Schlick T. Molecular Modeling and Simulation: An Interdisciplinary Guide

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180 6. Topics in Nucleic Acids Structure: DNA Interactions and Folding

Given this multilayered organization of hydration shells in DNA and the large

costs associated with fully-solvated simulations of nucleic acids, practitioners

have attempted to economize on system size by modeling a limited number of

water molecules to represent only the thin, ordered ﬁrst solvation shell around the

DNA [230,843].

Box 6.3: Counterion Condensation Theory

Counterion condensation theory essentially predicts formation of a condensed layer of

mobile and hydrated counterions at a critical polyionic charge density in the vicinity

of the DNA surface (∼7

A). For monovalent cations, the concentration of this cloud is

relatively independent of the bulk cation concentration. This concentrated cloud of ions

effectively neutralizes ∼76% of the DNA charge, thereby reducing the negative charge of

each phosphate to about one quarter its magnitude (hence the charge scaling done in early

nucleic-acid simulations [523, 1013, 1260]). Divalent and trivalent counterions reduce the

residual charge further according to this model (to about one tenth of its magnitude). The

resulting phosphate screening reduces the electrostatic stiffness of DNA and also explains

the favorable entropy of binding by cation ligands to DNA, since they lead to release of

counterions from the condensed ion layer to the bulk solvent.

Various experimental and theoretical models of DNA electrostatics support counterion con-

densation of polyion charge above a critical threshold of polyion charge density. Theories

differ mainly in the structure of the condensed layer [1419]. Work on assessment of models

in light of experimental observations continues; see [850,1373], for example, for reviews.

6.4 DNA/Protein Interactions

Fundamental biological processes involve the interaction of nucleic acids and

proteins. These complexes may involve various types of proteins: regulatory,

packaging, replication, repair, recombination, and more. Many questions are now

being addressed in this large area of research involving protein/DNA complexes,

including:

• How do these proteins recognize DNA? That is, how do the protein and the

DNA accommodate each other? What geometric, energetic mechanisms are

involved?

• How are the mutual interactions stabilized? What are the speciﬁc and

nonspeciﬁc interactions involved?

• How are nucleotide and/or amino acid substitutions tolerated in the target

DNA (e.g., [971]) and bound protein regions (e.g., [734,1100])? Numerous

mutation studies (experimental and theoretical) are shedding insights into

this question and highlighting the residues that are essential to structure

6.4. DNA/Protein Interactions 181

Table 6.2. Representative protein/DNA and drug/DNA complexes.

Complex Binding Binding Details of Complex

Motif

Groove

λ repressor HTH Mgr Canonical HTH; homodimers; 2 helices of Cro

dimer cradle Mgr, stabilized by direct H-bond

and vdW contacts; little DNA distortion.

CAP repressor HTH Mgr About 90

◦

bend.

trp repressor HTH Mgr Indirect, water-mediated base contacts.

Purine rep. HTH Mm α-helices inserted in mgr.

Yeast MATα2 HTH Mgr Homeobox domains bind as monomers.

Zif268 Zn Mgr Zinc ﬁnger subfamily; each Zn ﬁnger recognizes

3 bps.

GATA-1 Zn Mm Transcription factors subfamily; single domain

coordinated by 4 cysteines.

GAL4 Zn Mgr Metal binding subfamily; each of two Zn ions,

coordinated by 6 cysteines, recognizes 3 bps.

GCN4 Leu/Zip Mgr Canonical; basic region/leucine zipper (α he-

lices) motif; slight DNA bending.

fos/jun Leu/Zip Mgr α-helices resemble GCN4; unstructured basic

region folds upon DNA binding.

fos/jun/NFAT Leu/Zip Mgr α-helices bend to interact with NFAT.

MetJ β-ribbon Mgr Two anti-parallel β-strands in Mgr; bends each

DNA end by 25

papillomavirus

E2 DNA target

β-barrel Mgr Domed β-sheets form an 8-strand β-barrel dimer

interface with 2 α-helices in Mgr; strong tailored

ﬁt for every base of the recognition element; bent

DNA; compressed mgr; DNA target crystallized

without protein.

TBP β-saddle mgr Ten-β-strand saddle binds in Mgr; signiﬁcant

distortion, ≈90

◦

bend.

p53 tumor supp. Loop/other Mm Binds to DNA via protruding loop and helix

anchored to anti-parallel β-barrel.

SRY Loop/other mgr Isoleucine intercalated into mgr.

