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Chapter • Experimental Methods of Structure Determination
13
. Fig. 13.15 The accuracy of an NMR structure depends on the
density of the experimentally determined atomic distances. These
come from experiments that deliver information about the exchange
of the magnetic state of spatially adjacent, but not directly connected
atoms (so-called nuclear Overhauser effect, NOE). With the covalent
connectivity list and the NOE conditions, multiple structural models are generated by distance geometry. These models represent the
low-energy geometries that agree with the spectral parameters. In the
left part of the gure (left) the experimentally measured NOEs (black
dashed lines) are distributed over the 3D structure of adomain of the
guanine nucleotide exchange factor. For the sake of clarity, only the
determined distance conditions in the measured protein
molecule. If the spectral parameters for asection of the
structure are too sparsely distributed at too large distances, it will be very difcult to obtain an unambiguous
spatial conguration of the folded peptide chain. Therefore, the generation of astructural model by distance
geometry is coupled with molecular dynamics simulations (Sect.15.7). These calculations provide aset of
geometries of the molecule that represent energetically
favorable 3D structures consistent with the spectral
parameters. Several slightly divergent models are given
particularly in regions with few spectral conditions.
Therefore, NMR spectroscopists always propose aset
of structural solutions (. Fig.13.15).
Attempts are often made to compare the quality of
X-ray and NMR structures. Both methods measure different properties, and the structures are derived from
different measured variables. This must be considered
when making adirect comparison. The accuracy of an
NMR structure uctuates with the density and frequency
of spectral distance constraints, while that of an X-ray
structure mainly depends on the resolution of the diffraction experiment. The molecules are observed in different
long-range NOEs are shown. Most of the amino acid side chains are
also suppressed; many of these NOEs, therefore, indicate the positions
of atoms that are not shown. In areas in which very few distances
could be determined (e.g., in the green loop areas or at the termini),
the model is ambiguously dened. Multiple models are consistent with
the experimental data (right). The main chain of the protein fans out.
In areas where alarge number of NOE conditions are found (e.g., the
helices and the central β-strand), the structural models diverge only
slightly from one another. In their sum, they serve to fold the polymer
chain in space using the distance geometry method
physical states. The crystal structure is determined in the
solid state; the NMR structure in the dissolved state.
Thus, the strength of the information collected lies not
in the relative comparison of the procedures but rather
in their complementarity.
Resonance absorption of magnetically active nuclei
can also be induced and observed in the solid state.
However, very broad resonance signals are obtained.
They hardly show the richness of detail required for
high-resolution structure determination. This is mainly
due to so-called dipolar couplings. This coupling describes the interaction of neighboring nuclei in amolecule via the magnetic dipole–dipole interaction. It is
afunction of the distance between the nuclei and the
angle that the distance vector between the two nuclei
forms with respect to the external magnetic eld. In
solution, molecules of not too large amolecular weight
(up to about 300 kDa) rotate fast enough to average
out such anisotropic couplings and, thus, provide sharp
resonance lines. Over the last 25years, CP/MAS NMR
spectroscopy has been developed in which crystalline
samples are rotated extremely fast at amagic angle of
54.7° to the applied magnetic eld. This averages out the
. • How Relevant Are Structures in aCrystal or NMR Tube to aBiological System?
dipolar couplings and produces sharp signals comparable to solution spectra. Thus, solid-state NMR spectroscopy is available as an additional method for structure
determination.
But what new insights can this method provide, given
that crystal structure analysis is already such apowerful
method in the solid state? Does it lose the advantage of
solution NMR spectroscopy, which studies molecules
in solution where they can develop their dynamic properties? First of all, not every protein crystallizes; membrane proteins in particular pose problems. In addition,
high-resolution spectra in solution are limited to smaller
proteins. Here, solid-state NMR spectroscopy can extend
the scope to additional and larger proteins. Furthermore,
it can help to close the information chain from crystal
structure to solution NMR. Differences between the two
methods have been observed. They are often related to
the limited mobility in the solid state compared to solution. Or there are artifacts due to the crystal packing that
modify the protein geometry in the solid state. Solid-state
NMR spectroscopy can bridge the gap to solution NMR
and help determine whether there are structural differences in the solid that are reected in adifferent resonance behavior between solution and solid state. Such
acomparison can ll an important gap in the chain of
evidence for more detailed investigations.
