428 9.5  Extending Length and Time Scales to Quantum and Ecological Biophysics

in the water. But in terms of fluid dynamics effects, this is essentially the same argument as

rotating the order of cyclists in a team as they cycle together in a group.

Similar mechanical feedback is also exhibited in populations of plants. For example, the

leaf canopies of trees result in difficult to predict emergent patterns in airflow experienced

by other surrounding trees in a wood or forest population, sometimes extending far beyond

nearest neighbor effects. This is important since it potentially results in complex patterns of

rainfall over a population of trees and of the direction of dispersal of tree pollen.

Airflow considerations apply to the flocking of birds and the swarming of flies. However,

here other biophysical effects are also important, such as visual cues of surrounding birds in

the flock, potentially also audio cues as well. There is also evidence for cooperativity in fluid

dynamics in swimmers at a much smaller length scale, for example, microbial swimmers such

as bacteria. Under these low Reynolds numbers swimming conditions (see Chapter 6), the

complex flow patterns created by individual microbial swimmers can potentially result in a

local decrease in effective fluid viscosity ahead of the swimmer, which clearly has implications

to microbial swarming at different cell densities, and how these potentially lead to different

probabilities for forming microbial colonies from a population of free swimmers.

Other effects include the biophysical interactions between carbon dioxide in the atmos­

phere and water-​based ecosystems. For example, increased levels of atmospheric carbon

dioxide dissolve in the saltwater of the oceans and freshwater in rivers and lakes to result in

increased acidification. This can feedback into reduced calcification of crustaceous organisms

that possess external calcium carbonate shells. There is evidence that human-​driven increases

in atmospheric carbon dioxide (such as due to the burning of fossil fuels) can result in a local

decrease in pH in the ocean by >0.1 pH unit, equivalent to an increase in proton concentra­

tion of >25%. This may have a dramatic detrimental effect on crustaceous organisms, which

is particularly dangerous since marine plankton come into this category. Marine plankton

are at the bottom of the ocean food chain, and so changes to their population numbers may

have dramatic effects on higher organisms, such as fish numbers. Calcification also plays

a significant role in the formation of coral reefs, and since coral reefs form the mechanical

structure of the ecological environment of many marine species increased, ocean acidifica­

tion may again have a very detrimental effect on multiple ecosystems at a very early stage in

the food chain.

Worked Case Example 9.2: DNA Origami

A simple single-​stranded DNA origami motif was designed consisting of 21 nucleotide

base pairs of sequence 3′-​CCGGGCAAAAAAAAAGCCCGG-​5′. The construct was subjected

to thermal denaturing and annealing upon cooling at an ionic strength of 10 mM.

a

Draw the structure of the lowest-​energy time-​averaged origami motif you might

expect to form.

A blue dye EDANS [5-​((2-​aminoethyl)aminonaphthalene-​1-​sulfonic acid] was then

conjugated to the 3′ end and a quencher for EDANS called “Dabcyl” to the 5′.

b

Explain with the assistance of a graph of normalized fluorescence emission intensity

of the blue dye as a function of time what you might expect to observe if the thermal

denaturing and annealing upon cooling is performed on this construct.

c

How would the graph differ if a second construct is purified that has the quencher mol­

ecule placed on the central adenine nucleotide and intensity measurements are made

after the lowest free energy structure has formed? (Assume that the Förster radius for

the dye–​quencher pair in this case is 3.3 nm, and the persistence length of single-​ and

double-​stranded DNA at this ionic strength is ~0.7 and 50 nm, respectively.)

Answers

a

Watson–​Crick base pairing will result in a lowest energy structure, which has

the maximum number of base pair interactions, which will involve 6 base pair

KEY BIOLOGICAL

APPLICATIONS:

EXTENDING

BIOPHYSICS

LENGTH SCALES

Quantum mechanics modeling

of enzyme kinetics; Ecosystems

biomechanics analysis.