From Photon to Neuron: Light, Imaging, Vision

Cover......Page 1
Copyright information......Page 5
Brief contents......Page 8
Detailed contents......Page 10
Web resources......Page 21
Features of this book......Page 22
About you......Page 23
To the instructor......Page 26
0.1 Signpost: Uncertainty......Page 32
0.2.1 A probability distribution summarizes our knowledge about an uncertain situation......Page 33
0.2.3 A random variable can be partially described by its expectation and variance......Page 35
0.2.4 Joint distributions......Page 37
0.2.5 Some explicit discrete distributions......Page 38
Geometric distribution......Page 39
0.3 Dimensional Analysis......Page 40
0.4.1 Probability density functions......Page 41
0.4.2 Some explicit continuous distributions......Page 42
Uniform......Page 43
Exponential......Page 44
0.5 More Properties of, and Operations on, Probability Distributions......Page 45
0.5.2 The sample mean of many independent, identically distributed random variables has lower variance than any one of its constituents......Page 46
0.5.5 The convolution of two distributions describes the sum of their random variables......Page 47
Big Picture......Page 48
Key Formulas......Page 49
Problems......Page 50
Part I Doorways of Light......Page 52
1.1 Signpost: Photons......Page 54
1.2 Light Before 1905......Page 55
1.2.2 Light displays wavelike behavior in many situations......Page 56
1.3 Light Is Lumpy......Page 57
1.3.1 The discrete aspect of light is most apparent at extremely low intensity......Page 58
1.3.2 The photoelectric effect......Page 61
1.3.3 Einstein's proposal......Page 64
1.3.4 Light-induced phenomena in biology qualitatively support the Einstein relation......Page 65
1.4.1 A Poisson process can be defined as a continuous-time limit of repeated Bernoulli trials......Page 66
1.4.3 Waiting times are Exponentially distributed......Page 67
1.5.1 The Light Hypothesis, part 1......Page 68
1.5.3 Light can eject electrons from individual molecules, inducing photochemical reactions......Page 69
1.6 Fluorescence and Photoisomerization Can Occur after Photon Absorption......Page 70
1.6.1 The Electron State Hypothesis......Page 71
1.6.3 Molecules: fluorescence......Page 72
1.6.4 Molecules: photoisomerization......Page 76
1.7 Transparent Media Are Unchanged by the Passage of Light, but Slow It Down......Page 78
Key Formulas......Page 79
1.3.3'a The reality of photons......Page 81
1.3.3'b Light also carries momentum......Page 82
1.3.3'c The thermal radiation spectrum......Page 83
1.3.3'd The role of frequency......Page 84
1.5.1'a Gamma rays......Page 85
1.5.3' Mechanism of DNA photodamage......Page 86
1.6.2'b A Cauchy distribution in physics......Page 87
1.6.3'b Classical approximation for nuclear motion......Page 88
1.6.4' Fast conformational changes......Page 89
Problems......Page 90
2.2 Light-Induced DNA Damage......Page 92
Autofluorescence......Page 93
Induced fluorescence......Page 94
2.3.2 Fluorescence microscopy can reduce background and specifically show only objects of interest......Page 95
2.4.1 Electric currents involve ion motion......Page 97
2.4.3 Ion pumps maintain a resting electric potential drop across the cell membrane......Page 98
2.4.5 Action potentials can transmit information over long distances......Page 99
Output......Page 100
2.4.7 More about synaptic transmission......Page 101
Discrete release of vesicles......Page 102
2.5.1 Brains are hard to study......Page 103
2.5.2 Channelrhodopsin can depolarize selected neurons in response to light......Page 104
2.5.3 Halorhodopsin can hyperpolarize selected neurons in response to light......Page 105
2.5.4 Other methods......Page 106
2.6.1 Voltage-sensitive fluorescent reporters......Page 107
2.6.2 Split fluorescent proteins and genetically encoded calcium indicators......Page 108
Genetically encoded calcium indicators......Page 109
2.7.1 The problem of imaging thick samples......Page 110
2.7.2 Two-photon excitation depends sensitively on light intensity......Page 111
2.7.3 Multiphoton microscopy can excite a specific volume element of a specimen......Page 112
2.8.1 How to tell when two molecules are close to each other......Page 114
2.8.2 A physical model for FRET......Page 116
2.8.4 FRET can be used to create a spectroscopic ``ruler''......Page 118
2.8.5 Application of FRET to DNA bending flexibility......Page 120
2.8.6 FRET-based indicators......Page 121
The puzzle of low oxygen yield per chlorophyll......Page 124
