Lambda DNA ejection measurements and modeling

Hernan G. Garcia

APh161, Winter 2003Caltech

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

We can apply a pressure on the capsid, the ejection will stop when the expulsion force is canceled by the pressure:

Lambda Phage

Activating the ejection mechanism

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.

250 300 350 400nm

0.1

0.2

0.3

0.4

Absorptiona.u.E

ject

ed

DN

A

Results

Calibration of absorption vs. number of ejected base pairs.

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 10000 20000 30000 40000 50000

0.0

0.1

0.2

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0.6

A = (9E-6 ± 2E-6)*bp + (0.029 ± 0.009)

Abs

orpt

ion

(a.u

.)

Number of ejected base pairs

0 10 20 30 40 500

10000

20000

30000

40000

50000

60000

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80000

Num

ber

of e

ject

ed b

ase

pair

s

Osmotic pressure (atm)

Model: General outline

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 n

m

d s

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?

Position

PotentialThe ions will see DNA’s electriv 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.

Ve

Ve

e

e)(1

)2(2

Na

Mg

10Na

Mg1

2

eVe

ions#bp#

We will just consider the effect of the Mg2+ ions

We fit the data for 10 mM Mg2+ fromRau et al. (1984) to get the interaction term.

27.5 30 32.5 35 37.5 40DNADNA spacingamstrongs

6.5

7

7.5

logPressuredynecm2Analysis I

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

Analysis II

Using the “measured” DNA area (2.84 nm2).

Leaving the area as a free parameter we can fit it to(8 2) nm2.

Num

ber

of e

ject

ed D

NA

bp

Num

ber

of e

ject

ed D

NA

bp

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!!!