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Normalizing flows (NFs) provide uncorrelated samples from complex distributions, making them an appealing tool for parameter estimation. However, the practical utility of NFs remains limited by their tendency to collapse to a single mode of a multimodal distribution. In this study, we show that annealing with an adaptive schedule based on the effective sample size (ESS) can mitigate mode collapse. We demonstrate that our approach can converge the marginal likelihood for a biochemical oscillator model fit to time-series data in ten-fold less computation time than a widely used ensemble Markov chain Monte Carlo (MCMC) method. We show that the ESS can also be used to reduce variance by pruning the samples. We expect these developments to be of general use for sampling with NFs and discuss potential opportunities for further improvements. 

The cyanobacterial clock presents a unique opportunity to understand the biochemical basis of circadian rhythms. The core oscillator, composed of the KaiA, KaiB, and KaiC proteins, has been extensively studied, but a complete picture of its connection to the physiology of the cell is lacking. To identify previously unknown components of the clock, we used KaiB locked in its active fold as bait in an immunoprecipitation/mass spectrometry approach. We found that the most abundant interactor, other than KaiC, was a putative diguanylate cyclase protein predicted to contain multiple Per-Arnt-Sim (PAS) domains, which we propose to name KidA. Here we show that KidA directly binds to the fold-switched active form of KaiB through its N-terminal PAS domains. We found that KidA shortens the period of the circadian clock both in vivo and in vitro and alters the ability of the clock to entrain to light-dark cycles. The dose-dependent effect of KidA on the clock period could be quantitatively recapitulated by a mathematical model in which KidA stabilizes the fold-switched form of KaiB, favoring rebinding to KaiC. Put together, our results show that the period and amplitude of the clock can be modulated by regulating the access of KaiB to the fold-switched form.