The provided MATLAB code models the biomechanical properties of the whisker (vibrissal) system in rodents, focusing on the motor plant and its response to motor commands, particularly at small whisker angles. Here is a breakdown of the biological concepts being modeled and how they relate to whisker movement and sensory perception:

Biological Basis of the Model

Whisker System

• Whisker Arrangement: The model considers a row of five whiskers (N=5), with specific attention to the third one in the sequence (vib_num=3). The whiskers are represented by their resting angles, indicating their natural resting position without muscle activation.

Musculature and Activation

• Muscle Innervation: The parameter intrinsic_muscle_set defines which muscles are active (1) or inactive (0). This represents the neural control of the intrinsic muscles involved in whisker movement.
• Force Amplitude: force_factor simulates the strength of muscle contraction, affecting whisker dynamics. The modulation of these forces models how motor commands translate into whisker positioning.

Biomechanics of Whiskers

• Follicle and Hair Mass: Mf and Mh represent the masses of the follicle and the hair, respectively, crucial for understanding how forces affect whisker movement.
• Damping and Spring Constants: Parameters like zeta_up, zeta_dn, zeta_gr, and Kup, Kdn, Kgr represent damping and spring constants that simulate the mechanical properties of the whisker follicle and the surrounding tissue, impacting how the whiskers respond dynamically to forces.

Mechanical Properties

• Moment of Inertia and Center of Mass: I0 and C are critical for understanding rotational dynamics of the whiskers during movement.

Motor Dynamics

• Muscle Dynamics: The terms tauc and taur correspond to time constants affecting muscle contraction and relaxation, respectively. They determine how quickly the whisker can adjust in response to motor commands.

Small Angle Approximation

• The "small angles" section of the code indicates simplifications used to approximate whisker dynamics within limited angular movements, likely for focused study on subtle motor outputs and control.

Biomechanical Parameters and Units

• Units Translation: The conversion of measurements to MKS units allows for accurate simulation of physical phenomena, ensuring computational outputs correspond to realistic biological scales.

In essence, this model aims to capture the complexities of whisker movement due to intrinsic muscle contractions, focusing on the mechanical and dynamic behavior of the whisker system under small angle deviations. It's a comprehensive attempt to understand how motor commands translate into sensory experiences through precise control of whisker mechanics.