13.9 How Relevant Are Structures
in aCrystal or NMR Tube
to aBiological System?
The discussed structure determination techniques investigate molecules in acrystal assembly or in solution in
an NMR tube. Are these conditions at all relevant for
the biological conditions in an organism? Small exible
molecules change their geometry depending on the environment. They will adopt adifferent shape in acrystal,
in solution, or in the binding pocket of aprotein. Therefore, the question must be asked whether the data from
asmall-molecule crystal structure are suitable to deliver
information about the molecular geometry in abinding
pocket. From the numerous known crystal structures, and
in the meantime there are more than 1.25 million in the
public domain, some general principles about the molecular architecture of organic compounds can be deduced.
All of the published crystal structures are electronically
archived at the Cambridge Crystallographic Data Centre
in England. They can be retrieved and compared with one
another. It will be shown in Chaps.14 and16 that valuable information about possible molecular and interaction
geometries are available through astatistical evaluation
of these data, which also provide insights relevant for the
conditions in aprotein-binding pocket.
Nevertheless, are the structures in the protein crystal
too far away from the conditions in abiological system,
much further away than, for example, the solution-phase
state? There are many structure determinations that have
been made in solution and in acrystal in parallel. Experience has shown that the correlation is usually very high.
Deviations are most likely to be found on the surface of
proteins. This is where the amino acid side chains interact with the environment and can adopt alternative rotamer conformations. Therefore, these deviations are not
surprising. . Fig.13.10k shows the crystal packing of
the enzyme thrombin. Note the large holes in the crystal
packing. These areas are lled with water molecules that
are so loosely incorporated into the crystal that they are
largely free to move. Therefore, they cannot be located
in the electron density. Water-lled channels in protein
crystals can account for up to 70% of the crystal’s mass!
Therefore, the crystal can be considered as ahighly concentrated “ordered solution.” High concentrations are
also required for NMR measurements. They are considerably higher than under biological conditions, but still
10–100 times lower than in protein crystals.
The high water content of protein crystals allows
small molecules to diffuse into the crystals. In the water channels, they move as they would in an aqueous
solution. In favorable cases, the binding pocket of the
protein is directly accessible from one of these channels.
By placing the protein crystal directly in asolution of
the active agent (soaking), the active agent can penetrate
the crystal through the channels, diffuse into the binding
pockets, and dock there. Anew diffraction experiment is
then performed with the thus loaded crystal. The reections are measured and, based on the known structure
of the protein, the electron density map is generated. The
density of the uncomplexed protein is subtracted from
this map. The difference density of the incorporated ligand remains. This information is of vital importance
for understanding small molecule–protein interactions.
As long as crystal structures have been determined,
science has been concerned with the question of whether
the structures thus elucidated are really relevant to the
properties of the molecules under physiological conditions. As early as 1963, when only the structure of myoglobin was known, Doscher and Richards studied the
hydrolysis of the 2′,3′-cyclophosphates of uridine and
cytidine. These are cleaved by ribonucleaseS. The two scientists showed that the enzyme is still catalytically active
in the crystalline state. Catalysis at the crystal surface or
by partial dissolution of the crystals could be excluded.
