates the differentiation of Th17 and regulatory T cells

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Dose response curves for fractional enhancement of Treg cell differentiation and culture cellularity were analyzed in Matlab to identify EC50 and LD50 doses, at which 50% Treg enhancement and cytotoxicity are observed, respectively. Each compound was profiled across eight doses selected to sufficiently cover response dynamics. Dose response curves were fitted with either a single sigmoid or a double sigmoid function, depending on whether the response was asymptotic or impulse-like. An impulse function has the form:

$f = \frac{1}{r_{1}} s (d : d_{1}, r_{l}, r_{p}, α_{1}) \times s (d : d_{2}, r_{h}, r_{p}, α_{2}),$

where

$s (d : d_{m}, r_{i}, r_{f}, α) = r_{i} + (r_{f} - r_{i}) \frac{1}{1 + e^{- 4 α (d - d_{m})}},$

is a sigmoid function with a response that ranges from ri to rf with mid-point at dose dm and a slope of α*sign(rf − ri) at dose dm. The parameters of this model describe the dose of response onset (d1), dose of response offset (d2), initial response at lowest dose (rl), peak response (rp), final response at highest dose (rh), and two slope parameters to model the rate of response onset (α1) and offset (α2). A single-sigmoid function uses only four parameters (d, r1, r2, α). All models were fitted to data using fmincon function in Matlab. Fitted models were reverse-queried to estimate the dose at which 50% of the peak response parameter was observed.

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Readers should cite both the Bio-protocol preprint and the original research article where this protocol was used:

Xavier, R(2020). Dose response curve fitting. Bio-protocol Preprint. bio-protocol.org/prep564.
Khor, B., Gagnon, J. D., Goel, G., Roche, M. I., Conway, K. L., Tran, K., Aldrich, L. N., Sundberg, T. B., Paterson, A. M., Mordecai, S., Dombkowski, D., Schirmer, M., Tan, P. H., Bhan, A. K., Roychoudhuri, R., Restifo, N. P., O'Shea, J. J., Medoff, B. D., Shamji, A. F., Schreiber, S. L., Sharpe, A. H., Shaw, S. Y. and Xavier, R. J.(2015). The kinase DYRK1A reciprocally regulates the differentiation of Th17 and regulatory T cells. eLife. DOI: 10.7554/eLife.05920