NFAT Loop/other Mm Flexible binding loop stabilized by DNA.

histones Loop/other Mm Nonspeciﬁc PO

interactions.

distamycin (drug) mgr Selective to AT bps; binds in mgr without

distortion.

HTH: helix/turn/helix; Zn: Zinc-binding; β: β-strand motif; Leu/Zip: Leucine zipper/bZIP;

Loop/other: motifs with few representative members.

Mgr: binding mainly to major groove; mgr: binding mainly to minor groove; Mm: binding to

both grooves.

and function and those that are more variable, as evidenced by evolutionary

trends. Enhancing interactions by design is also an exciting application of

such studies.

• What is the relation between structural stability of the complex and biolog-

ical function? For example, Burley and co-workers [971] showed that TBP

can successfully bind to several single-bp mutation variants of the wild type

182 6. Topics in Nucleic Acids Structure: DNA Interactions and Folding

TATA-box octamer element of adenovirus major late promoter (AdMLP),



TATAAAAG 3



, but that the biological transcriptional activity can be

sensitively compromised by these mutations.

These are complex questions, but we are addressing them steadily as our

collection of complexes between proteins and DNA and between DNA and

other molecules (drugs, various polymers) is rapidly growing. See [808],

for example, for a review of protein/DNA and protein/RNA molecular dy-

namics simulations and [1313] for a comprehensive review of DNA/protein

interactions.

There are now hundreds of solved protein/DNA complexes known, a repre-

sentation of which is collected in Table 6.2 and illustrated in Figure 6.5.What

has certainly been established is that the observed protein/DNA interactions span

the whole gamut of possibilities — regarding binding speciﬁcity for sequence

or grooves, stabilizing motifs, protein topology, overall deformation, tolerance to

mutations, and more.

6.5 Cellular Organization of DNA

Thus far we have discussed the structure of DNA at the atomic and molecular

levels. Understanding the organization of DNA in the cell is important for appre-

ciating DNA’s role as the hereditary material and its versatility in structure and

function.

6.5.1 Compaction of Genomic DNA

DNA’s cellular organization is critical because of the enormous content of ge-

nomic DNA. The genome size — in terms of nucleotide bps per chromosome

haploid (eukaryotic chromosomes are each made of two haploids) — varies from

organism to organism. Though the number of bps that speciﬁes our makeup basi-

cally increases with the number of different cell types present in each organism,

it ranges greatly within an organism. Some organisms also have more genomic

content than mammals. For example, bacterial genomes have about 10

–10

bps

per haploid; for algae, the range is 10

to 10

; for mammals it is around 10

;yet

salamanders reach the large number of 10

–10

residues.

Table 6.3 shows representative examples of the genomic content of different or-

ganisms, along with the corresponding total length of DNA (assuming the DNA

is fully stretched). We see that this total DNA length isolated for bacterial chro-

mosomes is only of order 1 mm, but for human DNA the comparative length

is 3 orders of magnitude greater. In fact, if the genomic content in each human

chromosome would be stretched, 4 cm of DNA would result; stretching out all

6.5. Cellular Organization of DNA 183

Helix-turn-helix: λ cI repressor

Leucine zipper: fos/jun heterodimer

barrel: papilloma virus E2 factorβ

SRY (mgr intercalator)

Zinc finger: zif268

Zinc-stabilized with leucine zipper: GAL4

saddle: TATA-box binding proteinβ

Nucleosome (histones/DNA)

Figure 6.5. DNA/protein binding motifs for various complexes, with secondary structural

elements such as α-helices (red), β-strands (blue), metal ions (green), and DNA (grey)

shown.

184 6. Topics in Nucleic Acids Structure: DNA Interactions and Folding

Interwound Supercoil Solenoid Supercoil

Figure 6.6. Interwound and toroidal supercoiling. Interwound supercoiling with writhing

number Wr ≈−13 (left), and a solenoidal supercoil, drawn wrapped around a protein

core to mimic the nucleosome (right).

the DNA (two haploids for each of the 23 diploid human chromosomes) would

produce 2 meters of DNA! Yet, the eukaryotic nucleus size (or the cell size in

prokaryotes) is much smaller, around 5 μm, thus more than 5 orders of magnitude

smaller. This necessitates extreme condensation of the DNA.

