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Physics 414: Introduction to Biophysics

Professor Henry GreensideNovember 27, 2018

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Final topic of semester: biological pattern formation (Chapter 20 of PBOC2)

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Discuss three mechanisms of biological pattern formation

1) “French flag” or “gradient-threshold” models: externally established chemical gradient (morphogen) causes cells to differentiate when they sense a concentration greater than some threshold.

2) Turing instability: intrinsic pattern formation from homogeneous state caused by at last two reacting and diffusing morphogens, slow-diffusing activator and fast-diffusing inhibitor.

3) Lateral inhibition or the “Notch-Delta” concept that create checkboard-like two-dimensional grids of cells.

Discussion is chance to use what we have learned over the semester: diffusion, statistical physics, biology with some new material on chemical kinetics (rate equations) and linear stability

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Purpose of biological patterns can be difficult to understand

Many sea shells spend most of their life under sand and so are not visible, and they themselves have no vision. So why the spatial patterns?

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Stripe formation in Drosophila embryo:how to get precise reproducible stripes independent

of size of embryo?

1934 drawing by E. Wallace, Male on left, female on right

14 segments: 3 for head, 3 for thorax, 8 for abdomen

Fig. 2.44 page 80 PBOC2

Fig 2.45 p 80 PBOC2 Pattern of gene expression in Drosophilla embryo at 13th generation. Stained protein products of genes Bicoid in blue, Even-skipped (EVE) in green, Caudal in red.

There are ~6,000 < 213 = 8192 nuclei in one large cell membrane. Radii of nuclei about 6 microns, L ~ 600 microns so about 130 nuclei per stripe. Edges of bands precise to one nuclear diameter.

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Outline of how Drosophila develops from egg to adult fly

Fig 22-25 Molecular Biology of the Cell 5e, B. Alberts et al

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Earlier stages of the fly embryoFig 3.28 page 123 PBOC2 (read Section 3.3.4)

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syncytial blastoderm

More details in Chapter 22 of “Molecular Biology of the Cell, 5e”, B. Alberts et al

Each nucleus reproduces every 8 minutes until ~10th generation

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Later stages of the fly embryoFig 3.29 page 124 PBOC2

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Use light-sheet microscopy to visualize motion of surface cells of fly embryo as it evolves into larva

https://youtu.be/qiabYntNMC8

How motor proteins produce this smooth coordinated fluid-like motion of cells is hot current topic in biology and biophysics, facilitated by novel technology like

light-sheet microscopes

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Spatiotemporal activation and suppression of genes again one of the great unsolved biology problems

Figure 19.1 p. 803 PBOC2

Part of the gene regulatory network for developmental

pathway of a sea urchin

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Gene hierarchy: mutation of a single gene can transform one animal part into another

Recommended non-technical book: “Endless Forms Most Beautiful: The New Science of Evo Devo” by Sean Carroll (W. W. Norton, 2006)

Expression of genes is hierarchical, with certain master genes governing formation of entire structures like leg, eye, etc.

Fig 4.23 p. 172 PBOC2

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Human teratoma (“monster tumor”)Ectopic formation of hair, teeth, other tissues

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French flag model of how fruit fly embryo sets up precise reproducible structures: a morphogen gradient

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French-flag model of gradients with thresholds raises three quantitative problems

1) How does embryo produce precise gradients at precise times?

2) How do gradients take into account difference in size of embryos?

3) How does individual cell measure local concentration or local gradient with enough precision to make correct developmental decision?

Fly embryos from three different fly species at same stage of development,

differ by about 5 in length.

Fig 20.4 p. 900 PBOC2

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Spatially varying concentrations of transcription factors in Drosophila embryo determine segments

Figure 19.2 p. 804 of PBOC2

All four proteins are transcription factors (TFs) with Bicoid and Hunchback being activators, Giant and Kruppel being repressors

Stripe 2 of EVE gene

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At the blackboard: mathematics of a point source, diffusion, and uniform degradation leads to a puzzle:

length scale does not depend on size of domain

Bicoid is first morphogen in temporal development that shows a pattern, starts off successive morphogen patterns. How to get what seems to be exponential spatial profile? Anterior source + diffusion + uniform degradation of Bicoid protein product gives exponential.

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One-minute End-of-class Question