Cell-to-cell variations in gene regulation occur in a number of biological contexts such as development and cancer. dissociation and molecular profiling is especially problematic. and = 20% and = 0.48. Fig. 2. Inferring cellular subpopulations by maximum-likelihood inference of stochastic 10-cell samples Maackiain from an LN-LN mixture of regulatory states. (and = 1 creates a distribution that has ～37% overlap with that of a high lognormal state of = 0.5 and = 0.225 whereas = 3 causes only a ～6.3% overlap. We modeled two distinct regulatory states by restricting the simulations to rate parameters that caused negligible overlap with the high lognormal state (> 3). Together the different mixture models enabled us to simulate stochastic-profiling data by summing the expression of 10 cells randomly sampled from the appropriate two-state distribution (step 2 2 Fig. 2and and and and and individually while keeping the other three parameters fixed and simulated 50 random 10-cell samples. For a wide range of subpopulation log-means (and = 50% when the two subpopulations offset one another and disguise as a distribution with large (Fig. 2= 0-35% over the range of 0-50%). For the log-SD (reached ～0.8 corresponding to a ～95% CV that is higher than nearly all genes examined thus far (35 36 None of the mixture parameters could be reliably inferred from higher-order moments of the 10-cell distributions although low or high correlated with a slight increase in skewness (and were large enough to prevent overlap of the two regulatory states we found that parameter estimates were accurate although the variance of inferred was somewhat higher than in the LN-LN mixture (regulatory states among the ECM-attached cells (27 39 To apply maximum-likelihood inference we deeply sampled expression by quantitative PCR (qPCR) in 81 random samples of 10 ECM-attached cells (Fig. Maackiain 2and = 46) or a lognormal distribution with a very small log-mean (expression frequencies among ECM-attached cells: 23% (13-33%) Maackiain for the LN-LN mixture vs. 19% (12-27%) for the Rabbit Polyclonal to MMP-19. EXP-LN mixture. To determine the accuracy of this shared prediction we directly measured in 3D spheroids by RNA FISH (Fig. 2fluorescence intensity we calculated an expression frequency of ～26%. This measurement closely agreed with the inferred parameter of the LN-LN mixture (the better-scoring model; Fig. 2and data we found that at least 50 observations were required to arrive at an accurate result (and parameterization suggested that maximum-likelihood inference could correctly extract single-cell information from 10-cell sampling data. Maximum-Likelihood Inference of Coordinated Stochastic Transcriptional Profiles. Programs of gene expression are often controlled by common upstream factors that enforce Maackiain the regulatory state. We reasoned that coordinated single-cell gene programs would be the product of an overarching regulatory heterogeneity characterized by a shared and for the EXP-LN mixture) to account for gene-to-gene differences in expression level and detection sensitivity. Next we assumed that the genes within a cluster share a common and (or genes involved 2+ 2 or 2+ 3 parameters. Even for small gene programs (≤ 10) this parameter search space was too large for nonconvex optimization methods to maximize the global likelihood function quickly ((steps 1 and 2 Fig. 3(EXP-LN mixture) (steps 3 and 4 Fig. 3and were accurate within the coexpressed clusters we designed and validated riboprobes for four or five genes in each cluster and quantified their frequency Maackiain of high expression by RNA FISH (and and and and and parameters suggesting that our extended inference approach was effective and accurate. We evaluated the estimates of expression frequency more broadly by selecting four additional clusters from the same dataset for parameterization (estimates that ranged from less than 5% to greater than 25% (Fig. 4 and = 0.89 Fig. 4and = 2.3%). The very rare cluster was also distinguished by its strong concordance with the relaxed LN-LN mixture compared with the alternative mixture models ([alternatively called or (42)] the breast cancer-associated gene (43) and the zinc-finger gene alternatively called and (Fig. 5and was transcriptionally up-regulated with delayed kinetics compared with the other PI3K isoforms (Fig..