Laws of Biological Cycles

Atomic Circuit Analogy and New Laws for Electrophysiology

1. Ionic Current – ​​Law of Energy

Definition: Intracellular ion currents depend not only on voltage difference but also on metabolic energy status.

𝐼_bio = 𝑔(𝑉, 𝑡) ⋅ 𝑓(𝐸_ATP)

• Example: Na⁺/K⁺ pump → When ATP decreases, the current drops, and the membrane potential shifts.
• Comment: There is a direct multiplier effect between electric current and biochemical energy.

2. Law of Dynamic Capacitance

Definition: The capacitance of the cell membrane is not constant; it varies depending on ion concentration, pH, and temperature.

𝐶_bio(𝑡) = 𝐶₀⋅ 𝜙([ion], 𝑝𝐻, 𝑇)

• Example: In a nerve cell, a change in pH → a shift in capacitance → a change in the action potential threshold.
• Comment: Capacitance is an adaptive parameter of the biological environment.

3. Kirchhoff’s Law of Homeostatics

Definition: The cell balances the current difference at the node with pump currents.

∑𝐼_in− ∑𝐼_out = 𝐼_pump (𝐴𝑇𝑃)

• Example: The difference in Ca²⁺ input-output in a heart cell → the SERCA pump balances it with ATP.
• Comment: Kirchhoff’s law is completed in biology by the concept of energy consumption.

4. The Dual Law of Information-Energy

Definition: Energy flow is also a form of information encoding.

𝐻_info ∝ ∫ 𝑃_bio(𝑡) 𝑑𝑡

• Example: Neuron firing frequency → information entropy is directly proportional to energy consumption.
• Comment: Information and energy come into play as an inseparable pair.

5. Plasticity – Parameter Law

Definition: Circuit parameters are not fixed; they change with experience and adaptation.

𝑔_syn(𝑡 + Δ𝑡) = 𝑔_syn(𝑡) + Δ𝑔([Ca²⁺],timing)

• Example: Synaptic strengthening (LTP) → Increased conductivity via Ca²⁺ wave.
• Comment: Circuit parameters are updated through learning and adaptation.

6. Environmental Modulation Act

Definition: Environmental factors (pH, temperature, ionic strength) directly modulate circuit parameters.

𝑅_bio(𝑇, 𝑝𝐻) = 𝑅₀⋅ 𝜓(𝑇, 𝑝𝐻, [𝑖𝑜𝑛])

• Example: In a muscle cell, temperature increases → conduction velocity increases.
• Comment: The laws of the circuit are sensitive to environmental conditions.

7. The Law of Homeodynamic Equilibrium

Definition: A cell maintains internal balance by continuously adjusting its parameters.

𝑑𝑋/𝑑𝑡 = −𝑘(𝑋 − 𝑋_set)

• Example: Blood glucose → pancreatic circuit is brought into equilibrium by insulin flow.
• Comment: Circuits apply feedback to maintain their set points.

Conclusion

This declaration sets forth new laws of operation for biological processes:

• Energy–information combination
• Dynamic parameters
• Homeostatic equilibrium
• Plasticity and adaptation
• Environmental modulation

Thus, Electrophysiology goes beyond the classical laws of electronics to define the functional mathematics of life.