2.9.3 Resonance energy transfer resolves both puzzles......Page 125
Oxygen yield and the light-harvesting complex......Page 127
Key Formulas......Page 129
2.7.2' The -squared rule......Page 131
2.8.1' About FRET and its efficiency......Page 132
2.9.3' More details about the photosynthesis apparatus in plants......Page 133
Problems......Page 134
3.2 Color Vision Confers a Fitness Payoff......Page 138
3.3 Newton's Experiments on Color......Page 139
3.4 Background: More Properties of Poisson Processes......Page 140
3.4.1 Thinning property......Page 141
3.4.2 Merging property......Page 142
3.5 Combining Two Beams Corresponds to Summing Their Spectra......Page 143
3.6.3 Perceptual matching follows quantitative, reproducible, and context-independent rules......Page 144
3.7.2 Subtractive color scheme......Page 148
3.8.1 The color-matching function challenge......Page 149
3.8.2 Available wetware in the eye......Page 150
Anatomical......Page 151
3.8.3 The trichromatic model......Page 152
3.8.4 The trichromatic model explains why R+GY......Page 154
Interpretation of spectral sensitivity functions......Page 155
3.8.6 A mechanical analogy for color matching......Page 156
3.8.8 Quantitative comparison to experimentally observed color-matching functions......Page 158
3.9 Why the Sky Is Not Violet......Page 160
3.10 Direct Imaging of the Cone Mosaic......Page 161
Key Formulas......Page 162
3.6.3'b Colorblindness......Page 164
3.7' Perceptual color......Page 165
3.8.4'b Spectral analysis can discriminate many fluorophores and their combinations......Page 166
3.8.5'b Correction to predicted color matching due to absorption......Page 169
3.8.8'b Simplified color space......Page 170
Problems......Page 173
4.1 Signpost: Probability Amplitudes......Page 176
4.2 Summary of Key Phenomena......Page 177
4.3.1 Reconciling the particle and wave aspects of light requires the introduction of a new kind of physical quantity......Page 181
4.4 Background: Complex Numbers Simplify Many Calculations......Page 183
4.5 Light Hypothesis, part 2......Page 185
4.6.1 Two-slit interference explained via the Light Hypothesis......Page 187
4.6.2 Newton's rings illustrate interference in a three-dimensional setting......Page 189
4.6.3 An objection to the Light Hypothesis......Page 190
4.7.1 The Fresnel integral illustrates the stationary-phase principle......Page 192
4.7.2 The probability amplitude is computed as a sum over all possible photon paths......Page 194
4.7.3 Diffraction through a single, wide aperture......Page 196
4.7.4 Reconciliation of particle and wave aspects......Page 199
Key Formulas......Page 201
4.5'a More about the Light Hypothesis......Page 203
4.6.1' Which slit?......Page 204
4.6.3' More objections......Page 205
4.7.2'b Nonuniform media......Page 207
Problems......Page 208
5.2.1 Some animals create color by using nanostructures made from transparent materials......Page 211
5.2.2 An extension of the Light Hypothesis describes reflection and transmission at an interface......Page 214
5.2.3 A single thin, transparent layer reflects with weak wavelength dependence......Page 215
5.2.4 A stack of many thin, transparent layers can generate an optical bandgap......Page 217
5.2.5 Structural color in marine organisms......Page 219
5.3.1 The reflection law is a consequence of the stationary-phase principle......Page 221
5.3.2 Transmission and reflection gratings generate non-ray-optics behavior by editing the set of allowed photon paths......Page 222
5.3.3 Refraction arises from the stationary-phase principle applied to a piecewise-uniform medium......Page 223
Medical applications......Page 225
Total internal reflection fluorescence microscopy......Page 226
5.3.5 Refraction is generally wavelength dependent......Page 227
Key Formulas......Page 228
5.2.2' Transmission and reflection in classical electromagnetism......Page 230
5.2.4' More complicated layers......Page 231
Problems......Page 232
Part II Human and Superhuman Vision......Page 238
6.2.1 Shadow imaging......Page 240
6.2.2 Pinhole imaging suffices for some animals......Page 241
6.3 Addition of a Lens Allows Formation of Bright, Yet Sharp, Images......Page 242
6.3.1 The focusing criterion relates object and image distances to lens shape......Page 243
6.3.3 Formation of a complete image......Page 247
6.4.1 Image formation with an air-water interface......Page 249
6.4.2 Focusing powers add in a compound lens system......Page 252
