Biology

Nervous and endocrine systems

Neurons, synapses, hormones, and homeostasis — fast electrical and slower chemical signals.

Basics

Neurons

Dendrites collect input; the axon carries an action potential. Resting potential is mostly K⁺ leak, inside negative. Crossing threshold opens Na⁺ channels (depolarization), then K⁺ restores the rest. Myelin and nodes of Ranvier enable saltatory conduction, so thick insulated fibres are fast. Sensory, motor, and interneurons split the circuit.

Synapses

At a chemical synapse, vesicles release transmitter into the cleft; receptors open ions or start second messengers. Excitation (e.g. glutamate, nicotinic ACh) and inhibition (GABA, glycine) sum to set the next neuron’s threshold. Electrical synapses (gap junctions) are faster and less plastic. Reuptake and breakdown end the signal; many drugs target those steps.

Hormones

Endocrine glands send chemical news through blood to target cells. Peptides and amines use membrane receptors and second messengers; steroids and thyroid hormone mostly use nuclear receptors and transcription. The hypothalamus–pituitary axis paces many peripheral glands, and feedback shuts secretion. The same molecule can also be a transmitter (e.g. adrenaline), so the two systems touch.

Homeostasis

A sensor reads a variable, an integrator compares it to a set point, and effectors push back. Blood glucose uses insulin and glucagon; osmolarity uses ADH and thirst; temperature uses the hypothalamus plus skin flow and sweat. Negative feedback is the default; positive feedback (oxytocin in birth) amplifies briefly. Nerves act in seconds, hormones in minutes to days, overlapping on the same variables.

Formulas

Nernst potential (sketch)

E_ion = (RT / z F) ln ([ion]ₒ / [ion]ᵢ)

Equilibrium voltage if only that ion could flow. At 25 °C, ≈ (58 mV)/z · log₁₀(out/in).

Symbols

z ion charge number
F Faraday constant

Goldman–Hodgkin–Katz (sketch)

V_m ≈ (RT/F) ln ( (P_K[K]ₒ + P_Na[Na]ₒ + …) / (P_K[K]ᵢ + P_Na[Na]ᵢ + …) )

Resting voltage as a permeability-weighted mix of ions.

Symbols

P membrane permeability

Firing rate (sketch)

rate ≳ 0 when V_m > V_threshold (after refractory period)

More suprathreshold input raises rate, but a refractory period caps it.

Symbols

V_threshold threshold potential

Feedback error

error = set point − measured

Negative feedback drives effectors so as to shrink the error.

Key table

Typical resting potential	neuron about −70 mV (inside relative to outside)
Peptide vs steroid	peptide: membrane receptor, fast. steroid: genes, slower
Hypothalamus–pituitary	releasing hormone → anterior pituitary → peripheral gland (thyroid, adrenal, gonad…)