Crystalline hemoglobin can reversibly absorb and release
oxygen. Using the enzyme cyclophilin3, apeptidylprolyl isomerase, the group of Malcolm Walkinshaw at the
University of Edinburgh in Scotland was even able to
demonstrate quantitative agreement of ligand binding in
both crystalline and dissolved states. Different concentrations of an inhibiting prolyl dipeptide were allowed to
diffuse into the crystal. The occupancy of this inhibitor,
obtained from the different concentrations of soaking
Chapter • Experimental Methods of Structure Determination
13
solutions, was then determined in acrystallographic experiment. The binding constants were then determined
from the occupancy data. They were in quantitative
agreement with the inhibition constants determined in
afunctional assay in solution.
The diffraction data can be very quickly collected
with even more intense, so-called white X-rays from
asynchrotron source (the so-called Laue technique). With
this experiment, it was possible to observe stable intermediates of enzyme reactions. Structural changes of the
two-dimensional crystals of the acetylcholine receptor
(Sect.30.4) could be observed with electron microscopy
after loading with the natural ligand. This and other
experiments have proven that proteins exist in acrystal
lattice that must be, at the very least, very similar to the
biologically active form.
The X-ray free-electron laser (XFEL) is expected to
provide further insights. It is abillion times more intense
source of radiation for diffraction experiments. Tiny crystals (200 nm to 2 μm) are injected into the X-ray beam of
such asource in the form of acontinuous stream. Each of
these crystals provides adiffraction pattern before bursting in the intense beam. However, the duration of the
diffraction experiment is ve powers of ten shorter than
the time that elapses before the crystal explodes. Each
crystal provides alimited diffraction pattern. However,
since many crystals come into the reection position in all
possible orientations relative to the X-ray beam, acomplete dataset can be collected in this way. Thus, acomprehensive structure determination (so-called serial crys-
tallography) is possible. Due to the extremely short time
between the injection of the crystalline samples into the
beam and the measurement of the diffraction experiment,
the method is ideally suited for the study of time-dependent phenomena. For example, light-dependent processes
can be initiated by alaser pulse. In this way, the lightdriven proton pump bacteriorhodopsin could be followed
at work as it shufes protons across the membrane. Like
amovie, snapshots of the electron density distribution
were recorded in steps of 16 ns to 1.7 ms. They show how
retinal is rearranged, how amino acid residues are spatially
shifted, and how water molecules accompany the process.
To observe processes such as enzyme reactions, the tiny
crystals are mixed with the reactants in the ow leading to
the measuring beam. XFELs are currently being built at
several locations around the world. They are not cheap to
operate because they rst require akilometer-long linear
accelerator for electrons as aradiation source. Over avery
long distance using suitable alternating electrical elds
the electrons are accelerated to almost the speed of light
where relativistic effects dominate their behavior. They
are injected as extremely short pulses and form individual
particle bunches. Along specially arranged magnets, the
electrons are then forced to follow akind of slalom course,
emitting laser-like X-ray pulses. These X-rays, traveling at
the speed of light, interact with the electron bunches y-
ing in front of them on the slalom course, by this slowing
some of them down and accelerating others. In this way,
akind of “synchronization” of the electrons in the particle bunches is achieved along the further trajectory, and
they emit their X-ray light in phase along the direction of
travel, resulting in the pulsed, extremely intense, coherent
and monochromatic laser-like beam. This beam hits the
target, while the electron ow is deected slightly in front
of the target to avoid a collision with the sample. Unlike
asynchrotron or aneutron reactor, where many experimental setups share the expensive radiation source, the
XFEL allows only one experimental setup. However, it
is hoped that this technology will enable completely new
insights to be gained in the future, in particular into the
dynamics and, thus, the detailed function of proteins.
13.10 Synopsis
The most powerful methods to determine the spatial
-
structure of molecules are X-ray crystallography and
NMR spectroscopy. The former requires the biomolecules to be arranged in periodic arrays in acrystal,
and the latter studies them in solution, usually in an
isotopically labeled form.
Crystals need special conditions to grow from sat-
-
urated solutions. They spatially arrange in periodic
arrays, and the molecules pack through translational
symmetry in three dimensions. In addition to the pure
shifting of basic motifs, usually one molecule that
represents the asymmetric unit, symmetry operation
such as mirror reection, two-, three-, four-, and sixfold rotation or inversion can be applied.
