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Physical Cell BiologyLecture 6: Physical Fundamentals II: Energy, Water

and statistical mechanics

Phillips, Chapter 12 , Chapter 6

Viscosity of water

Dynamic viscosity ! of water: 1.0 ×10-3 Pa·s

v

dF= !# $%

of area A

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some things are not just a fluid or a solid = viscoelasticity

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• ferrofluidic droplets

Serwane et al. Nat. Methods. (2017)0 10 20 30 40051015202530

Time(τ)

Strain(%

)

0.00.20.40.60.81.0

f

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More tools

• laser ablation

Hutson, 2009

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is wounded, the surrounding cells always recoil away from the wound site (Fig 1). By 10 s after ablation, the nearest neighbors of the wounded cell(s) recoil about � of a cell diameter (average velocity ~ 1 �m/s). The maximum recoil of about � a cell diameter is reached within 20-60 s. The neighboring cells then move back towards the ablation site as wound healing begins.

In these experiments, the ablated region is much smaller than a single cell. This is most clearly seen via the hole created in the embryo’s overlying vitelline membrane (e.g. the dark region with a hyper-fluorescent ring in Fig 1E). This hole is bounded by a coverslip and the glue holding the fly embryo onto the coverslip. Thus, it expands little and does not allow material to flow in or out. The hole apparent in Fig 1E is elliptical with semiminor and semimajor axes of 0.50 and 0.75 �m – approximately one-tenth the size of a typical cell.

To assess the extent of ablation in the z-direction, i.e. through the cell layer, we imaged the one-cell-thick epithelium in cross-section (Fig 1GH). The laser wounds cut cleanly through the epithelium (~6 �m thick in stage 13), so that the apical and basal surfaces both move freely. As the cells recoil, they do not shear. There is some apparent shear in the first image after wounding (second frame from top in Fig 1G), but this is just a motion artifact. The apparent shear is reversed when the z-scans are collected from bottom-to-top (second frame from bottom in Fig 1H).

FIGURE 1. Mechanical response of an embryonic epithelium to single-pulse laser ablation. The epithelium was the amnioserosa in stage 13 fruit fly embryos expressing GFP-cadherin. (A-C) are a series of confocal images taken before, 10 s and 20 s after ablation. The post-ablation images are overlays comparing the cell border positions before (magenta) and after ablation (green). As denoted by the crosshairs in A, the laser was targeted to the border between two cells. (D-F) are a similar series in which the laser targets a single cell’s apical surface. For each image, anterior is to the right. (G-H) are each a temporal series of four cross-sectional images through the amnioserosa (dorsal up). Cell borders appear as nearly vertical bright lines. The crosshairs mark the location and time of ablation (t = 0 s). The cross-sections in (G) were collected dorsal-to-ventral, so time increases as one goes down a single image and from one image to the next. The cross-sections in (H) were collected ventral-to-dorsal, so time increases as one goes up a single image.

Energy!What is Energy:Energy is an indirectly observed quantity that is often understood as the ability of a physical system to do work on other physical systems. Since work is defined as a force acting through a distance (a length of space), energy is always equivalent to the ability to exert pulls or pushes against the basic forces of nature, along a path of a certain length.Some Energies: Potential Energies, Kinetic Energy, Gravitational Energy.Energy is conserved!

Measures of Energy: (SI unit: Joule [J])1kBT is equivalent to 4.11x10−21 J, 4.11 pN·nm, 9.83x10−22 cal, 0.0256 eV, 2.479 kJ/mol or 0.593 kcal/mol

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typical energy magnitudes

Ionic Bond

~250kcal/mol ~1000kJ/mol ~400kBT

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Covalent Bond

~100kcal/mol ~400kJ/mol ~160kBT

Dipole-Dipole Bond

~1kcal/mol ~4kJ/mol ~1.5kBT

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London Forces (Van der Waals)

<1kcal/mol <4kJ/mol ~<1.5kBT

The hydrogen bond

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The hydrogen bond

~15kcal/mol ~60kJ/mol ~20kBT

Typical Interaction Strengths

• Ionic bond: ~250kcal/mol ~1000kJ/mol ~400kBT• Covalent bonds: ~100kcal/mol ~400kJ/mol ~160kBT• Hydrogen bonds: ~15kcal/mol ~60kJ/mol ~20kBT• Dipole–dipole: ~1kcal/mol ~4kJ/mol ~1.5kBT• London Forces <1kcal/mol <4kJ/mol ~<1.5kBT(van der Waals)

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Super Quick Statistical Mechanics Primer

The Usual Procedure: Counting States and Giving Them Weight

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The Usual Procedure: Counting States and Giving Them Weight

The Probability is Easy Once We Know the States