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1/ Our new #neuroscience paper, "Emergent elasticity in the neural code for space" just appeared in @PNASNews: pnas.org/content/early/… Awesome work lead by @SamOcko, with @kiahhardcastle and @lisa_giocomo . Take home messages... 
2/ We ask: how do we learn where we are? two info sources are needed: 1) our recent history of velocity; 2) what landmarks we have encountered. How can neurons/synapses fuse these two sources to build a consistent spatial map as we explore a new place we have never seen before?
3/ We show a simple attractor network with velocity inputs that move an attractor bump and landmark inputs that pin the attractor bump can do this - with Hebbian plasticity from landmark inputs to the attractor network.
4/ We prove analytically that the combined neural dynamics and synaptic learning solves a fundamental consistency condition: if landmark A pins the attractor bump to a certain state, motion from landmark A to B moves it precisely to the state that landmark B pins the bump to
5/ In fact we prove the combined neural/synaptic dynamics reduces to a spring mass system: each landmark cell’s efferent synapses reduces to a particle in physical space; pairs of particles are connected by springs w/ rest length = the physical distance separating the landmarks
6/ Because neural learning reduces to this emergent spring mass system, exploration of a new environment will provably self-organize a consistent map of space; but this theory makes testable predictions about grid cells too, assuming borders are prominent landmarks…
7/ First, we predict grid cell activity patterns will be sucked towards the last border the animal just came from; this turns out to be true! They get sucked about 2cm towards the last border; note this may be a feature not a bug (biased estimators can outperform unbiased ones)
8/ Our theory naturally explains why and how grid cells become deformed in irregular environments; boundaries pin the attractor bump, and so firing in the interior is influenced by the boundary pinning. The left figure is data, the right figure is simulations of our theory
9/ Our theory makes a prediction that we could create topological defects in grid cells through specific environmental manipulations. This suggests new experiments!
10/ And a special case of our theory explains how grid cells respond to altered virtual reality experiments in which landmarks and path integration disagree. If the disagreement is small (large) grid cells phase shift (remap). See our paper @NatureNeuro: nature.com/articles/s4159…