Crystal lattices diffract X-rays and the diffraction ex-
-
periment can be understood as athree-dimensional interference of elementary spherical waves generated at
the positions of the atoms in the lattice. The diffraction
phenomenon at a3D lattice can be treated formally as
reections at the multiple crystal planes in the lattice.
Because the relative phases of the generated elemen-
-
tary spherical waves, superimposed in the various
reections, are not accessible by experiment, they
must be regenerated by sophisticated phasing methods. Only then can aFourier transform be calculated
from the measured reections that represents the spa
tial distribution of the electron density in the crystal.
Amodel of the crystallized molecules is assigned to
this electron density.
The diffraction power and resolution of the crystals
-
determine the accuracy of the resolved structure. For
proteins, aresolution of 1.5–3 Å is usually achieved.
At the lower end, molecular building blocks such as
phenyl rings are well resolved, and individual water
molecules are visible. At the upper limit, only the
overall topology is determined, and the water molecules usually cannot be assigned.
-
Bibliography and Further Reading
The crystal structure is an average structure over
-
space and time. Enhanced B-factors give an estimate
of the residual mobility of molecular portions in
amolecule.
Electron microscopy is an alternative method for
-
determining the structure of very large, often mem-
brane-bound proteins. One either performs diffrac-
tion experiments (micro-ED method) or collects
thousands of shadow projections of individual
molecules in the electron beam in microscope mode
(cryo-EM method). In the case of diffraction, reec-
tion data are collected from many thousands of tiny
and wafer-thin crystals. Alternatively, the intensity
of the beam can be reduced to collect larger diffrac-
tion datasets from the crystals. Micro-ED can also
be applied to tiny crystals of low molecular weight
compounds. Cryo-EM requires the inclusion of com-
pound samples in frozen water droplets to collect
many thousands of shadow projections of individual
molecules. The projection images are then assembled
into an averaged 3D structure in the computer.
If only small substance samples are available or if
-
crystallization fails, dissolved organic substances can
be diffused into crystalline sponges. There they place
themselves in cavities of the lattice. Structure deter-
mination succeeds by collecting diffraction data on
the crystalline sponges with their absorbed “guest
molecules.”
NMR spectroscopy records the resonance of magnetic
-
nuclei such as 1H, 13C, or 15N oriented in astrong
magnetic eld. The transition between parallel and
antiparallel orientation of the nuclear spins can be
induced by additional elds. Because the frequency
at which these transitions take place depends on the
chemical environment in amolecule, the spectral pa-
rameters contain information about the 3D structure
of the molecules in solution.
The large number of recorded spectral parameters,
-
in particular information about the spatial neighbor-
hood of atoms determined by the nuclear Overhauser
effect (NOEs), can be translated into distance maps
between individual magnetic nuclei. From this, the
spatial structure of the protein can be folded in the
computer. Adistance geometry approach is used in
combination with molecular dynamics simulations.
It could be shown for many cases that the NMR struc-
-
ture of aprotein in solution and the X-ray structure
in acrystal largely coincide with each other. Differ-
ences are observed for the surface-exposed residues.
Protein crystals contain up to 70% water and exhibit
-
large water channels that pass through the crystal.
Where appropriate, small-molecule ligands can diffuse
through these water-containing channels to reach bind-
ing sites on the surface or in accessible binding pockets
of the proteins. The binding modes of small-molecule
ligands can be easily determined by using these soaking techniques.
The signicance of the architecture of proteins de-
-
termined in acrystalline environment for biologically
relevant conditions has been demonstrated. Examples are known of enzyme reactions that are usually
carried out on the dissolved protein, but which also
occur in aprotein when it is in crystalline state.
Structural data of proteins can also be collected with
-
neutron radiation. In such determined structures,
hydrogen atoms are revealed as strong scatterers.
