Turing pattern or system heterogeneity? A numerical continuation approach to assessing the role of Turing instabilities in heterogeneous reaction-diffusion systems

Turing patterns in reaction-diffusion (RD) systems have classically been studied only in RD systems which do not explicitly depend on independent variables such as space. In practise, many systems for which Turing patterning is important are not homogeneous with ideal boundary conditions. In heterogeneous systems with stable steady states, the steady states are also necessarily heterogeneous which is problematic for applying the classical analysis. Whilst there has been some work done to extend Turing analysis to some heterogeneous systems, for many systems it is still difficult to determine if a stable patterned state is driven purely by system heterogeneity or if a Turing instability is playing a role. In this work, we try to define a framework which uses numerical continuation to map heterogeneous RD systems onto a sensible nearby homogeneous system. This framework may be used for discussing the role of Turing instabilities in establishing patterns in heterogeneous RD systems. We study the Schnakenberg and Gierer-Meinhardt models with spatially heterogeneous production as test problems. It is shown that for sufficiently large system heterogeneity (large amplitude spatial variations in morphogen production) it is possible that Turing-patterned and base states become coincident and therefore impossible to distinguish. Other exotic behaviour is also shown to be possible. We also study a novel scenario in which morphogen is produced locally at levels that could support Turing patterning but on intervals/patches which are on the scale of classical critical domain lengths. Without classical domain boundaries, Turing patterns are allowed to bleed through; an effect noted by other authors. In this case, this phenomena effectively changes the critical domain length. Indeed, we even note that this phenomena may also effectively couple local patches together and drive instability in this way.Comment: 10 figure

AI is a viable alternative to high throughput screening: a 318-target study

: High throughput screening (HTS) is routinely used to identify bioactive small molecules. This requires physical compounds, which limits coverage of accessible chemical space. Computational approaches combined with vast on-demand chemical libraries can access far greater chemical space, provided that the predictive accuracy is sufficient to identify useful molecules. Through the largest and most diverse virtual HTS campaign reported to date, comprising 318 individual projects, we demonstrate that our AtomNet® convolutional neural network successfully finds novel hits across every major therapeutic area and protein class. We address historical limitations of computational screening by demonstrating success for target proteins without known binders, high-quality X-ray crystal structures, or manual cherry-picking of compounds. We show that the molecules selected by the AtomNet® model are novel drug-like scaffolds rather than minor modifications to known bioactive compounds. Our empirical results suggest that computational methods can substantially replace HTS as the first step of small-molecule drug discovery