6.4.3 A deformable lens implements focal accommodation......Page 253
6.5.1 ``Rays of light'' are a useful idealization in the ray-optics regime......Page 255
6.5.3 Spherical aberration......Page 256
6.5.4 Dispersion gives rise to chromatic aberration......Page 257
6.5.5 Confocal microscopy suppresses out-of-focus background light......Page 259
6.7.1 Angles......Page 261
6.7.2 Angular area......Page 262
6.8.1 Even a perfect lens will not focus light perfectly......Page 263
6.8.2 Three dimensions: The Rayleigh criterion......Page 265
Human......Page 266
Key Formulas......Page 267
6.8.2' The Abbe criterion......Page 270
Problems......Page 271
7.1 Signpost: Information......Page 278
7.2.1 The Bayes formula tells how to update a probability estimate......Page 279
7.2.3 Inferring the center of a distribution......Page 280
7.2.5 Binning data reduces its information content......Page 281
7.3.2 Formulation of a probabilistic model......Page 282
Stray light......Page 283
7.3.3 Maximum-likelihood analysis of image data......Page 284
7.3.4 Results for molecular motor stepping......Page 286
7.4 Localization Microscopy......Page 287
7.5 Defocused Orientation Imaging......Page 289
Big Picture......Page 291
Key Formulas......Page 292
7.3.3' Advantages of the maximum likelihood method......Page 293
7.4' Interferometric PALM imaging......Page 294
7.5' More about anisotropy......Page 297
Problems......Page 298
8.1 Signpost: Inversion......Page 303
8.2 It's Hard to See Atoms......Page 304
8.3.1 A periodic array of narrow slits creates a diffraction pattern of sharp lines......Page 305
8.3.2 Generalizations to the setup needed to handle x-ray crystallography......Page 307
8.3.3 An array of slits with substructure gives a diffraction pattern modulated by a form factor......Page 308
8.3.5 3D crystals can be analyzed by similar methods......Page 309
8.4 The Diffraction Pattern of DNA Encodes Its Double-Helical Character......Page 310
8.4.1 The helical pitch, base pair rise, helix offset, and diameter of DNA can be obtained from its diffraction pattern......Page 311
8.4.2 Accurate determination of size parameters led to a breakthrough on the puzzle of DNA structure and function......Page 313
Key Formulas......Page 314
8.4.1'a How to treat fiber samples of DNA......Page 316
8.4.1'b The phase problem......Page 317
Problems......Page 318
9.2.1 Many ecological niches are dimly lit......Page 321
9.2.3 Measures of detector performance......Page 322
Optimal conditions: Dark adaptation......Page 324
Probability of seeing......Page 325
9.3.2 Rod cells must be able to respond to individual photon absorptions......Page 326
9.3.3 The eigengrau hypothesis states that true photon signals are merged with a background of spontaneous events......Page 327
9.3.4 Forced-choice experiments characterize the dim-light response......Page 329
9.4.1 Vertebrate photoreceptors can be monitored via the suction pipette method......Page 331
9.4.2 Determination of threshold, quantum catch, and spontaneous signaling rate......Page 333
Multiple photon absorptions......Page 336
9.4.5 Questions raised by the single-cell measurements......Page 338
Big Picture......Page 339
Key Formulas......Page 340
9.4.2'a The fraction of light absorbed by a sample depends exponentially on thickness......Page 342
9.4.2'b The quantum yield for rod signaling......Page 343
9.4.2'd The whole-retina quantum catch is the product of several factors......Page 344
Problems......Page 346
10.2.1 Photoreceptors are a specialized class of neurons......Page 349
Cat eye......Page 351
10.3.1 Cells can control enzyme activities via allosteric modulation......Page 352
10.3.2 Single-cell organisms can alter their behavior in response to environmental cues, including light......Page 353
10.3.3 The two-component signaling pathway motif......Page 354
10.3.4 Network diagrams summarize complex reaction networks......Page 355
10.3.5 Cooperativity can increase the sensitivity of a network element......Page 356
10.4 Photon Response Events Localized to One Disk......Page 358
10.4.1 Step 1: photoisomerization of rhodopsin in the disk membrane......Page 359
10.4.3 Steps 3–4: activation of phosphodiesterase in the disk membrane, and hydrolysis of cyclic GMP in the cytosol......Page 360
10.5.1 Ion pumps in the rod cell plasma membrane maintain nonequilibrium ion concentrations......Page 362
10.5.2 Step 5: ion channel closing in the plasma membrane......Page 363
10.6.1 Step 6: hyperpolarization of the plasma membrane......Page 365