Protonation states of functional groups and the arrangement and dynamics of water molecules can be
determined.
Very strong synchrotron radiation from the X-ray la-
-
ser can be used to resolve fast dynamic processes in
protein crystals by serial crystallography.
Bibliography and Further Reading
General Literature
J. P. Glusker, K. N. Trueblood, Crystal Structure Analysis, A Primer,
2nd edn., Oxford Univ. Press, New York (1985)
J. P. Glusker, M. Lewis, M. Rossi, Crystal Structure Analysis for Chem-
ists and Biologists, VCH, Weinheim (1994)
T. L. Blundell, L. N. Johnson, Protein Crystallography, Academic Press,
London (1976)
J. D. Dunitz, X-Ray Analysis and the Structure of Organic Molecules,
Cornell Univ. Press, Ithaca (1979)
J. Drenth, Principles of Protein X-ray Crystallography, Springer Verlag,
Berlin (1994)
A. McPherson, Science in Pictures: Macromolecular Crystals, Scient.
American, 260 (3), 62–69 (1989)
H. Friebolin, Basic One- and Two-Dimensional NMR Spectroscopy,
Wiley-VCH, Weinheim (2010)
F. A. L. Anet, A. J. R. Bourn, P. Carter, S. Winstein Nuclear Magnetic
Resonance Spectral Assignments from Nuclear Overhauser Effects,
J. Am. Chem. Soc. 87, 5250–5251 (1965)
K. Wüthrich, NMR of Proteins and Nucleic Acids, Wiley, New York
(1986)
M. Pellecchia, I. Bertini, D. Cowburn etal., Perspectives on NMR
in Drug Discovery: A Technique Comes of Age, Nat. Rev. Drug
Discov., 7, 738–745 (2008)
A. Watts, Solid-State NMR in Drug Design and Discovery for Mem-
brane-embedded Targets, Nat. Rev. Drug Discov., 4, 555–568
(2005)
M. Carroni, H. R. Saibil, Cryo electron microscopy to determine the
structure of macromolecular complexes, Methods, 95, 78–85 (2016)
M. Beckers, D. Mann, C. Sachse, Structural interpretation of cryo-EM
image reconstructions, Prog. Biophys. Mol. Biol., 160, 26–36 (2021)
G. Lander, A 3-minute introduction to CryoEM, https://www.youtube.
com/watch?v=BJKkC0W-6Qk (Last accessed Nov. 17, 2024)
Special Literature
T. S. Koritsanszky and P. Coppens, Chemical Applications of X-ray
Charge-Density Analysis, Chem. Rev., 101, 1583–1627 (2001)
E. Keller, Röntgenstrukturanalyse von Molekülen I, II, Chemie in un-
serer Zeit, 16, 71–88 and 116–123 (1982)
D. J. DeRosier, Turn-of-the-Century Electron Microscopy, Curr. Biol.,
3, 690–692 (1993)
Chapter • Experimental Methods of Structure Determination
M. A. Wear, D. Kan, A. Rabu and M. D. Walkinshaw, Experimental
Determination of van der Waals Energies in a Biological System,
Angew. Chem. Int. Ed., 46, 6453–6456 (2007)
Y. Inokuma, S. Yoshioka, J. Ariyoshi, T. Arai, Y. Hitora, K. Takada, S.
Matsunaga, K. Rissanen, M. Fujita, X-ray analysis on the nano-
gram to microgram scale using porous complexes, Nature, 495,
461–466 (2013)
L. Rosenberger, C. v. Essen, A. Khutia, C. Kühn, K. Urbahns, K.
Georgi, R. W. Hartmann, L. Badolo, Crystalline Sponges as a Sen-
sitive and Fast Method for Metabolite Identication: Application
to Gembrozil and its PhaseI and II Metabolites, Drug Metab.
