Rotstein Horacio G
Department of Mathematical Sciences and Institute for Brain and Neuroscience, Research New Jersey Institute of Technology, Newark, NJ, 07102, USA.
J Comput Neurosci. 2017 Aug;43(1):35-63. doi: 10.1007/s10827-017-0646-8. Epub 2017 May 31.
Subthreshold (membrane potential) resonance and phasonance (preferred amplitude and zero-phase responses to oscillatory inputs) in single neurons arise from the interaction between positive and negative feedback effects provided by relatively fast amplifying currents and slower resonant currents. In 2D neuronal systems, amplifying currents are required to be slave to voltage (instantaneously fast) for these phenomena to occur. In higher dimensional systems, additional currents operating at various effective time scales may modulate and annihilate existing resonances and generate antiresonance (minimum amplitude response) and antiphasonance (zero-phase response with phase monotonic properties opposite to phasonance). We use mathematical modeling, numerical simulations and dynamical systems tools to investigate the mechanisms underlying these phenomena in 3D linear models, which are obtained as the linearization of biophysical (conductance-based) models. We characterize the parameter regimes for which the system exhibits the various types of behavior mentioned above in the rather general case in which the underlying 2D system exhibits resonance. We consider two cases: (i) the interplay of two resonant gating variables, and (ii) the interplay of one resonant and one amplifying gating variables. Increasing levels of an amplifying current cause (i) a response amplification if the amplifying current is faster than the resonant current, (ii) resonance and phasonance attenuation and annihilation if the amplifying and resonant currents have identical dynamics, and (iii) antiresonance and antiphasonance if the amplifying current is slower than the resonant current. We investigate the underlying mechanisms by extending the envelope-plane diagram approach developed in previous work (for 2D systems) to three dimensions to include the additional gating variable, and constructing the corresponding envelope curves in these envelope-space diagrams. We find that antiresonance and antiphasonance emerge as the result of an asymptotic boundary layer problem in the frequency domain created by the different balances between the intrinsic time constants of the cell and the input frequency f as it changes. For large enough values of f the envelope curves are quasi-2D and the impedance profile decreases with the input frequency. In contrast, for f ≪ 1 the dynamics are quasi-1D and the impedance profile increases above the limiting value in the other regime. Antiresonance is created because the continuity of the solution requires the impedance profile to connect the portions belonging to the two regimes. If in doing so the phase profile crosses the zero value, then antiphasonance is also generated.
单个神经元中的阈下（膜电位）共振和相位共振（对振荡输入的偏好幅度和零相位响应）源于相对快速的放大电流和较慢的共振电流所提供的正反馈和负反馈效应之间的相互作用。在二维神经元系统中，为了使这些现象发生，放大电流需要受电压支配（瞬间快速）。在更高维系统中，在各种有效时间尺度上运行的额外电流可能会调制并消除现有的共振，并产生反共振（最小幅度响应）和反相位共振（具有与相位共振相反的相位单调特性的零相位响应）。我们使用数学建模、数值模拟和动力系统工具来研究三维线性模型中这些现象背后的机制，这些三维线性模型是通过生物物理（基于电导）模型的线性化得到的。我们刻画了在相当一般的情况下系统表现出上述各种行为的参数范围，在这种情况下，基础二维系统表现出共振。我们考虑两种情况：（i）两个共振门控变量的相互作用，以及（ii）一个共振门控变量和一个放大门控变量的相互作用。放大电流水平的增加会导致：（i）如果放大电流比共振电流快，则响应放大；（ii）如果放大电流和共振电流具有相同的动力学，则共振和相位共振衰减并消失；（iii）如果放大电流比共振电流慢，则产生反共振和反相位共振。我们通过将先前工作中（针对二维系统）开发的包络平面图方法扩展到三维以纳入额外的门控变量，并在这些包络空间图中构建相应的包络曲线，来研究其潜在机制。我们发现，反共振和反相位共振是由细胞的固有时间常数与输入频率f变化时的不同平衡在频域中产生的渐近边界层问题导致的。对于足够大的f值，包络曲线是准二维的，并且阻抗分布随输入频率降低。相反，对于f≪1，动力学是准一维的，并且阻抗分布在另一种情况下高于极限值。产生反共振是因为解的连续性要求阻抗分布连接属于两种情况的部分。如果这样做时相位分布穿过零值，那么也会产生反相位共振。
