Separate recruitment from rate coding in a finite muscle model

1. Identify the structure and functional question

A motor unit consists of a motor neuron and the skeletal muscle fibers it innervates. Recruiting additional units can increase total force, while changing firing frequency alters the time course and overlap of responses in already active units. These mechanisms do not require action potentials to become proportionally taller. A fiber’s all-or-none electrical event is distinct from graded force of a whole muscle.

2. Connect architecture, mechanism and assumptions

A twitch has a latent interval, rising force and relaxation. Repeated activation can produce temporal summation because mechanical and calcium responses outlast a single action potential. At sufficiently rapid stimulation, force can become more sustained. Recruitment order and unit properties matter, but real units are heterogeneous and fatigue or changing muscle length alters the response.

The original finite model recruits the first n of four units with stipulated maximum forces 1,2,3,4. Their summed maximum is n(n+1)/2. At shared frequency f, each expresses fraction f/(f+20), giving total force [n(n+1)/2]f/(f+20). This smooth supplied curve illustrates saturation; it is not a fitted twitch, a stimulation protocol or a measured recruitment threshold.

Increasing frequency and adding a unit can produce similar headline force changes through different mechanisms. Compare the recruited capacity sum, expressed fraction and resulting force separately. A force trace alone does not establish which motor units fired or diagnose neural function. Use only virtual settings and retain the evidence that would distinguish recruitment from rate coding.

3. Reconstruct the original worked case

With n=3, maximum sum is 1+2+3=6. At f=20 Hz, expressed fraction is 1/2 and force is 3 units. Recruiting all four at the same frequency gives force 5, while increasing frequency to 40 Hz with three units gives force 4.

4. Predict and investigate

Predict first: Can equal changes in total force arise from different recruitment and firing-rate changes?

Compare recruitment at fixed frequency and frequency at fixed recruitment. Retain maximum capacity and activation fraction separately, and reject the explanation that a larger whole-muscle force necessarily means taller action potentials.

5. Transfer to a changed mechanism or boundary

Apply the mechanism to a changed boundary

For all four units at 40 Hz, calculate capacity sum, fraction and force.

Retain the first response, units, uncertainty and any prior feedback exposure in the notebook before comparing this public explanation.

Compare a worked response

Capacity sum is 10; fraction is 40/60=2/3; force is 20/3 units. Neither number estimates actual human strength or a safe stimulation setting.

6. Retain a bounded functional explanation

Preserve first predictions, settings, complete quantities and an independent observation that could reject the explanation in the Anatomy and Physiology course workspace. Public feedback and invented models are not clinical evaluation, supervised specimen work or independently assessed reasoning. No physical exercise, temperature exposure, electrical stimulation, personal measurements or treatment is requested.

Supporting anatomical mechanism, checked 30 October 2026. Original teaching prose, numerical packets, schematic diagrams and exercises; no real physiological measurement or injury threshold is inferred.