Dispos., 48, 587–593 (2020)
C. G. Jones, M. W. Martynowycz, J. Hattne, T. J. Fulton, B. M. Stoltz,
J. A. Rodriguez, H. M. Nelson, T. Gonen, The CryoEM Method
MicroED as a Powerful Tool for Small Molecule Structure Deter-
mination, ACS Cent. Sci., 4, 1587–1592 (2018)
K. M. Yip, N. Fischer, E. Paknia, A. Chari, H. Stark, Atomic-reso-
lution protein structure determination by cryo-EM, Nature, 587,
157–161 (2020)
M. S. Doscher, F. M. Richards, The Activity of an Enzyme in the Crys-
talline State: Ribonuclease S, J. Biol. Chem., 238, 2399–2405 (1963)
S. Wu, J. Dornan, G. Kontopidis, P. Taylor, M. D. Walkinshaw, The
First Direct Determination of a Ligand Binding Constant in Pro-
tein Crystals, Angew. Chem. Int. Ed. Engl., 40, 582–586 (2001)
A. R. Pearson, P. Mehrabi, Serial synchrotron crystallography for
time-resolved structural biology, Curr. Op. Struct. Biol., 65, 168–
174(2020)
E. Nango etal. The three-dimensional movie of structural changes in
bacteriorhodopsin, Science, 364, 1552–1556 (2020), https://www.
science.org/doi/10.1126/science.aah3497 Suppl. Mat.: aah3497s1.
mp4, aah3497s2.mp4, aah3497s3.mp4
13
Three-Dimensional Structure
Contents
14.1 The Amide Bond: Backbone of Proteins – 216
α
14.2 Proteins Fold in Space to Form
14.3 From Secondary Structure Via Motifs and Domains
to Tertiary and Quaternary Structure – 220
14.4 Are the Fold Structure and Biological Function
of Proteins Correlated? – 223
14.5 Proteases Recognize and Cleave Substrates
in Well-Tailored Pockets – 224
-Helices and β-Strands – 217
14.6 From Substrate to Inhibitor: Screening
of Substrate Libraries – 224
14.7 When Crystal Structures Learn to Move: From Static Structures
to Dynamics and Reactivity – 226
14.8 Solutions to the Same Problem: Serine Proteases with
Diering Folds Have Identical Function – 227
14.9 DNA as aTarget Structure of Drugs – 228
14.10 Synopsis – 230
Bibliography and further reading – 231
© The Author(s), under exclusive license to Springer-Verlag GmbH, DE, part of Springer Nature 2024
G. Klebe, Drug Design, https://doi.org/10.1007/978-3-662-68998-1_14
Chapter • Three-Dimensional Structure of Biomolecules
Drug design focuses on the ligand, which is typically
asmall organic molecule with amolecular weight of less
than 500 Da. It interacts with amacromolecular receptor and inuences the properties of this receptor. On the
other hand, the surrounding receptor can also determine
the properties of the bound active ligand. Selective manipulation of these interactions requires an understanding
of both the ligand and the receptor. After reviewing the
methods used to determine the structure of biomolecules
in the previous chapter, we will now look at what can be
learned about the structural principles and properties of
these macromolecules. Proteins consist of 20basic building blocks, the proteinogenic amino acids (see pageIX).
Adipeptide is formed by linking two amino acids through
an amide bond. Larger peptides and proteins are formed
by the addition of many more amide bonds.
The simplest molecule with an amide bond is formamide 14.1. Its structure is shown in . Fig.14.1. This
bond occurs many hundreds of times in proteins, for
example, over 50,000 times in the envelope of the rhinovirus (Sect.31.6). The length of the bond between
the carbon, oxygen, and nitrogen atoms can be determined from the crystal structure of formamide. The microwave spectrum of formamide in the gas phase also
provides bond lengths, but different values are obtained.