This condensation is largely achieved by supercoiling, the coiling imposed on

top of the double-helical coiling, involving the twisting and bending of the DNA

about the global double helix axis itself. The right-handed B-DNA form is most

suitable for this coiling, as ﬁrst shown via modeling by Levitt [745]: B-DNA

can be bent smoothly about itself to form a (left-handed) superhelical structure

with minimal changes in the local structure. This property facilitates the cellular

packaging of DNA, not only by reducing the overall volume DNA occupies but

also by promoting protein wrapping in the chromatin ﬁber complex.

Different types of DNA compaction can be distinguished for prokaryotes and

eukaryotes. The former have supercoiled closed circular genomes (leading to the

solenoids introduced below), while the latter have linear DNA duplexes and nu-

cleosomes (leading to the toroids discussed below). Multivalent cations, such as

polyamines, are known to be important in the spontaneous condensation of DNA

to form compact, orderly toroids [138] and are likely to have a signiﬁcant role in

chromosomal condensation.

6.5.2 Coiling of the DNA Helix Itself

Supercoiling is a property of both free and protein-bound DNA. When this

wrapping of the global DNA helix itself involves self-interaction, like a braid,

a plectoneme or interwound conﬁguration results. If instead, the winding oc-

curs around the imaginary axis of a torus, a toroidal or solenoidal supercoil (or

superhelix) is formed (see Figure 6.6).

Interwound supercoiling is common for circular DNA, such as found in the

genomes of many viruses and bacteria, as well as for topologically constrained

DNA in higher organisms. In addition, eukaryotic DNA is circular in certain

6.5. Cellular Organization of DNA 185

Table 6.3. DNA content of representative genomes.

Organism

Total DNA

(# haploids)

Bacteriophage λ virus 49 17 μm

Haemophilus inﬂuenzae bacterium 1800 0.6 mm

E. coli bacterium 5000 1.6 mm

Yeast (S. cerevisiae) 13,000 4.6 mm (16)

Roundworm (C. elegans) 100,000 3.4 cm (6)

Mustard plant (Arabidopsis thaliana) 135,000 4.6 cm (5)

Fruitﬂy (Drosophila) 137,000 4.7 cm (4)

Mouse (M. musculus) 3,100,000 1.1 m (21)

Human (H. sapiens) 3,300,000 1.1 m (23)

Salamander (A. tigrinum, axolotl) 42,000,000 14.3 m (14)

All listed are eukaryotes except the virus and bacteria; a bacteriophage is a virus that invades

bacteria.

One kb = 1000 bps.

Contour lengths of stretched DNA are calculated based on 3.4

A per bp. The number of haploids

reﬂected in this total DNA length is given in parentheses.

energy-producing organelles, the mitochondria. Toroidal-type supercoiling is

characteristic of the packaged form of chromosomal DNA in the chromatin ﬁber

(see below).

The orderly packaging of the DNA in the cell has two major roles. It con-

tributes to the ﬂexibility of the DNA ﬁber and to the accessibility of DNA for

performing vital biological processes — replication, transcription, and transla-

tion — all of which require the DNA to unwind. The packaging also compacts the

chromosomal material by orders of magnitude, as required.

6.5.3 Chromosomal Packaging of Coiled DNA

Cellular DNA is organized in the chromosomes. Each chromosome in eukary-

otes (two haploids) is made up of a ﬁber called the chromatin that contains DNA

wound around proteins. Speciﬁcally, in this packaged form of the DNA, DNA

wraps around many large histone protein aggregates like a long piece of yarn

around many spools (see Figure 6.7). The diameter of this DNA/protein ﬁber in

its compact form is around 300

A, an order of magnitude greater than the diameter

of the double helix [1384].

Several levels of folding are recognized for the chromatin ﬁber, but only the

basic units of the chromatin ﬁber and the associated low-level packaging are

well characterized; see [383, 567] for an overview of the basic components of

chromatin and levels of structure. This view has been deduced from various exper-

imental studies of the individual globular histone proteins (class types H1, H2A,

H2B, H3, H4) as well as of the chromatin ﬁber. Techniques used for the ﬁber

186 6. Topics in Nucleic Acids Structure: DNA Interactions and Folding

analysis include electron microscopy, X-ray diffraction, neutron diffraction, nu-

clease digestion combined with gel electrophoresis,

and chromatin reconstitution

in vitro.

The Nucleosome: DNA + Histones

A key fact established in 1974 by Roger Kornberg and Jean Thomas was that

the repeating unit of the chromatin is the nucleosome [674]. This unit consists

of about 200 bps of DNA, most of which is wound around the outside core of

histones; the remainder, linker DNA, joins adjacent nucleosomes (Figures 6.6 and

6.7).

