( em C /em ) Schematic of proposed deformation routine that could yield a topological defect in grid cell firing patterns. the space of all possible firing patterns. Just as indexes a family of neurons within the neural sheet, the coordinate indexes the different stable neural activity patterns, with a particular value of related to a stable bump within the neural ring centered at coordinate along the neural ring and the coordinate along the ring of stable attractor patterns are both perspectives, defined modulo and are phase variables denoting position along the neural ring and the ring of bump-attractor patterns, respectively. Open in a separate windows Fig. 1. Schematic of a ring attractor with short-range excitation (reddish arrows) and longer-range inhibition (blue arrows). This yields a 1D family of bump-attractor claims representing the maximum of the bump pattern. Motions Along the Attractor Manifold Due to External Inputs. So far, the attractor network explained above has a ring of stable bump activity patterns parameterized from the periodic coordinate along the attractor manifold to the actual position of the animal in physical space. However, to appropriately form such an internal map of position, and therefore map Rabbit Polyclonal to CD97beta (Cleaved-Ser531) the environment, the attractor state must be affected by external inputs from both velocity- and landmark-sensitive cells Glycolic acid oxidase inhibitor 1 inside a self-consistent manner. Path Integration Through Velocity-Conjunctive Attractor Cells. Following refs. 28 and 29, we accomplish path integration by coupling the attractor network to velocity-conjunctive attractor cells such that east (west) movement-selective cells form feedforward synapses onto the attractor ring that are shifted in the positive (bad) direction (Fig. 2 and is a constant of proportionality that relates animal Glycolic acid oxidase inhibitor 1 velocity to the rate of phase advance in the attractor network (and ensures that as the animal techniques east (western) along a 1D track, the attractor phase techniques clockwise (counterclockwise), at a rate proportional to velocity. Solving Eq. 2 allows us to recover path integration (Fig. 2as a purely sensory-driven cell having a firing rate that depends on location through is the firing field of the landmark cell. An example of a landmark cell could, for example, become an entorhinal border cell (4). Every landmark cell forms feedforward contacts onto each cell in the attractor network at ring position having a synaptic strength like a function of position within the neural ring consists of a solitary bump centered at a particular location (Fig. 2on the ring at which the landmark cell provides its maximum synaptic strength. Thus, we expect the attractor phase to move to and be pinned in the phase is a pressure legislation that determines how a landmark cell with maximum synaptic strength at causes the attractor phase to move. We have also launched a parameter that settings how strongly landmark cells influence the attractor phase. Generically, the pressure law is definitely positive (bad) when its discussion is definitely positive (bad). Therefore, it acts like a repairing pressure: When each landmark cell fires, it causes the attractor phase to circulation toward the phase corresponding to Glycolic acid oxidase inhibitor 1 the location of the landmark cells maximum outgoing synaptic strength. An attractor phase that is smaller (larger) than the landmark cell synapses maximum location will increase (decrease) and Glycolic acid oxidase inhibitor 1 settle down at (Fig. 2governing the velocity of the bump maximum; in general, the pressure legislation will have the same qualitative features as is exactly through Eq. 4. However, there is as yet no mechanism to enforce regularity between Glycolic acid oxidase inhibitor 1 the attractor phases arrived at through path integration and the various attractor phases arrived at through pinning by landmark cells. We next expose Hebbian plasticity of efferent landmark cell synapses during exploration while both.