MEJORAS INTRODUCIDAS EN EL NUEVO CODIGO PROCESAL CIVIL.

In eukaryotic organisms the genome is organized in extremely compact structures called chromatin

The nucleosome is built of a small piece of DNA–approximately 150 bp–wrapped around a structure

that can be loosely thought of as a cylindrical disc formed of four pairs of histone proteins: H2A,

H2B, H3 and H4 (see Fig. 1.2 and 5.1). There are two copies each of these four proteins, and their

assembly is termed the histone core. The histone core can be modeled approximately as a cylinder

of 6nm diameter with a height of around 6 nm. The DNA of around 150 bp is wrapped roughly

1.75 times around the histone core [27]. Two short pieces of approximately 50 bp each, called linker

DNA, are present on either side to connect adjacent nucleosomes [27]. The radius of the DNA is

around 2nm; taking that into account, the effective nucleosome diameter is the histone diameter plus the DNA thickness of 2nm and is around 10nm. In physiological conditions the persistence length

of the DNA (described in Chapter 3) is around 50 nm, while the diameter of the histone core is

around 10 nm. This means that the DNA is bent at length scales much shorter than its persistence

length and, hence, the bending energy expended to form the nucleosome is really high. Fortunately,

the energetically favorable interactions of the negatively charged DNA with the positively charged

arginine and lysine residues of the histone core make up for the energy to be used up while bending

the DNA to form a stable nucleosome.

We saw in Chapter 1 that the genome is segmented into a hundred to a thousand base pairs

long sections called genes. Each gene has a code to synthesize various proteins that are composed

of amino acids. The DNA code is converted into a messenger RNA (mRNA) code by an enzyme

protein RNA polymerase (RNAP) in a process called “transcription.” The mRNA code is then

deciphered by transfer RNA (tRNA) to synthesize the corresponding amino acids and polymerize them to form various proteins by a process termed “translation.” Thus, loosely speaking, the flow

of genetic information is from DNA to mRNA to proteins. On the other hand, the real transcription

process is not that straight forward. Each gene is preceded by a small segment of tens of base pairs

called the promoter site, where RNAP is supposed to bind and start the mRNA transcription by

translocating along the DNA. The rate of gene expression is proportional to the efficiency of the

RNAP activity. The entire process of transcription, or gene expression, is regulated depending on

the cellular environment. This gene regulation is effected by different regulatory proteins which bind

at various places around the promoter to either enhance or suppress the activity of the RNAP. The

genome is also required to be accessible to various proteins that carry on important processes like

DNA replication and repair. In short, different parts of the DNA in this tightly packed nucleosome are supposed to be accessible to various proteins at different times. The question then is how do the

proteins overcome the tight compaction and access the nucleosomal DNA to perform key genomic

processes? It has been convincingly shown, in at least in vitro situations, that the nucleosomal

DNA spontaneously unwraps from the histone core to transiently expose its binding sites to the

corresponding proteins [24, 22, 23] and then re-wraps. This process happens constantly, and the

a)

b)

c)

50 nm

Figure 5.1: Structure of a nucleosome.a) High resolution X-ray diffraction structure of the complete nucleosome. Color-coding of proteins: H2A, orange; H2B, red; H3 blue; H4 green (figure from Luger et al. [121]. b) Electron micrograph of the condensed chromatin (figure from Alberts et al. [27].) c) Electron micrograph of chromatin that has been experimentally unpacked, or decondensed after isolation to show the nucleosomes (figure from Alberts et al. [27]).

addition to unequivocally demonstrating the feasibility of this particular mechanism of DNA ac-

cess, the above mentioned experiments from Widom and co workers also measure the the rates

for wrapping and rewrapping and the corresponding equilibrium constant. In this chapter we will

address the measurements from these experiments and make new predictions to stimulate further

experimentation.