The histone proteins have a large proportion of the positively-charged residues

Arg and Lys. Both residues make up between 20 and 30% of all residues: the

percentages of Lys/Arg residues for H1, H2A, H2B, H3, and H4 are 29/1, 11/9,

16/6, 10/13, and 11/14, respectively. (These proteins have 215, 129, 125, 135, and

102 amino acids, respectively). Therefore, electrostatic interactions between the

negatively charged DNA backbone and the positively-charged histone side chains

are thought to stabilize this protein/DNA complex.

In addition, as mentioned in connection to our heightening appreciation for the

subtle, sequence-dependent effects in nucleic acids, the DNA wrapped around

nucleosomes has speciﬁc regions that are more favorable to bind to nucleosomes.

Such recent discoveries concerning a “second genetic code”, the nucleosome

positioning code [1157, 1288,1425], are actively being pursued.

Nucleosome Structure

The earlier works, combined with recent chemical, enzymatic, and structural

studies (e.g., [55, 790, 1020]) suggest detailed organization of the nucleosome

units and reveal some aspects of stabilizing electrostatic interactions. For ex-

ample, based on a nucleosome crystal structure without the wound DNA [55],

Moudrianakis and collaborators have shown that the nucleosome has a tripartite

organization — assembly of two dimers of H2A–H2B, one on each side of a

centrally located H3–H4 tetramer [55]. The nucleosome was later shown to be

surrounded by a positive ion cloud with an average local density exceeding the

bulk ion concentration signiﬁcantly.

In 1997, the 11-nanometer nucleosome core particle, including the wrapped

DNA, was solved by X-ray crystallography at 1.9

A resolution [790](see

Figure 6.8 for a rendering of the nucleosome reﬁned later [287] with the histone

tails), revealing further details. Namely, 146 bps of core DNA are wound on

In this procedure, the phosphodiester bond of DNA in solution is cleaved. This leaves chromatin

protected and therefore reveals overall chromatin organization when analyzed by gel electrophoresis.

Reconstitution can involve the construction of a chromatin-like ﬁber by adding histones to

speciﬁc sequences of DNA.

The lengths associated with the total nucleosomal DNA and with the linker component vary

from organism to organism and tissue to tissue. Speciﬁcally, the total length ranges from around 160

to 260 bps; the length of linker DNA ranges broadly from about 10 to 110 bps, though it is usually

around 55 bps.

6.5. Cellular Organization of DNA 187

H2A

H2B

6 nm

Linker DNA ~60 bp

Wrapped DNA

~146 bp

12 nm

10 bp 3.4 nm

Duplex DNA

Nucleosome Core

146 bp wrapped DNA/

histone core

Compact Chromatin

(hypothetical structure)

Chromatin

Extended ‘Beadsonastring’

12 nm

Total DNA

Length

~0.1 p

(7 nm)

~1 p

(60 nm)

~4 p

(200 nm)

~10

(2 cm)

2.4 nm

DNA in the Cell

1500 nm

Metaphase Chromosome

30 nm

Figure 6.7. Schematic view of DNA’s many levels of folding. On length scales much

smaller than the persistence length, p

, DNA can be considered straight. In eukaryotic

cells, DNA wraps around a core of histone proteins (see also Figure 6.8) to form the chro-

matin ﬁber. The ﬁber is shown in both the extended view and a hypothetical compact zigzag

view (the ‘30-nm ﬁber’) deduced from a modeling study [483]; the compact structure of the

chromatin ﬁber is unknown. Chromosomes are made up of a dense chromatin ﬁber, shown

here in the metaphase stage. For reference, we highlight with pink in all the DNA/protein

views the hierarchical organizational unit preceding it. The length scale at right indicates

the level of compaction involved.

188 6. Topics in Nucleic Acids Structure: DNA Interactions and Folding

the outside of an octamer core of the histone proteins (two dimers each of proteins

H2A, H2B, H3, and H4) to form 1.75 turns of a left-handed supercoil; the linker

histone component H1 is thought to be a key player in regulation through binding

to the outside of this core particle and contacting the linker DNA. The wrapped

DNA has a structure very different from free oligonucleotides as well as DNA

in other protein/DNA complexes [1050]. Distinct features include excess cur-

vature, bending into the minor groove, twist alterations, and DNA stretching.

