Time Constant and Length Constant: Graphical Illustrations for Effective Teaching and Learning

Abstract

IntroductionThis is a teacher‐guided students’ presentation. The time constant (τ) and the length constant (λ) are the cell membrane’s passive cable properties that influence the velocity of the spread of graded potentials and thus the velocity of the propagation of action potentials. In teaching and learning the electrophysiology of the cell membrane, we noticed that the information about the two concepts in many current physiology textbooks are incomplete and inconsistent. Some books introduce both τ and λ, whereas some other books do not introduce them. Some books introduce only τ, whereas some other books introduce only λ. Some books use the rising phase of a graded potential to illustrate τ, whereas some other books use the falling phase. Graphical illustrations about these concepts are generally not available in these physiology textbooks. This situation makes it confusing for students to understand the two concepts. In this presentation, we address the above problems and share our figures to facilitate the learning of the two concepts.MethodTextbook comparisons and graphical illustrations.Results1) The incompleteness and the inconsistency about the two concepts will be addressed in a table using a few sampled textbooks. 2) A set of figures (not shown) are used to provide a complete illustration about τ in both the rising phase and the falling phase of a graded potential; and the rising phase is then used to graphically illustrate how τ affects the propagation of an action potential (Figure 1). 3) How λ affects the propagation of an action potential is illustrated graphically using the falling phase of a graded potential (Figure 2).ConclusionGraphical illustrations are of great value for the effective teaching and learning of the concepts of time constant and the length constant.Time constant (τ) determines how fast a local current depolarizes Vm to Vthreshold to trigger an action potential.Figure 1Length constant (λ). A: The λ influences the spread of a local current (or the graded potential it generates). The greater the λ, the farther the local current (or the graded potential) spreads. B: The greater the λ, the farther the local current (or the graded potential) spreads, so the more voltage‐gated Na+ channels (VGSCs) in a regional area are likely to open and the faster the AP propagation. VGKC: voltage‐gated K+ channels.Figure 2