Lambda DNA ejection
measurements and modeling
Hernan G. Garcia
APh161, Winter 2003
Caltech
Introduction
Viruses can package DNA with efficiencies that
range between 60% and 1%.
Studying the packaging process allows we test
our understanding of the energetics involved in
forcing DNA to adopt a certain configuration.
It is also interesting in the sense of
understanding the molecular motors that are
involved.
Smith et al. (2001) have already measured the
stalling force of a motor involved in packaging
in 29 using optical tweezers.
Smith et al. (2001)
Experiment: Concept
Activating the ejection mechanism
Lambda Phage
We can apply a pressure on the capsid, the ejection will stop when
the expulsion force is canceled by the pressure:
Applied pressure
Figures inspired by and partially taken from Grayson et al. (2004)
Experiment: How to do it?
The capsid acts as a semi-permeable membrane: big molecules in the
solution won’t be able to get into the capsid, exerting an osmotic pressure
on it.
We use different concentrations of polyethylene glycol (PEG) and apply the
formulas derived by Parsegian et al. (1986) to calculate the pressure.
LamB will induce the ejection process, while the non-specific restriction
enzyme DNase I will cut the ejected DNA into chunks.
Ejected DNA will absorb UV light (c=260nm).
Taking an absorption curve for each sample we can find the amount of ejected
DNA.
Absorption a.u.
Ejected DNA
0.4
0.3
0.2
0.1
nm
250
300
350
400
Results
Calibration of absorption vs.
number of ejected base pairs.
0.6
A = (9E-6 ± 2E-6)*bp + (0.029 ± 0.009)
Absorption (a.u.)
0.5
We have a sample with no
ejected DNA and a sample with
no PEG, where all of the DNA
should have been ejected.
Error  20% !!!
0.4
0.3
0.2
0.1
0.0
0
10000
80000
70000
50000
40000
30000
20000
10000
0
10
20
30
Osmotic pressure (atm)
40
50
Number of ejected base pairs
60000
0
20000
30000
40000
Number of ejected base pairs
50000
Lambda can be approximated by a
55 nm diameter sphere. Its DNA has
48,502 bp.
Bending energy:
Same model we used in class.
DNA-DNA interaction:
We want to use the same functional
form, but with the right parameters for
the present experiment.
55 nm
Model: General outline
Model: DNA-DNA Interaction
DNA is charged: 2 e/bp.
We used a buffer with 10 mM Mg2+ and 10 mM Na1+:
Which of these ions will be the most relevant in canceling
DNA’s field?
The ions will see DNA’s electriv
Potential
Position
potential, which will in part be canceled
by the counterions (V).
The probability of having an ion in the
capsid will be proportional to its
Boltzmann factor.
 # bp# ions 
Mg  e
Na  e
2
1
  ( 2 e )V
  (  e )V
Mg   e
Na 
2
1
eV
 10
We will just consider the effect of the Mg2+ ions
Analysis I
We fit the data for
10 mM Mg2+ from
Rau et al. (1984) to get
the interaction term.
log Pressure dyne cm2
7.5
7
6.5
DNA DNA spacing amstrongs
27.5
30
32.5
35
37.5
40
To match our model (force) to the data (pressure) we
have to know the area over which the osmotic pressure is
exerted.
dDNA 1.9 nm
Leaving the area as a free
parameter we can fit it to
(8 2) nm2.
Number of ejected DNA bp
Using the “measured” DNA
area (2.84 nm2).
Number of ejected DNA bp
Analysis II
Conclusions
There is a 65% discrepancy in the obtained DNA area over
which the pressure is applied.
Is DNA going out the capsid’s mouth in a simple way?
Most of the error is due to the Absorption vs. bp calibration.
Combining the data around the absorption peak should lead to an
error reduction.
The experiment’s concept seems to be suitable to answer
questions about DNA packing, however there are still some
factors to be taken in account:
The Na+ contribution, which can be solved using buffers which
include only Mg2+.
Find a better fit for the DNA-DNA interaction term.
The samples are crowded with PEG (spacing  nm), how is this
going to affect the ejection of DNA?
Acknowledgments
Thanks to Paul Grayson for answering
each one of my annoying emails, to
George Matheou for the crash course
in Matlab and to Nate Bode for
checking my English!!!