Five years later, a high-resolution nucleosome structure with tails resolved was

published [287].

Figure 6.8 illustrates the electrostatic view that emerges from Poisson-

Boltzmann calculations (see discussion of theory and methodology at the end of

Chapter 10) for the high-resolution nucleosome core particle with resolved tails

[287]. Note the positively charged (blue) H3 and H2B tails and histone regions

inside the complex, as well as the negatively charged (red) wrapped DNA.

In 2005, a tetranucleosome was solved crystallographically [1094], and sev-

eral other nucleosome structures have since become available, with modiﬁed tails

[786], modiﬁed DNA sequences [88], as shown in Figure 6.9, and bound to drugs

like cisplatin [1392]. The nucleosome core structure shows that each histone con-

tains unstructured end regions which make important points of contact between

the protein and the DNA. Speciﬁcally, an underwinding (10.2 vs. 10.25 bp/turn)

of the nucleosome-bound DNA superhelix lines up neighboring DNA grooves to

form a channel through which the histone ends can pass. These tails likely play

key roles in regulating biological processes, such as transcription, that require a

conformational change of the complex for initiation. Ongoing investigations of

the transition between the more open and more compact nucleosome structure

will help us understand better transcriptional regulation and DNA packaging.

Polynucleosome Assembly

The nucleosomal packing described above — superhelical DNA around a his-

tone core — represents only a tenfold compression of the DNA. This is because

≈166 bps of DNA (or ≈ 560

A of contour length if stretched) are organized as

a core cylindrical particle of dimensions 110 ×110×55

A, where 110

Aisthe

diameter and 55

A represents the height of this unit. Chromatin ﬁbers within inter-

phase chromosomes possess a hierarchical structure. At low salt concentrations, a

beads-on-a-string model is produced which compacts the DNA further by a fac-

tor of about 40. At physiological ionic strengths, it is believed that a next level of

chromosomal organization is the so called “30 nm” (300

A) chromatin ﬁlament

observed by electron microscopy.

Several models for this polynucleosomal level of folding have been sug-

gested based on X-ray crystallography and electron microscopy imaging. Yet,

a consensus has not been reached despite decades of intense research, as reviewed

recently [1271, 1297]. The two broad classes of structures for the chromatin

ﬁber [330] include two-start zigzag structures, where the nucleosomes criss-

cross one another around the helical axis with straight linker DNA and dominant

interactions between next-nearest neighbors (i

±2), and one-start solenoid struc-

6.5. Cellular Organization of DNA 189

Figure 6.8. The nucleosome core particle (left) [287] and its corresponding electrostatic

surface potential (right) as computed from the Poisson Boltzmann (PB) equation with

the PBEQ module [586]intheCHARMM program [175] (see Chapter 10 for theoret-

ical framework and algorithms). The grid resolution for solving the linear PB equation

was 1.5

A and 1.0

A after focusing; the salt concentration was set to 0.15 M, and par-

tial charges from the CHARMM program were used as input. As customarily done for

macromolecules [903], the unitless (i.e., relative) dielectric constant 

is set to the numer-

ical value of 2 inside and 80 outside the macromolecule (i.e., 2 and 80 times the vacuum

dielectric constant 

tures, where nucleosomes arrange helically around the ﬁber axis with bent linker

DNA and dominant interactions between nearest neighbors of nucleosomes (i±1)

(see Figure 6.10).

The solenoid was proposed in 1977 by John Finch, Aaron Klug, and collab-

orators [401] based on electron micrographs that suggested a helical form with

6 nucleosomes per turn stabilized by contacting linker histone molecules. The

zigzag form [330] is evident in the recent crystallographic structure of the tetranu-

cleosome [1094], for example, with short linker DNAs between nucleosome and

without linker histones.

Indeed, this unsettled puzzle for the ﬁber’s organization is evident in views pre-

sented over 22 years in various editions of the classic Molecular Biology textbook

[17]. The 1986 (second) edition showed chromatin as a zigzag, while the 1994

(third) edition presented a solenoid; eight years later, the solenoid remained in

the fourth edition, but the 2008 (ﬁfth) edition illustrates both zigzag and solenoid

models.

Only recently, have researchers begun to dissect the inﬂuence of key inter-

nal and external factors such as length of the connecting linker DNA segments

between nucleosomes (which can vary from 10 to 70 bp), the binding of linker

histones, and the presence of various concentrations of monovalent and divalent

ions on chromatin structure. For example, electron microscopy of reconstituted