Numerical Problems/ICSE/Class 10
Created by Titas Mallick
Biology Teacher • M.Sc. Botany • B.Ed. • CTET (CBSE) • CISCE Examiner
BioNotesBioNotesCreated by Titas Mallick
Biology Teacher • M.Sc. Botany • B.Ed. • CTET (CBSE) • CISCE Examiner
Online
Numerical Problems - Control and Coordination
Reflex arcs provide an excellent opportunity to understand the physics of nerve impulse conduction. By calculating conduction velocities, synaptic delays, and the effects of myelination, we can quantitatively analyze how our nervous system responds to stimuli in milliseconds.
A person accidentally touches a hot stove. The reflex arc involves a sensory neuron ( long), a spinal interneuron ( long), and a motor neuron ( long). The sensory and motor neurons are myelinated with an average conduction velocity of . The interneuron is unmyelinated with a conduction velocity of . There is a synaptic delay of at each synapse.
Calculate the total time (in milliseconds) taken from the receptor stimulation to the arrival of the impulse at the effector muscle.
Pathway: [Receptor] ➔ (Sensory Neuron: 0.8m, 120m/s) ➔ (Synapse 1) ➔ (Interneuron: 0.05m, 2m/s) ➔ (Synapse 2) ➔ (Motor Neuron: 0.9m, 120m/s) ➔ [Effector Muscle]
1. Calculate the conduction time for each neuron: Use the formula:
2. Calculate the total synaptic delay:
3. Calculate the total reflex time:
Answer: The total time taken for the impulse to reach the effector is 40.17 milliseconds.
[!WARNING] The Synapse Count Trap: Students often assume a "3-neuron pathway" has 3 synapses. A sequence of 3 neurons (A B C) only has 2 synapses. Always draw a quick sketch to count the connections, not just the neurons!
The Unit Trap: Mixing meters, centimeters, seconds, and milliseconds. Always convert to base standard units (meters and seconds) for intermediate calculations before converting the final answer to milliseconds.
In a healthy individual, a patellar reflex (knee-jerk) arc consists of a sensory neuron and a motor neuron (a monosynaptic reflex) covering a total distance of . The nerve impulse travels at , and there is a single synaptic delay of . In a patient suffering from a demyelinating disease, the conduction velocity of the affected motor neuron (which covers half the total distance) drops by .
Calculate the percentage increase in the reflex response time for the patient compared to a healthy individual.
Pathway: [Receptor] ➔ (Sensory Neuron: 0.75m) ➔ (Synapse) ➔ (Motor Neuron: 0.75m) ➔ [Muscle Effector]
1. Calculate normal reflex time (Healthy Individual):
2. Analyze the demyelinated state (Patient):
3. Calculate total patient reflex time:
4. Calculate percentage increase:
Answer: The reflex response time increases by 187.5% due to demyelination.
[!CAUTION] The Velocity Drop Trap: When a problem states "drops by 80%", it means the new value is 20% of the original (). A common mistake is to use as the new speed, which would be "drops to 80%". Read carefully!
Assuming uniform damage: The problem specifically states only the motor neuron is affected. Recalculating the entire 1.5m distance at the slower speed is a major conceptual error.
A sensory receptor generates action potentials at a frequency of (50 impulses per second) when a light pressure is applied. For every action potential that reaches the presynaptic terminal, vesicles of neurotransmitter are released into the synaptic cleft. If the threshold for the postsynaptic neuron to fire an action potential requires the simultaneous binding of neurotransmitters from at least vesicles within a window (temporal summation), will the postsynaptic neuron fire under this light pressure?
1. Determine the number of impulses arriving in the given time window:
2. Analyze the physical reality of the calculation: Since an action potential is an "all-or-none" event, you cannot have "half" an impulse. In a window, the neuron will realistically receive either 0 or 1 impulse (depending on exactly when the window starts).
3. Calculate maximum vesicle release in the time window:
4. Compare against threshold:
Answer: No, the postsynaptic neuron will not fire. The frequency of action potentials from the light pressure stimulus is too low to cause sufficient temporal summation.
[!IMPORTANT] The "Fractional Impulse" Trap: Mathematical formulas might give you fractional impulses (like 0.5), but biologically, action potentials are discrete, all-or-nothing events. You must round down or consider the maximum whole number of impulses possible in that timeframe.
Temporal Summation Concept: This problem tests whether you understand why strong stimuli cause reflexes while weak ones don't. It's not about the size of the action potential (which is constant), but the frequency of action potentials leading to neurotransmitter accumulation.