Approximate Bayesian computation (ABC) methods can be used to evaluate posterior distributions without having to calculate likelihoods. In this paper, we discuss and apply an ABC method based on sequential Monte Carlo (SMC) to estimate parameters of dynamical models. We show that ABC SMC provides information about the inferability of parameters and model sensitivity to changes in parameters, and tends to perform better than other ABC approaches. The algorithm is applied to several well-known biological systems, for which parameters and their credible intervals are inferred. Moreover, we develop ABC SMC as a tool for model selection; given a range of different mathematical descriptions, ABC SMC is able to choose the best model using the standard Bayesian model selection apparatus.

The seasonal influenza A virus undergoes rapid evolution to escape human immune response. Adaptive changes occur primarily in antigenic epitopes, the antibody-binding domains of the viral hemagglutinin. This process involves recurrent selective sweeps, in which clusters of simultaneous nucleotide fixations in the hemagglutinin coding sequence are observed about every 4 years. Here, we show that influenza A (H3N2) evolves by strong clonal interference. This mode of evolution is a red queen race between viral strains with different beneficial mutations. Clonal interference explains and quantifies the observed sweep pattern: we find an average of at least one strongly beneficial amino acid substitution per year, and a given selective sweep has three to four driving mutations on average. The inference of selection and clonal interference is based on frequency time series of single-nucleotide polymorphisms, which are obtained from a sample of influenza genome sequences over 39 years. Our results imply that mode and speed of influenza evolution are governed not only by positive selection within, but also by background selection outside antigenic epitopes: immune adaptation and conservation of other viral functions interfere with each other. Hence, adapting viral proteins are predicted to be particularly brittle. We conclude that a quantitative understanding of influenza’s evolutionary and epidemiological dynamics must be based on all genomic domains and functions coupled by clonal interference.

Ring topologies of repressing genes have qualitatively different long-term dynamics if the number of genes is odd (they oscillate) or even (they exhibit bistability). However, these attractors may not fully explain the observed behaviour in transient and stochastic environments such as the cell. We show here that even repressilators possess quasi-stable, travelling wave periodic solutions that are reachable, long-lived and robust to parameter changes. These solutions underlie the sustained oscillations observed in even rings in the stochastic regime, even if these circuits are expected to behave as switches. The existence of such solutions can also be exploited for control purposes: operation of the system around the quasi-stable orbit allows us to turn on and off the oscillations reliably and on demand. We illustrate these ideas with a simple protocol based on optical interference that can induce oscillations robustly both in the stochastic and deterministic regimes.

The applications of synthetic biology will involve the release of artificial life forms into the environment. These organisms will present unique safety challenges that need to be addressed by researchers and regulators to win public engagement and support.