Controlling brain dynamics: Landscape and transition path for working memory
Fig 3
Barrier height and transition path characterize the switching process in working memory.
(A) The illustration for the definition of barrier height (potential difference between the potential at local minimum and saddle point) and relative barrier height (the difference between the two barrier heights) to quantify the stability of attractors. If the system tries to escape from the current attractor, it needs to cross the corresponding barrier. (B) To quantify the difficulty of state transition for the formation of memory, we define the barrier height USR as the potential difference between the Usaddle (the potential at the saddle point between R and MA state) and the Umin (the potential at the minimum of R state). The USR decreases for higher strength of target stimulus, suggesting the easier formation of memory. (C) The projected transition path with dimension reduction on the landscape between R state and MA state for Itarget = 0.034nA. The transition from R to MA represents the formation of memory and the reverse path represents the clearance of memory. (D) The high-dimensional transition path from MA to MB before dimension reduction for a given time T = 10. The X-axis represents the 90 system variables and the Y-axis represents the time points along the transition path. (E) The transition paths between MA and MB for Idistractor = 0.04nA, which pass through the intermediate state R. The transition from MA to MB signifies the change of memory. (F) The deactivation sequence of population A in 30 brain areas shows a high correlation with the anatomical hierarchy as defined by layer-dependent connections [32]. This suggests that the information of distractors flows along the hierarchy, from early sensory areas to association areas. (G) The robustness against distractors during the delay epoch. The increase of relative barrier height between MA and MB as a function of the strength of distractors suggests that MA is becoming more unstable while MB is becoming more stable, thus decreasing the robustness of the system to distractors. R: resting state, MA: memory state encoded by population A, MB: memory state encoded by population B.