Analysis of cellular interactions in limiting dilution cultures

Limiting dilution (LD) cultures are often used to study cellular heterogeneity in responses of murine splenocytes to specific or polyclonal activation. LD titration curves often reveal a nonlinear dependence of response on input cell dose. Although ‘zigzag’ shaped curves of this kind are often interpreted and analyzed as resulting from interactions among three distinct cell types, we observe that a more parsimonious two cell model, including a cell type that can generate both positive and negative effects, provides better fit to a wide range of experimental data. We have developed mathematical models for the accurate estimation of the frequencies of both interacting cell types and of the parameters for their multi-hit interaction. We show examples of LD cultures in which specific experimental manipulations alter the frequency of only one of the two cell types, or alter the interaction parameters without a change in responder frequency. We also provide a simplified method for approximation of the model parameters using graphical approaches and simple algebra. Lastly, we present an improved method for calculation of the effect generated per responder cell in microclonal cultures.