The head direction (HD) system provides a continuous representation of the animal’s facing direction and is a core component of the spatial navigation network. Although mature HD circuits have been studied extensively, their developmental origin remains unclear, particularly because young animals already show attractor-like internal coherence before stable visual anchoring is established. Here we propose a developmental computational framework of the lateral mammillary nucleus and dorsal tegmental nucleus (LMN–DTN) circuit, in which a functional HD ring attractor emerges through staged self-organization without preconfigured topology or early external supervision. In the model, a randomly connected LMN network first generates stable travelling waves through relative refractoriness. These waves provide a temporal scaffold for subsequent learning. Local STDP-like and structural plasticity then consolidate wave-based statistics into locally enhanced recurrent connectivity, followed by direction-selective shift-feedback learning in the DTN → LMN pathway. At a later stage, recruited long-range inhibition transforms the travelling-wave manifold into a stable single activity profile (bump) attractor. Visual input acts mainly as a late calibration signal for global integration gain: it improves short-timescale path integration, but does not remove long-term drift. The framework provides a testable account of the developmental dissociation between early internal organization and later sensory anchoring. More broadly, it suggests that key components of classical ring attractor models, including local recurrent structure, direction-selective shift feedback, and late stabilizing mechanisms, can arise through a staged developmental process rather than relying on a preconfigured network architecture.
In this article, a control strategy is proposed to control the energy level and firing modes in a memristive neuron with hybrid ion channel, in which this branch circuit connects a memristor in series with an inductor. Energy and current are shunted from the hybrid ion channel for further saving in the external applied control device. Another memristor connects a constant voltage source for producing memristive current as external excitation and this design generates forcing currents within finite frequency band like realistic stimuli applied to biological neurons. A sub-branch circuit containing a capacitor is intervened into the hybrid ion channel (combining memristor and inductor), and the shunting current is changed when the capacitor parameter in the control branch circuit is tamed following continuous energy shunting from the neural circuit, as a result, the energy level in the neuron is modified to support appropriate firing patterns. In presence of noisy disturbance, coherence resonance is induced and affected by the parameter setting in the sub-branch circuit. Our results provide a feasible strategy for controlling electrical activities in neurons and their equivalent neural circuits, and also offer guidance for further local pacing in neural networks by injecting or shunting energy flow.
The dynamical behaviour of a population-based rate model with firing adaptation is studied. An excitatory and inhibitory population of neurons is recurrently coupled and a negative feedback term is added to the excitatory population as firing adaptation. In several studies of these models, the UP-DOWN transitions are in focus, which are also exhibited by the investigated model. In this paper we provide a full characterization of equilibrium points with the precise conditions for their existence and stability. Calculations can be performed analytically and explicit formulas can be provided due to the fact that the activation function is a threshold linear function. We use bifurcation analysis to detect significant changes in the phase space. Complete list of bifurcation diagrams is provided with respect to the number of steady states. Oscillatory dynamics of neurobiological relevance are examined through local bifurcation analysis. The study demonstrates that sharp wave-ripple oscillations may emerge in certain regions of the parameter space.
Understanding complex neuronal behavior in our brain requires accurate estimation of neuronal models from observed time-series data. In this study, we propose a data-driven sparse modeling method to estimate multi-dimensional latent variables and electrical properties while extracting essential membrane currents from partially observable time series data. First, we derive a nonlinear state space model from a conductance-based neuron model that couples membrane potential and calcium concentration including a set of candidate membrane currents. Then, we derive a sparse modeling-based expectation-maximization (EM) algorithm. In the expectation step, the expectation of the log-likelihood with Laplace prior distribution is evaluated using the posterior distribution of latent states, which is approximated by a sequential Monte Carlo (SMC) method under one-dimensional noisy observations. In the maximization step, the conductances are estimated as zero value for unnecessary currents whereas those are estimated as non-zero value for necessary currents. We show using simulation with conductance-based neuron model that the proposed method can extract the latent nonlinear neuronal dynamics from partially observable data by estimating latent variables and biophysical parameters and extracting only necessary membrane currents.
Altered connectivity in the prefrontal cortex-amygdala circuit in Major Depressive Disorder is associated with abnormal circuit states. Although substantial evidence from neuroimaging studies has demonstrated that changes in functional connectivity within this circuit during depressive states are commonly reported as a key feature, little is known about how these changes may relate to circuit functioning. In this study, we propose a biophysical computational model that incorporates an improved Jansen-Rit neural mass model to construct the circuit. Resting-state functional magnetic resonance imaging is used to calculate the functional connectivity of the circuit and simulate brain signals. The aim is to investigate how abnormalities in functional connectivity may contribute to or be associated with the underlying mechanisms of circuit dysfunction. The numerical simulation results indicate that under normal conditions, the amygdala plays a key regulatory role in this circuit. When the amygdala is strongly activated in the model, it suppresses the ventromedial prefrontal cortex and activates the rostral anterior cingulate cortex, leading to an abnormal circuit state. In a healthy state, the amygdala maintains activation through bottom-up regulation, supporting emotional regulation and network stability. The amygdala plays a key regulatory role in this circuit, and changes in functional connectivity are a potential factor that may contribute to the imbalance between cognitive control and emotional regulation. We also show within the modeling framework that alterations in functional connectivity are associated with an abnormal circuit state, which may be an important mechanism underlying the expression of depressive symptoms. This study combines data and theoretical modeling techniques, providing a computational perspective on the potential pathological mechanisms of depression and suggests potential therapeutic targets.