Voltage-gated channels......Page 366
Neurotransmitter release......Page 367
10.7 Summary of the Visual Cascade......Page 370
Big Picture......Page 369
Key Formulas......Page 371
10.3.4' More about adaptation in chemotaxis......Page 372
10.4.1' Cone and cone bipolar cells......Page 375
10.6' Glutamate removal......Page 376
10.7'b Negative feedback implements adaptation and standardizes signals from rod cells......Page 377
10.7'c Recycling of retinal......Page 379
Problems......Page 381
11.2.1 The synapse from rod to rod bipolar cells inverts its signal via another G protein cascade......Page 383
11.2.2 The first synapse also rejects rod signals below a transmission breakpoint......Page 384
11.3 Synthesis of Psychophysics and Single-Cell Physiology......Page 386
11.3.2 Review of the eigengrau hypothesis......Page 387
11.3.4 Processing beyond the first synapse is highly efficient......Page 389
11.4.1 The classical rod pathway implements the single-photon response......Page 391
11.4.3 Optogenetic retinal prostheses......Page 392
11.5.1 Darwin's difficulty, revisited......Page 393
11.5.2 Parallels between vision, olfaction, and hormone reception......Page 395
Big Picture......Page 397
Key Formulas......Page 398
11.2.2'd Why discrimination at the first synapse is advantageous......Page 399
11.4.1'a ON and OFF pathways......Page 400
11.4.1'b Image processing in the retina......Page 401
11.5.1' Rhabdomeric photoreceptors......Page 404
Problems......Page 406
Part III Advanced Topics......Page 410
12.1 Signpost: Universality......Page 412
12.2.2 The action functional singles out classical trajectories as its stationary points......Page 413
12.2.4 States and operators arise from partial summation over trajectories......Page 415
12.2.6 A confined-electron problem......Page 416
12.2.7 Light absorption by ring-shaped molecules......Page 418
12.2.8 The Schrodinger equation emerges in the limit of an infinitesimal time step......Page 420
12.3 Photons......Page 422
12.3.1 The action functional for photon trajectories......Page 423
12.3.2 The special case of a monochromatic light source reduces to our earlier formulation......Page 424
12.3.3 Vista: reflection, transmission, and the index of refraction......Page 425
Reflection......Page 426
Transmission......Page 427
Big Picture......Page 428
13.1 Signpost: Fields......Page 429
13.3 Classical Field Theory of Light......Page 430
13.4 Quantization Replaces Field Variables by Operators......Page 432
Step 2: Diagonalize energy......Page 433
13.5.1 Basis states can be formed by applying creation operators to the vacuum state......Page 434
13.5.2 Coherent states mimic classical states in the limit of large occupation numbers......Page 436
13.6.1 Classical interactions involve adding source terms to the field equations......Page 437
13.6.2 Electromagnetic interactions can be treated perturbatively......Page 438
13.6.3 The dipole emission pattern......Page 439
13.7.1 Connection to the approach used in earlier chapters......Page 440
13.7.3 Invertebrate photoreceptors have a different morphology from vertebrates'......Page 441
13.7.6 Lasers exploit a preference for emission into an already occupied state......Page 443
13.7.7 Fluorescence polarization anisotropy......Page 444
Big Picture......Page 445
14.2.1 FRET displays both classical and quantum aspects......Page 446
14.2.2 An isolated two-state system oscillates in time......Page 447
14.2.4 The density operator summarizes the effect of the environment......Page 448
14.2.5 Time development of the density operator......Page 449
14.3.1 The weakly coupled, strongly incoherent limit displays first-order kinetics......Page 450
14.3.2 Förster's formula arises in the electric dipole approximation......Page 451
14.3.3 More realistic treatment of the role of FRET in photosynthesis......Page 452
Big Picture......Page 453
Follow the rabbit......Page 454
Wonder......Page 455
Last......Page 456
Acknowledgments......Page 458
Last......Page 460
Other modifiers......Page 462
Relations......Page 463
Latin alphabet......Page 464
Greek alphabet......Page 468
B.1 Base Units......Page 470
B.2 Dimensions Versus Units......Page 471
B.3 About Graphs......Page 472
B.4 Payoff......Page 473
C.2.1 Index of refraction for visible light......Page 477
C.3.2 Rod cells......Page 478
C.4 B-Form DNA......Page 479
D Complex Numbers......Page 480
Bibliography......Page 484
Credits......Page 498
Index......Page 502