A Closed-Form Bayesian Framework for DNA Replication Reveals Intrinsic Origin Timing and Activation Delays

We present an analytical framework for modeling eukaryotic DNA replication that, given experimental Replication Fork Directionality (RFD) data, enables Bayesian inference of origin number, activation delay (t) and intrinsic timing ({lambda}), the mean replication time if each origin were isolated. By deriving closed-form expressions for RFD and Mean Replication Timing (MRT) under exponential and a specific Weibull firing-time distributions as functions of (t) and ({lambda}), we eliminate the need for stochastic simulations. These analytical results reveal that RFD, as a ratio of fork directions, is invariant under joint rescaling of intrinsic timing and fork speed; absolute intrinsic timing can nonetheless be inferred when fork speed is independently measured. We demonstrate that under exponential firing distribution for the origin, the observed efficiency (E), i.e. the probability for an origin to fire which accounts for nearby origins, is simply MRT(x)/{lambda}. The closed-form RFD expressions allow use of a Bayesian method that achieves 0.96-0.99 correlation with yeast RFD profiles and resolves [~]780 origins in S. cerevisiae. Our framework identifies about 150 origins with biologically significant delays ([≥] 3 minutes), revealing regulated activation kinetics undetectable by existing methods. By quantifying how origin intrinsic timing and delays shape replication timing landscapes, this work confirms yeast as a paradigm organism for studying DNA replication control mechanisms.