Friday, 20 April 2012

Information and entanglement in DNA

Deoxyribonucleic acid or DNA is the biological molecule that carries genetic information in all known organisms except for certain viruses. It is a nucleic acid consisting of two long chains, or strands, of basic units called nucleotides. The two strands are arranged in a twisted ladder structure known as a double helix, and is shown below.

Each nucleotide is composed of a nitrogen-containing base attached to a sugar phosphate molecule.  (The sugar in DNA is deoxyribose, which is a sugar with five carbon molecules, hence the name.)

There are four types of DNA bases: adenine(A), guanine (G), cytosine (C), and thymine (T). It is the sequence of these four bases that carry genetic information along segments of DNA called genes. That is, the 'language' of genes uses an alphabet with these four letters.

Genes encode information for creating proteins responsible for various biological traits, and are passed onto offspring.  (Those genes with hereditary variants are more properly referred to as alleles.)  The main purpose of DNA is long-term storage of this genetic information. 

The bases found in the two strands of DNA come together to form base pairs. The pairings go this way: A forms a base pair with T, while C forms a base pair with G. 

For example, if one strand carries the sequence of bases ATCGGACAGCAGTC, then the other strand will carry the sequence TAGCCTGTCGTCAC, in accordance to the base pairing rule.

The double helix structure of DNA is held together primarily by two kinds of attractive forces. One is the force that creates the base pairs called hydrogen bonding. The other one is the base-stacking interaction between bases along the backbone of the double helix called the van der Waals interaction. 

Recent studies on energies involved in base-stacking suggest the interaction between neighboring bases along a single strand of DNA can be partly explained by the presence of quantum entanglement between the electron clouds of these adjacent bases. 

As was discussed in an earlier post, quantum effects in a biological system are possible as long as the ratio of the important interaction energies J to thermal energies k due to noise from the environment is large enough. For DNA, a rough estimate of J/k is about 20.

We demonstrate that entanglement exists by picturing a strand of DNA as a chain of oscillating dipoles. A dipole is just a separation of negative and positive charges. Looking at the diagram below, imagine the base to be made up of a positively charged molecule surrounded by a negatively charged electron cloud (oval). 

The dipole on the left is labeled an 'up' dipole. The one on the right is a 'down' dipole.

On the left, most of the electron cloud is distributed below the molecule; this would be a dipole with the positive charge on top and the negative charge in the bottom (an 'up' dipole). On the right, most of the electron cloud is distributed above the molecule; this would be a dipole with the charges reversed (a 'down' dipole). An oscillating dipole means that our base switches back and forth from being one kind of dipole to the other.

(In physics terms, the non-permanent dipoles are modeled as harmonic oscillators and neighboring dipoles are made to interact via an dipole-dipole interaction called London dispersion force.)

Aside from the interaction between dipoles within a single strand, we also have dipole-dipole interactions between dipoles in a base pair, since these are also neighbors.

We can calculate the entanglement between electron clouds by checking correlations between adjacent dipoles in the oscillating dipole model The numerical results indicate that the amount of entanglement can be directly related to the binding energies in DNA.

Binding energy refers to energy needed to break apart a composite system into its basic parts. For example, atomic binding energy is required to separate an atom into its constituent nucleus and electrons. The nucleus itself can be split into protons and neutrons, requiring nuclear binding energy.

The two binding energies in DNA that indicate entanglement are the binding energy for adjacent dipoles in each strand, and the binding energy for dipoles found in base pairs. 

Furthermore, we can also identify the nature of the entanglement. For dipoles in a single strand, they tend to be correlated--that is, 'up' matches with 'up', 'down' matches with 'down'. For dipoles in a base pair, they are more likely to be anti-correlated; in this case, 'up' pairs with 'down'.

Neg is for negativity, a quantity that measures entanglement. Entanglement exists if Neg > 0.  The distance between neighboring bases is r. The important lines are the top three ones (green, blue, red). S1 and S2 refer to correlation and anti-correlation. The colors refer to different trapping frequencies, which can be compared to experimental data.

What exactly is the implication of this entanglement? First, it must be said that the entanglement does not change the information encoded in the DNA bases. The bases are either A, C, T, or G.There are no superpositions like A+T or C+G so there is nothing quantum about how genetic information is stored. 

The quantum part comes from how the information is processed.  Since the bases have entangled components (namely their electron clouds), it is strictly not correct to imagine them to be separate objects. 

In fact, the entanglement tells us that any single base contains some quantum information about its neighbors. This means that understanding the specific biochemistry of DNA transcription and replication might involve a picture where information is transmitted through quantum channels. 

For instance, in replication, as one base is being copied, it already possesses some information about the next base. This means that the DNA polymerase (the DNA-copying enzyme) can partially anticipate what comes next and it may be possible for it to adjust according to this advanced information.

Of course, it must be said that our simple model above makes no quantitative claims. DNA is simply too complicated for our oscillating dipoles to capture all the necessary details. What is established is a qualitative picture of how the energy level structure DNA can be connected to some amount of quantum entanglement it possesses. At the moment, it is considered highly speculative, but nonetheless, it is an interesting sort of speculation.


E. Rieper, J. Anders, V. Vedral, "Quantum entanglement between the electron clouds of nucleic acids in DNA", Preprint, arXiv:1006.4053v2 [quant-ph] (2010).

E. Rieper,  "Classical and Quantum Information in DNA",  Google Workshop on Quantum Biology (2010).

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