Physics 414: Introduction to Biophysics Professor Henry Greenside August 31, 2017

Today’s groups

Continue class discussion: Why do animals have heads?

Simple way to measure visual reflex time Guessing a 10 m/s propagation speed of action potentials from brain to arm (likely on the high end), transit time is ~1 m / 10 m/s = 0.1 s, that leaves ~0.3 - 0.1 s ~ 0.2 s for other neurons to communicate and calculate. If there are about ten neurons along the path from retina to finger muscles, that leaves an average time of 0.2s / 9 ~ 20 ms for one neuron to activate the next neuron. But maximum distance between neurons in one half of brain is about 0.1m so travel time is 0.1m / 10 m/s = 10 ms, that leaves 10 ms unaccounted for. This is synaptic delay time, mainly associated with mechanical motors that push vesicles filled with neurotransmitter to surface of synapse, where contents are dumped into the synaptic cleft.

Visualization of action potentials traveling from retina to LGN Movie shows artistic interpretation of action potentials (the bright yellow blobs moving along the axonal wires) from the retina to the lateral geniculate body (LGN, an important central relay station) and finally to V1 or visual cortex, where the first substantial data analysis is carried out in the brain. Although this movie doesn’t get many details right (action potentials are not visible since they don’t generate any light, brains are far more densely packed than indicated in the movie), it does make clear the extraordinary fact that everything you sense, think, remember, and learn is just some large collection of neurons sending digital pulses to one another. How does the “you” of your awareness emerge from these basic spikes?

One reason chemical synapses are slow: internal mechanical motion Another reason: rate of chemical reactions, not easily understood from first principles

Biophysics: speed of pulses along axon increases with axon radius while speed of signals in wire independent of radius Speed of pulses (action potentials) for unmyelinated or myelinated axons: Radial dependence has profound impact on brain architecture: to be faster, need thicker wires which take up more volume and consume more energy. :( So why not shrink everything to bring neurons closer together, then don’t need to increase v?

A biophysics insight: axons cannot be too small because of thermal noise (kT), so biological brains cannot be too small “Ion-Channel Noise Places Limits on the Miniaturization of the Brain’s Wiring”, A. Faisal et al, Current Biology, Vol. 15, 1143–1149, June 21, 2005

Why “thermal fluctuations” cause random neural action potentials

Opening and closing of the Na+ channel is stochastic, because of thermal noise <=== We will predict this functional form in Chapter 7!

Organisms live at room temperature T ~ 300 K Extremely important for biophysics!

Some energies in units of kT energy to break hydrogen bond between water molecules ~ 1-2 kT energy to move e across 40 mV membrane ~ 2 kT ATP → ADP + P ~ 20 kT green photon energy ~120 kT C-C bond ~140 kT, C=C bond, ~240 kT Complete glucose oxidation ~ 1200 kT

Equipartition theorem of classical statistical physics Each quadratic term in the energy of some small system that is interacting with an equilibrium system with temperature T has average energy (1/2)kT. For center of mass of molecule of mass m: For 1d spring with spring constant ks, At board: use equipartition to estimate speed of water molecules at room temperate, get vrms ~ 500 m/s, fast!

Group calculations: collision time of molecules Estimate average collision time τ of water molecules in liquid water at room temperature, if moving at average speed v. Your answer is one of the faster time scales that needs to be resolved in computer simulations or in experiments to understand what happens to biomolecules over time.

“Force spectroscopy”: data of force F versus length L for individual molecules (!) (A) double stranded DNA (abbreviated dsDNA) (B) RNA (C) protein made of repeats of part of cardiac titin muscle molecule Note scale of phenomena, the forces are in piconewtons, extensions in nm, so indeed writing kT = 4 pN nm makes good sense at the biomolecular level. What causes the kinks in curves (B) and ( C )?

Remarkable single-molecule methods for measuring tiny (pN) forces

Class calculation: how many numbers needed to teleport you successfully by nanoassembly?

One-minute End-of-class Question