How should biologists engage with controversial mathematical theory?

Mathematics is beautiful and precise and often necessary to understand complex biological phenomena. And yet biologists cannot always hope to fully understand the mathematical foundations of the theory they are using or testing. How then should biologists behave when mathematicians themselves are in dispute? Using the on-going controversy over Hamilton's rule as an example, I argue that biologists should be free to treat mathematical theory with a healthy dose of agnosticism. In doing so biologists should equip themselves with a disclaimer that publicly admits that they cannot entirely attest to the veracity of the mathematics underlying the theory they are using or testing. The disclaimer will only help if it is accompanied by three responsibilities - stay bipartisan in a dispute among mathematicians, stay vigilant and help expose dissent among mathematicians, and make the biology larger than the mathematics. I must emphasize that my goal here is not to take sides in the on-going dispute over the mathematical validity of Hamilton's rule, indeed my goal is to argue that we should refrain from taking sides.

Weak conservation of structural features in the interfaces of homologous transient protein-protein complexes

Residue types at the interface of protein-protein complexes (PPCs) are known to be reasonably well conserved. However, we show, using a dataset of known 3-D structures of homologous transient PPCs, that the 3-D location of interfacial residues and their interaction patterns are only moderately and poorly conserved, respectively. Another surprising observation is that a residue at the interface that is conserved is not necessarily in the interface in the homolog. Such differences in homologous complexes are manifested by substitution of the residues that are spatially proximal to the conserved residue and structural differences at the interfaces as well as differences in spatial orientations of the interacting proteins. Conservation of interface location and the interaction pattern at the core of the interfaces is higher than at the periphery of the interface patch. Extents of variability of various structural features reported here for homologous transient PPCs are higher than the variation in homologous permanent homomers. Our findings suggest that straightforward extrapolation of interfacial nature and inter-residue interaction patterns from template to target could lead to serious errors in the modeled complex structure. Understanding the evolution of interfaces provides insights to improve comparative modeling of PPC structures.

Perturbation of nucleo-cytoplasmic transport affects size of nucleus and nucleolus in human cells

Size regulation of human cell nucleus and nucleolus are poorly understood subjects. 3D reconstruction of live image shows that the karyoplasmic ratio (KR) increases by 30-80% in transformed cell lines compared to their immortalized counterpart. The attenuation of nucleo-cytoplasmic transport causes the KR value to increase by 30-50% in immortalized cell lines. Nucleolus volumes are significantly increased in transformed cell lines and the attenuation of nucleo-cytoplasmic transport causes a significant increase in the nucleolus volume of immortalized cell lines. A cytosol and nuclear fraction swapping experiment emphasizes the potential role of unknown cytosolic factors in nuclear and nucleolar size regulation.