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2.5  Physical Quantities in Biology

scale of 10⁻¹⁵ s, but arguably the most rapid events, which make detectable differences to

biomolecular components, are collisions from surrounding water molecules, whose typical

separation time scale is 10⁻⁹ s. Electron transfer processes between molecules are slower

at 10⁻⁶ s.

Molecular conformational changes occur over more like 10⁻³ s. Molecular components

also turnover typically over a time scale from a few seconds to several minutes. The life­

time of molecules in cells varies considerably with cell type, but several minutes to hours

is not atypical. Cellular lifetimes can vary from minutes through years, as therefore do

organism lifetimes, though certain microbial spores can survive several hundred million

years. Potentially, the range of time scale for biological activity, at a conservative estimate, is

~20 orders of magnitude. In exceptional cases, some biological molecules go into quiescent

states and remain dormant for potentially up to several hundred million years. In principle,

the complete time scale could be argued to extend from 10⁻¹⁵ s up to the duration over which

life is thought to have existed on Earth—​4 billion years, or 10¹⁸ s.

2.5.5  CONCENTRATION AND MASS

Molecules can number anything from just 1 to 10 per cell, up to over 10⁴, depending on the

type of molecule and cell. The highest concentration, obviously involving the largest number

of molecules in the smallest cells, is found in some proteins in bacteria that contain several

tens of thousands of copies of a particular protein (many bacteria have a typically small diam­

eter of 1 μm). Biologists often refer to concentration as molarity (M), which is the number

of moles (mol) of a substance in 1 L of water solvent, such that 1 mol equals Avogadro’s

number of particles (6.022 × 10²³, the number of atoms of the C-​12 isotope present in 12 g

of pure carbon-​12). Typical cellular molarity values for biological molecules are 10⁻⁹ M or

nanomolar (nM). Some biologists also cite molality, which is the moles of dissolved sub­

stance divided by the solvent mass used in kg (units mol kg⁻¹). Dissolved salts in cells have

higher concentrations, for example, the concentration of sodium chloride in a cell is about

200 mM (pronounced millimolar) that is also equal in this case to a “200 millimolal” molality.

Mass, for biochemical assays, is often referred to in milligram units (mg). The molecular

mass, also called the “molecular weight” (Mw), is the mass of the substance in grams, which

contains Avogadro’s number of molecules, but is cited in units of the Dalton (Da) or more

commonly for proteins the kilodalton (kDa). For example, the mean molecular weight taken

from all the natural amino acids is 137 Da. The largest single protein is an isomer of titin that

has a molecular weight of 3.8 MDa. The “molecular weight” of a single ribosome is 4.2 MDa,

though note that a ribosome is really not a single molecule but is a complex composed of sev­

eral subunits. Mass concentration is also used by biologists, typical units of being how many

milligrams of that substance is dissolved in an milliliters of water, or milligrams per milliliter

(mg mL⁻¹; often pronounced “miggs per mill”).

An alternative unit, which relates to mass but also to length scale, is the svedberg (S, some­

times referred to as Sv). This is used for relatively large molecular complexes and refers to

the time it takes to sediment the molecule during centrifugation (see Chapter 6), and so is

dependent on its mass and frictional drag. A common example of this includes ribosomes,

and their component subunit; the prokaryote ribosome is 70 S. The svedberg is an example

of a sedimentation coefficient (see Chapter 6), which is the ratio of a particle’s acceleration

to its speed and which therefore has the dimensions of time; 1 S is equivalent to exactly

100 femtoseconds (i.e., 100 fs or 10⁻¹³ s). Svedberg units are not directly additive, since they

depend both on the mass of the components and to their fractional drag with the surrounding

fluid environment that scales with the exposed surface area, which obviously depends on

how separate components are bound together in a complex. When two or more particles

bind together, there is inevitably a loss of surface area. This can be seen again in the case of

the ribosome; the 70 S prokaryotic ribosome has a sedimentation coefficient of 70 S, but is

composed of a large subunit of 50 S and a small subunit of 30 S (which in turn includes the

16 S rRNA subunit).