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Generative models, especially diffusion models (DMs), have achieved promising results for generating feature-rich geometries and advancing foundational science problems such as molecule design. Inspired by the recent huge success of Stable (latent) Diffusion models, we proposed a novel and principled method for 3D molecule generation named Geometric Latent Diffusion Models (GeoLDM). GeoLDM is the first latent DM model for the molecular geometry domain, composed of autoencoders encoding structures into continuous latent codes and DMs operating in the latent space. Our key innovation is that for modeling the 3D molecular geometries, we capture its critical roto-translational equivariance constraints by building a point-structured latent space with both invariant scalars and equivariant tensors. Extensive experiments demonstrate that GeoLDM can consistently achieve better performance on multiple molecule generation benchmarks, with up to 7% improvement for the valid percentage of large biomolecules. Results also demonstrate GeoLDM’s higher capacity for controllable generation thanks to the latent modeling. 

Cells adapt and respond to changes by regulating the activity of their genes. To turn genes on or off, they use a family of proteins called transcription factors. Transcription factors influence specific but overlapping groups of genes, so that each gene is controlled by several transcription factors that act together like a dimmer switch to regulate gene activity. The presence of transcription factors attracts proteins such as the Mediator complex, which activates genes by gathering the protein machines that read the genes. The more transcription factors are found near a specific gene, the more strongly they attract Mediator and the more active the gene is. A specific region on the transcription factor called the activation domain is necessary for this process. The biochemical sequences of these domains vary greatly between species, yet activation domains from, for example, yeast and human proteins are often interchangeable. To understand why this is the case, Sanborn et al. analyzed the genome of baker’s yeast and identified 150 activation domains, each very different in sequence. Three-quarters of them bound to a subunit of the Mediator complex called Med15. Sanborn et al. then developed a machine learning algorithm to predict activation domains in both yeast and humans. This algorithm also showed that negatively charged and greasy regions on the activation domains were essential to be activated by the Mediator complex. Further analyses revealed that activation domains used different poses to bind multiple sites on Med15, a behavior known as ‘fuzzy’ binding. This creates a high overall affinity even though the binding strength at each individual site is low, enabling the protein complexes to remain dynamic. These weak interactions together permit fine control over the activity of several genes, allowing cells to respond quickly and precisely to many changes. The computer algorithm used here provides a new way to identify activation domains across species and could improve our understanding of how living things grow, adapt and evolve. It could also give new insights into mechanisms of disease, particularly cancer, where transcription factors are often faulty.