Powerpoint Slides to Accompany
Micro- and Nanoscale Fluid Mechanics:
Transport in Microfluidic Devices
Brian J. Kirby, PhD
Sibley School of
Mechanical and
Aerospace Engineering,
Cornell University, Ithaca,
NY
© Cambridge University Press 2010
Chapter
14
Ch 14: DNA Transport and Analysis
• DNA is among the most important biomolecules
to analyze
• DNA in aqueous solution is also a prototype for
linear polymers in good solvents
• Idealized models can be used to predict DNA’s
diffusive and electrophoretic transport, which
collectively are inconsistent with the NernstPlanck equation for transport of point ions
• DNA is free-draining in electrophoresis and
obeys Rouse dynamics
• DNA is non-draining in diffusion and obeys
Zimm dynamics
© Cambridge University Press 2010
Sec 14.1.1: Chemical Structure of B-DNA
• DNA has a hydrophilic sugar
(deoxyribose) backbonse with
negatively charge phosphate
groups and a sequence of
nitrogenous bases (A, G, C, T)
• DNA can melt (i.e. denature)
and anneal (hydrogen bond)
based on temperature and
other solution factors
• hydrogen bonding between
DNA or RNA from two
different sources is called
hybridization
© Cambridge University Press 2010
Sec 14.1.2: Physical Properties of dsDNA
• the physical properties of
dsDNA are primarily a
function of polymer contour
length and solution
conditions, but not base pair
order
• we model DNA physically as
an idealized contour through
space
• geometric definitions for DNA
include the diameter, radius of
gyration, and persistence
length
© Cambridge University Press 2010
Sec 14.1.2: Physical Properties of dsDNA
• the coordinate system of a
DNA polymer contour is
defined using the arclength s
from one end
© Cambridge University Press 2010
Sec 14.1.2: Physical Properties of dsDNA
• the persistence length is a
measure of the rigidity of a
linear polymer
• the persistence length is
evaluated by determining how
quickly the orientation of a
polymer backbone changes
as we traverse the contour
© Cambridge University Press 2010
Sec 14.1.2: Physical Properties of dsDNA
• the radius of gyration is a
measure of the space taken
up by the linear polymer
• the radius of gyration is
evaluated by calculating the
time average of the rootmean-square distance of the
polymer components from the
centroid:
© Cambridge University Press 2010
Sec 14.2: DNA Transport
• DNA diffuses as if it were a
rigid sphere with a radius
equal to about one third of the
radius of gyration.
• DNA behaves like a rigid
sphere because viscous
interactions are long range
(i.e. they decay as 1/r) and the
viscous connections between
the polymer components are
stronger than the viscous
interaction of the DNA
molecule as a whole with the
surrounding fluid
© Cambridge University Press 2010
Sec 14.2: DNA Transport
• unlike for diffusion, DNA’s
electrophoretic mobility is
independent of contour length
for all but oligomeric DNA
• DNA electrophoresis is
independent of length
because electrostatic
interactions are short range
(i.e. they decay as exp-r/λD)
and the electrostatic
connections between the
polymer components are
weak
© Cambridge University Press 2010
Sec 14.3: Ideal Chain Models for Bulk DNA
Physical Properties
• The Kratky-Porod or
wormlike chain model
describes DNA as if it
were a beam with flexural
rigidity YI
© Cambridge University Press 2010
Sec 14.3: Ideal Chain Models for Bulk DNA
Physical Properties
• The freely jointed chain
model describes DNA as
if it were a series of rigid
rods connected by free
ball joints
• The joints are imagined to
be of a length given by
the Kuhn length lK
© Cambridge University Press 2010
Sec 14.3: Ideal Chain Models for Bulk DNA
Physical Properties
• The freely rotating chain
model describes DNA as
if it were a series of rigid
rods connected by ball
joints with fixed
colatitudinal angle but
free azimuthal angle (i.e.
like an alkane polymer)
• The joints are imagined to
be of a length given by
the Kuhn length lK
© Cambridge University Press 2010
Sec 14.3: Ideal Chain Models for Bulk DNA
Physical Properties
• The Gaussian beadspring model modifies
the freely jointed chain
model to incorporate
springs of finite stiffness.
• This model leads to the
simplest mathematical
results
• The joints are imagined to
be of a length given by
the Kuhn length lK
© Cambridge University Press 2010
Sec 14.4: Real Polymer Models for DNA
• Idealized polymer models are only correct for
DNA in theta solvents, for which the electrostatic
DNA–solvent interaction is identical to the DNA–
DNA interaction.
• Idealized polymer models can describe only
entropic interactions.
• In a good solvent, such as aqueous solution,
DNA acquires a negative charge and exhibits
electrostatic interactions that dictate polymer
conformation.
© Cambridge University Press 2010
Sec 14.5: dsDNA in Confining Geometries
• DNA confined in a
nanochannel is influenced by
electrostatic (energetic) forces
as well as confinement
(entropic) forces.
• DNA whose end-to-end length
is controlled exhibits entropic
spring behavior
© Cambridge University Press 2010