Lecture 09: Theoretical Biophysics in Cell Biology
Biological systems are highly complex. Measuring all components does not automatically lead to understanding. True understanding requires
identifying:
• Causal mechanisms
• Physical constraints
• Quantitative relationships
• Simplifying assumptions
A deterministic system can be fully specified yet remain uninterpretable. Therefore: Understanding = knowing the cause of something, not just
observing correlations.
Physics provides:
• A framework for causality
• Logical consistency through mathematics
• Predictive power through quantitative models
Correlation vs. Causation:
Correlations can arise from hidden variables.
• Example:
o Chocolate consumption correlates with Nobel Prize winners.
o The hidden variable: wealth.
• Key principle:
o Correlation ≠ causation.
o Establishing causation requires mechanistic models grounded in physics.
Biology often provides correlations. Physics provides causal structure.
Thinking in Units: Dimensional Analysis
Two Essential Rules:
1. Only quantities with the same units can be added or subtracted.
2. Arguments of functions like exp(), log(), sin() must be unitless.
Example: Exponential Growth
Formula exponential growth: N(t) = N0 ∙ ekt
• Since the exponent must be unitless:
o k has units of 1/time
• Dimensional analysis allows you to:
o Validate equations
o Infer unknown units
o Detect conceptual errors
o Understand physical meaning
Example: Membrane potential and Units
Formula membrane potential: V = (RT/zF) ∙ ln (Co/Ci)
• If V has units of volts:
o RT/zF must also have units of volts.
o Since R has units J / (K · mol), T is K and z is unitless,
o Faraday constant F must have units: J / (mol ∙ V)
Cellular Energetics and the Thermal Energy Scale:
• Ideal Gas Law: pV = nRT
• Energy per molecule: kB = R / NA
• At room temperature: kBT ≈ 4.1 pN ∙ nm (N-12 ∙ m-9) → natural energy scale inside cells
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, Why This Matters:
• Molecular interactions occur on the order of kB
• Too strong → rigid system
• Too weak → unstable system
• Biological systems operate in the thermal fluctuation regime
Free Energy of ATP Hydrolysis:
Free energy per ATP hydrolysis: ∆G ≈ 25 kT ≈ 100 pN ∙ nm
Implication:
• Molecular machines are limited by this energy budget.
• Every mechanical action must obey: E = F ∙ x
Predicting Kinesin Step Size from Physics:
• Given: Motor uses 1 ATP per step → free energy per ATP hydrolysis ≈ 100 pN ∙ nm and stall force of motor = 8 pN
• Maximum step size: x = E / F = 100 pN ∙ nm / 8 pN = 12.5 nm
• Observed kinesin step ≈ 8 nm.
Conclusion:
• Simple physical reasoning predicts biological behavior.
• Biology obeys energetic constraints.
Statements vs. Facts:
• “Evolution makes organisms better.” → vague statement.
• “Energy cannot be created or destroyed.” → physical law.
• “Entropy increases.” → foundational physical principle.
Scientific understanding requires:
• Clearly defined quantities
• Quantitative testability
• Logical consistency
Organized Complexity in Biology
Biological systems are:
• Non-linear
• Non-equilibrium (energy-consuming)
• Structurally organized
• Highly variable
Cells maintain ordered states far from equilibrium using energy.
Pipeline: Observing → Describing → Controlling (much harder in biology than in physics).
Molecular Motors in Optical Traps:
• Context: How do molecular motors respond to force?
• Experimental Setup:
o Motor attached to bead
o Bead trapped in laser (optical trap)
o Trap stiffness is adjustable
o Motor walks on microtubule
o Increasing force → motor stalls → detaches
• Insights:
o Force affects stepping rate and detachment
o Mechanical properties can be modelled quantitatively
o Trap stiffness is a control parameter
• This connects:
o Mechanical force, ATP energy and stepping kinetics
2|Page
Biological systems are highly complex. Measuring all components does not automatically lead to understanding. True understanding requires
identifying:
• Causal mechanisms
• Physical constraints
• Quantitative relationships
• Simplifying assumptions
A deterministic system can be fully specified yet remain uninterpretable. Therefore: Understanding = knowing the cause of something, not just
observing correlations.
Physics provides:
• A framework for causality
• Logical consistency through mathematics
• Predictive power through quantitative models
Correlation vs. Causation:
Correlations can arise from hidden variables.
• Example:
o Chocolate consumption correlates with Nobel Prize winners.
o The hidden variable: wealth.
• Key principle:
o Correlation ≠ causation.
o Establishing causation requires mechanistic models grounded in physics.
Biology often provides correlations. Physics provides causal structure.
Thinking in Units: Dimensional Analysis
Two Essential Rules:
1. Only quantities with the same units can be added or subtracted.
2. Arguments of functions like exp(), log(), sin() must be unitless.
Example: Exponential Growth
Formula exponential growth: N(t) = N0 ∙ ekt
• Since the exponent must be unitless:
o k has units of 1/time
• Dimensional analysis allows you to:
o Validate equations
o Infer unknown units
o Detect conceptual errors
o Understand physical meaning
Example: Membrane potential and Units
Formula membrane potential: V = (RT/zF) ∙ ln (Co/Ci)
• If V has units of volts:
o RT/zF must also have units of volts.
o Since R has units J / (K · mol), T is K and z is unitless,
o Faraday constant F must have units: J / (mol ∙ V)
Cellular Energetics and the Thermal Energy Scale:
• Ideal Gas Law: pV = nRT
• Energy per molecule: kB = R / NA
• At room temperature: kBT ≈ 4.1 pN ∙ nm (N-12 ∙ m-9) → natural energy scale inside cells
1|Page
, Why This Matters:
• Molecular interactions occur on the order of kB
• Too strong → rigid system
• Too weak → unstable system
• Biological systems operate in the thermal fluctuation regime
Free Energy of ATP Hydrolysis:
Free energy per ATP hydrolysis: ∆G ≈ 25 kT ≈ 100 pN ∙ nm
Implication:
• Molecular machines are limited by this energy budget.
• Every mechanical action must obey: E = F ∙ x
Predicting Kinesin Step Size from Physics:
• Given: Motor uses 1 ATP per step → free energy per ATP hydrolysis ≈ 100 pN ∙ nm and stall force of motor = 8 pN
• Maximum step size: x = E / F = 100 pN ∙ nm / 8 pN = 12.5 nm
• Observed kinesin step ≈ 8 nm.
Conclusion:
• Simple physical reasoning predicts biological behavior.
• Biology obeys energetic constraints.
Statements vs. Facts:
• “Evolution makes organisms better.” → vague statement.
• “Energy cannot be created or destroyed.” → physical law.
• “Entropy increases.” → foundational physical principle.
Scientific understanding requires:
• Clearly defined quantities
• Quantitative testability
• Logical consistency
Organized Complexity in Biology
Biological systems are:
• Non-linear
• Non-equilibrium (energy-consuming)
• Structurally organized
• Highly variable
Cells maintain ordered states far from equilibrium using energy.
Pipeline: Observing → Describing → Controlling (much harder in biology than in physics).
Molecular Motors in Optical Traps:
• Context: How do molecular motors respond to force?
• Experimental Setup:
o Motor attached to bead
o Bead trapped in laser (optical trap)
o Trap stiffness is adjustable
o Motor walks on microtubule
o Increasing force → motor stalls → detaches
• Insights:
o Force affects stepping rate and detachment
o Mechanical properties can be modelled quantitatively
o Trap stiffness is a control parameter
• This connects:
o Mechanical force, ATP energy and stepping kinetics
2|Page
