Bias-free estimation of information content in temporally sparse neuronal activity

Applying information theoretic measures to neuronal activity data enables the quantification of neuronal encoding quality. However, when the sample size is limited, a naïve estimation of information typically contains an upward bias, which may lead to misinterpretation of coding characteristics. This bias is exacerbated in Ca2+ imaging because of the temporal sparsity of detected Ca2+ signals. Here, we introduce methods to correct the bias in the naïve estimation of information from limited sample sizes and temporally sparse activity. We demonstrate the higher accuracy of our methods over previous ones, when applied to Ca2+ imaging data recorded from the mouse hippocampus and primary visual cortex, and to simulated data with matching tuning properties and firing statistics. Our bias-correction methods allowed an accurate estimation of the spatial information carried by place cells and revealed the spatial resolution of the hippocampal code. Furthermore, using our methods, we found that cells with higher within-field firing rates carry higher information per spike, and exposed the long-term evolution of the spatial code across distinct hippocampal subfields. Overall, a bias-free estimation of information can uncover properties of the neural code that could be masked by the bias when applying the commonly used naïve calculation of information.