The buried sites on the eukaryotic genome can be accessed by corresponding proteins via transient

exposure of the nucleosomal DNA due to its unwrapping from the histone. The unwrapping can

be effected by ATP-dependent nucleosome remodeling factors, which unwrap nucleosomal DNA, or

drive nucleosomes to new locations along DNA. This mechanism, though experimentally observed,

begs an explanation of how the remodeling factors know which nucleosomes to model. Similarly,

increasing evidence suggests that remodeling factors are recruited to specific nucleosomes by site-

specific DNA-binding proteins. This raises the question of how those DNA-biding proteins gain

access to their target sites. Also, remodeling factors may not always be required to allow access to

the nucleosomal DNA. Nucleosomes spontaneously undergo conformational fluctuations in which a

stretch of their DNA transiently lifts off the histone surface, allowing free but transient access to proteins that would not otherwise be able to bind. The equilibrium constants describing this DNA

accessibility are as large as–10−2 _{to 10}−1 _{for sites located a short distance inside the nucleosome,} decreasing to 10−4 _{to 10}−5 _{for sites located near the middle of the nucleosome [24]. Studies by} Li and Widom [22] using fluorescence resonance energy transfer (FRET) reveal that site exposure

involves large increases in separation between a fluorescence donor on one end of the nucleosomal

occurs by progressive unwrapping of the nucleosomal DNA starting from one end of the nucleosome

(see Fig. 5.2a).

a) Keq conf = k21 k₁₂ b)

Figure 5.2: The experimental setting of Li et al. [23] addressed to by our theoretical model. a)The nucleosomal DNA undergoes transient thermal fluctuations, thereby unwrapping from the histone core and transiently exposing the binding site to the corresponding protein (LexA in this case). b) The experimental procedure by Li et al. [23] involves using a Cy3 FRET donor (green) attached to the end of the nucleosomal DNA. The binding site for LexA is situated close to the end. As can be seen, the DNA should unwrap at least 27bp to allow LexA binding. There are two Cy5 FRET acceptors (red) on two copies of H3 histone proteins (blue). When the LexA binds to the DNA the spacing between the Cy3 and Cy5 becomes large and the FRET loses efficiency. At saturating concentrations of LexA (see Section 5.2) the total FRET efficiency becomes minimally low. At such high concentrations of LexA the rate of decrease of FRET efficiency is related to the rate of LexA binding and provides the unwrapping ratek12 (figures from Li et al. [23]).

A consequence of this behavior of nucleosomes is that when nucleosomal DNA contains a target

sequence for a site-specific DNA binding protein, the presence of the protein in the solution causes

nucleosomes to respond by shifting their conformational equilibrium towards the exposed, unwrapped

state. This unwrapping of the nucleosomal DNA allows stable binding by the protein. As a result a

dynamic equilibrium is established between the wrapped state (W) and the unwrapped state without

the binding protein (U) and between U and unwrapped state with the regulatory protein (U R) (see

Fig. 5.2).

Widom and coworkers have obtained the the equilibrium constant Keqconfig[24, 22] and the rate

constants [23] for the DNA wrapping and rewrapping process shown in Fig. 5.2. We will formulate a simple model using statistical mechanics to obtain the the equilibrium constant Kconfig

eq and sup- plement it with the Fokker-Planck equation to obtain the rate constantsk12 andk21, respectively,

for the DNA unwrapping and re-wrapping. Using this simple model, we predict the equilibrium

constantKconfig

eq as a function ofz, the depth of the protein binding site from the edge of the DNA. The organization of the chapter is as follows. In Section 5.2 we describe briefly the experiments

we wish to address. We lay out the theoretical model in Section 5.3. We perform the required

symbolic calculations in Section 5.4 and the corresponding numerical calculation in Section 5.5. We

E E E + E + + E + E ++ k12 k21 k₂₃ k32 k23 k32 k34 k34 Nucleosomes R R + k12 k21 k23 k₃₂ Nucleosomes Naked DNA R E + k23 k₃₂ Naked DNA z (a) (b)

Figure 5.3: The idea behind the experiment by Polach and Widom [24] (figure adapted from Polach and Widom [24]).a) The mechanism hypothesized by Polach and Widom [24] for binding of a regulatory protein (R) to a specific DNA target sequence (gray) on the nucleosomal DNA. It was hypothesized that nucleosomes are dynamic structures, transiently exposing their DNA. In the exposed state, proteins can bind as though they were binding to naked DNA. The related rate constants are indicated. (b) In order to quantify the hypothesized equilibrium between the wrapped and the unwrapped states of the nucleosomes, Polach and Widom used a restriction enzyme binding to its recognition sequence (gray) in the place of regulatory protein (R). The restriction enzyme can catalyze the cleavage of DNA to yield detectable products. Rates of cleavage for nucleosomal DNA are compared with cleavage of naked DNA in identical solution conditions.