Diez Martinez O, Pérez P, Budelli R, Segundo J P
Departamento de Fisiología, Facultad de Medicina, Universidad Nacional Autónoma, México.
Biol Cybern. 1988;60(1):49-58. doi: 10.1007/BF00205971.
Slowly adapting stretch receptor (SAO) pacemaker neurons, driven with periodic tugs, were analyzed by way of Poincaré mappings (Appendix). Two behaviors were apparent. i) Intermittency characterized previously unclear situations: discharges shifted irregularly between prolonged epochs where spike phases (relative to tugs) and intervals barely changed (slid), and brief bursts with marked variations (skipped). ii) Locking was well-known: phases and intervals remained almost fixed, regardless of the initiation. Changing frequencies, map domains with locking (ordered according to spikes/tugs ratios), alternated with intermittent ones. The best fit for any experimental map was a curve, not straight but certainly unidimensional, continuous and monotonic; it varied characteristically with frequency. This suggested relations called diffeomorphisms, implying periodicity and quasi-periodicity. Outcomes, expanding previous knowledge and meaningful biologically, were i) a precise, exhaustive behavior list (including between behavior transitions) and ii) a thorough understanding or model. This, in turn, provides norms for more specific models (single-variable ones suffice), constraints upon basic mechanisms (one variable, reflecting several real ones combined, should behave as the phase), and forecasts for future experimentation (e.g., unexamined tug frequencies and amplitudes).
通过庞加莱映射（附录）对由周期性牵引驱动的慢适应性牵张感受器（SAO）起搏器神经元进行了分析。有两种行为很明显。i）间歇性表征了以前不清楚的情况：放电在延长的时间段内不规则地转移，在这些时间段内，峰值相位（相对于牵引）和间隔几乎没有变化（滑动），以及具有明显变化的短暂爆发（跳跃）。ii）锁定是众所周知的：相位和间隔几乎保持固定，无论起始情况如何。改变频率时，具有锁定的映射域（根据峰值/牵引比率排序）与间歇性映射域交替出现。任何实验映射的最佳拟合都是一条曲线，不是直线但肯定是一维的、连续的和单调的；它随频率有特征性变化。这表明了称为微分同胚的关系，意味着周期性和准周期性。结果扩展了先前的知识并且在生物学上具有意义，即i）一个精确、详尽的行为列表（包括行为转变之间的情况）和ii）一个透彻的理解或模型。反过来，这为更具体的模型（单变量模型就足够了）提供了规范，对基本机制施加了约束（一个反映几个实际变量组合的变量应表现为相位），并对未来的实验进行了预测（例如，未研究的牵引频率和幅度）。