In the gas phase, formamide is “isolated,” i.e., it does
not “sense” any neighbors in its immediate vicinity. The
C═O double bond is shorter and the C–N single bonds
are longer than in crystalline formamide. In the crystal
assembly, the individual formamide molecules are not
“alone.” They are connected to neighboring molecules
by intermolecular hydrogen bonds. Ahydrogen bond is
anoncovalent interaction. It couples afunctional group
carrying ahydrogen atom (e.g., NH or OH) to an electronegative heteroatom (e.g., N, O; Sect.4.4). Obviously,
the involvement of amolecule in anetwork of hydrogen bonds causes achange in its geometry. The electron
density between the atoms is shifted so that the C═O
double bonds become longer and consequently weaker.
At the same time, the C–N single bonds become shorter
and stronger. Twisting the molecule away from planarity
around this bond is, therefore, made much more difcult.
The amide bond is the fundamental building block
of proteins. Every third bond in the polymer chain is an
amide bond. They have planar geometry, meaning that
aplane can be dened by their atoms, as we saw with
formamide. The folding of the polymer chain and the
resulting spatial structure of the protein is determined by
the twist angle at the plane of the amide bonds against
each other (. Fig.14.2). The stiffness and planarity of
the amide bonds determine the stability of the spatially
folded protein. If one formulates aLewis formula for
such an amide bond embedded in ahydrogen bond network, the polar nature with the double-bond character
of this bond becomes clear (. Fig.14.1). In proteins,
amide bonds practically only occur in the trans con-
guration (except for amide bonds adjacent to proline
14
. Fig. 14.1 Formamide 14.1 is the smallest molecule that has an
amide group. Its molecular structure is shown on the left. Because of
thermal motion in the solid state, the molecule carries out vibrational
movements. Its electron density is, therefore, distributed over alarger area. This is described by using ellipsoids that encompass the 50%
probability of occurrence of the atom (left). Two hydrogen bonds are
incurred between the carbonyl group and the amide group of aneigh-
boring molecule in the crystal packing. An extended H-bond network
stabilizes the crystal structure and polarizes the amide group. The
bond lengths (inÅ) are different in the crystal structure and in the gas
phase (Table). If we consider an amide bond in aprotein, it will also
be involved in hydrogen-bond contacts (right). It can be expressed as
aLewis formula, which indicates the polar nature and double bond
character of the amide bond
. • Proteins Fold in Space to Form α-Helices and β-Strands
. Fig. 14.2 Left The spatial course of apolypeptide chain is deter-
mined by the relative orientation of the planar peptide bonds. The
mutual twist of these planes against each other is measured on the
basis of the two twisting or dihedral anglesΦ and Ψ. These do not
assume any value around the bond axes, but rather are limited to afew
residues, which show both congurations). The only remaining degrees of freedom for the polymer chain are the
rotations about the entire amide bond planes. These rotations (Chap.16) occur around the bonds that lie between
the Cα carbon atoms. As shown in the comparison of
the bond length between gaseous and crystalline formamide, the decisive additional stiffening of the amide bond
is caused by its incorporation into ahydrogen-bonding
network.
α
β
Typically, the angles namedΦ andΨ are used to describe
the two dihedral angles around the Cα carbon atom, and
these angles usually take on value pairs from two ranges.
These ranges are related to ahelical or sheet-like course
of the polymer chain (. Fig.14.2). In an α-helix with
aright-handed turn, all CO and NH groups orient in the
same direction (. Fig.14.3). Between them, a H-bond
network is formed. Each amino acid in the helix is in
contact with the next fourth amino acid in the sequence.
combinations of value ranges. Right In the diagram, aso-called Ramachandran plot, the values for both angles along the peptide chain
are plotted. The angle combinations for an α-helix (. Fig.14.3) are
found in the middle left, and those for aβ-pleated sheet (. Fig.14.4)
in the top left
This unidirectional orientation of the polar groups of the
amide bonds in an α-helix has consequences for the electrostatic properties, and asignicant dipole moment can
build up along the helix (Sect.15.5). At the tip of such
helices, preferred binding sites for positively or negatively
charged particles are formed (cf. the architecture of ion
channels, Sects.30.2 and30.8). While ahelix is composed
of amino acids from asingle contiguous segment of the
peptide chain, amino acids from at least two sequence
segments must come together to form aβ-pleated sheet.
Both strands can be bonded with each other in either
aparallel or antiparallel orientation relative to the polymer chain (. Fig.14.4). This network exhibits adifferent
progression of H-bonds for both orientations. The side
chains alternate above and below the pleated sheet. The
entire strand is slightly twisted upon itself. Because of
this, apleated sheet of multiple strands has atwist to it
when viewed from the side (. Fig.14.5).
In addition to these two common secondary structures, there are other typical combinations of torsion angles. Apolymer chain that folds into aglobular structure
in space must reverse its direction. This is accomplished
in what is called the turn or loop region. Turns can be clas-
ab
Chapter • Three-Dimensional Structure of Biomolecules
. Fig. 14.3 The α-helix is acommon-
ly found secondary structure. Left The
polypeptide chain forms aright-handed spiral with apitch of 7 Å, and
3.6amino acids per turn. All carbonyl
groups (oxygen atoms red) are oriented
parallel to the helix axis in the same direction. The NH functionalities (nitrogen atoms blue, hydrogen atoms cyan)
are oriented in the opposite direction.
Right The groups form apronounced
hydrogen-bonding network (violet
dashed line) between themselves. The
side chains(R) on the Cα atoms are
on the outside pointing away from the
helix axis. This creates atypical groove
pattern that spirals across the surface.
This “ridge and groove” pattern determines the mutual packing of α-helices
in proteins
14
sied according to the number of amino acids involved
and the type of interaction that closes the loop. Turns
that form aC═O⋯H–N hydrogen bond in the direction
of the polymer chain, inverse turns with hydrogen bonds
in the opposite direction, and open turns in the chain held
together by van der Waals and polar interactions can be
distinguished from one another (. Fig.14.6). Atotal of
158 turn classes have been summarized in acomprehensive evaluation by Oliver Koch.
What force governs the organization of aprotein?
Amino acids have hydrophilic and hydrophobic side
chains. Hydrophobic groups avoid aqueous environ-
ments (Sect.4.2). During folding of the polymer chain
in an aqueous medium, the hydrophobic amino acids
aggregate to diminish their shared hydrophobic surface
area. Therefore, the hydrophobic amino acids are predominantly found in the interior of a folded protein.
The polar groups of the main chain amide bonds are
saturated in the secondary structure by hydrogen bonds.
The side chains of polar amino acids will only be found
inside aprotein if they can form apolar interaction with
another surrounding amino acid. Otherwise, they are
oriented towards the outside of the protein, protruding
into the surrounding water environment. Proteins can
also span acell membrane. In the areas where they are in
contact with the membrane, they have alarge, contiguous
hydrophobic surface (Sect.14.7). The packing density
inside the protein is of the same order of magnitude as
that found in crystals of small organic molecules. The
interactions that determine the molecular packing are
virtually identical in both cases.
. • Proteins Fold in Space to Form α-Helices and β-Strands
. Fig. 14.4 A second important secondary structure, the β-strand
is composed of multiple sections of the polymer chain that exist in
astretched conformation (top). The strands can run parallel or antiparallel. They are crosslinked to each other via hydrogen bonds
. Fig. 14.5 Within aβ-pleated sheet of multiple strands, here shown
with aparallel orientation, aright-handed twist occurs. For simplication, the single β-strands are indicated with an arrow. The twist can
(violet). The sheet-like structure displays azigzag fold and is called
aβ-pleated sheet. The side chains(R) of the amino acids point away
from it, alternating above and below the pleated sheet
be seen by the internal rotation of the arrow. The pleated sheet here is
shown in two perpendicular views