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CONTENTS
2.5.2 Water Shell Analysis Software . . . . . . . . . . . . . . . . . . . . . . .
38
3 Preparation of the Initial Conformations
41
3.1 Random Conformations from Vacuum . . . . . . . . . . . . . . . . . . . . . .
41
3.1.1 Data Analysis
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
42
3.1.1.1
Initial Modeled
-Helix Conformation . . . . . . . . . . . . .
42
3.1.1.2
Comparison of Independent Starting Conformations . . . . . .
44
3.1.1.3
Independent Concatenated Data . . . . . . . . . . . . . . . . .
47
3.2 Extended Trajectories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
50
3.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
56
4 Water Percolation
59
4.1 Hydration Water Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . .
59
4.2 Hydration Water Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
61
4.2.1 Temperature-Induced Percolation Transition of Hydration Water . . . . .
61
4.2.2 Effect of the Spanning Water Network on Peptide Properties . . . . . . .
66
4.2.3 Effect of Peptide Structure on the Spanning Network of Hydration Water
70
4.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
71
5 Comparing hIAPP and rIAPP in Liquid Water
73
5.1 Conformational Changes of Oxidized hIAPP at 330 K . . . . . . . . . . . . . .
73
5.1.1 Conformational Properties of IAPP--R
g
, r
eted
, and SASA . . . . . . . .
74
5.2 Compact hIAPP Conformation at 330 K . . . . . . . . . . . . . . . . . . . . . .
80
5.2.1 Aromatic-Aromatic Interactions . . . . . . . . . . . . . . . . . . . . . .
80
5.2.2 Secondary Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . .
86
5.2.2.1
Ramachandran Angles . . . . . . . . . . . . . . . . . . . . . .
86
5.2.2.2
DSSPcont . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
91
5.2.3 Snapshots of IAPP . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
96
5.2.4 H-bond Patterns and Secondary Structure of Oxidized hIAPP at 330 K . .
97
5.2.5 System Perturbation . . . . . . . . . . . . . . . . . . . . . . . . . . . .
101
5.2.5.1
Thermal Induced "Unfolding" . . . . . . . . . . . . . . . . . .
101
5.2.5.2
In silico Point Mutations on Oxidized hIAPP at 330 K . . . . .
102
5.3 Discussion and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . .
102
5.3.1 Compact, but not Entirely Disordered, Polypeptide . . . . . . . . . . . .
102
5.3.2 Effect of P28 on the C-Terminal Region . . . . . . . . . . . . . . . . . .
104
5.3.3 Effect of Aromatic Residues . . . . . . . . . . . . . . . . . . . . . . . .
105
5.3.4 Temperature Effect on Oxidized hIAPP . . . . . . . . . . . . . . . . . .
105
5.3.5 Effect of the Disulfide Bond . . . . . . . . . . . . . . . . . . . . . . . .
106
6 Outlook
107
A Proceedings
109
B Poster Presentations
117
Bibliography
123
ii
List of Figures
2.1 Initial Conformations for MD Production Runs . . . . . . . . . . . . . . . . . .
18
2.2 Bland-Altman Plots at 350 K -- Comparing Charges . . . . . . . . . . . . . . .
21
2.3 Bland-Altman Plots at 350 K -- Comparing Runs
. . . . . . . . . . . . . . . .
23
2.4 Ramachandran Plots at 350 K -- Helix Cutoffs . . . . . . . . . . . . . . . . . .
25
2.5 Ramachandran Plots at 350 K --
-strands Cutoffs . . . . . . . . . . . . . . . .
26
2.6 Ramachandran Plots at 350 K -- poly(Pro) Cutoffs . . . . . . . . . . . . . . . .
27
2.7 Ramachandran Plots at 350 K -- Charge Scaling . . . . . . . . . . . . . . . . .
28
2.8 Radial Distribution of r
eted
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
33
2.9 Water Density Temperature Dependence . . . . . . . . . . . . . . . . . . . . .
34
2.10 Comparing L
max
vs. Box Size for Independent Runs at 350 K . . . . . . . . . .
37
3.1 Time Dependence of R
g
and r
eted
at 350 K . . . . . . . . . . . . . . . . . . . .
42
3.2 Comparing R
g
and r
eted
for Independent Runs at 350 K . . . . . . . . . . . . . .
45
3.3 Curve Fitting R
g
and r
eted
Distributions at 350 K . . . . . . . . . . . . . . . . .
49
3.4 Temperature Dependence of R
g
and r
eted
for All Concatenated Trajectories . . .
52
3.5 R
g
and r
eted
Uncertainty for Concatenated Trajectories . . . . . . . . . . . . . .
53
3.6 Temperature Dependence of R
g
and r
eted
for Selected Concatenated Trajectories
55
3.7 Time Dependence of R
g
and r
eted
and Data Distribution from 290 K to 350 K . .
57
4.1 Probability Distribution of S
max
/N
w
and H
max
. . . . . . . . . . . . . . . . . . .
62
4.2 Temperature Dependence of
(S
max
/N
w
)
av
, SP, and
H
max
. . . . . . . . . . . .
63
4.3 Temperature Dependence of
(S
max
/N
w
) and S
mean
. . . . . . . . . . . . . . . .
64
4.4 Dependence of
(H
max
)
av
on
(S
max
/N
w
)
av
. . . . . . . . . . . . . . . . . . . . .
65
4.5 Temperature Dependence of d
f
. . . . . . . . . . . . . . . . . . . . . . . . . .
66
4.6 Oxygen-Oxygen Pair Correlation Function g
OO
. . . . . . . . . . . . . . . . . .
67
4.7 Temperature Dependence of R
g
and SASA compared to SP . . . . . . . . . . .
68
4.8 Temperature Dependence of
(n
pp
H
) and (S
max
/N
w
)
av
. . . . . . . . . . . . . . .
68
4.9 Temperature Dependence of Helical Content and n
pp
H
; Helical Cooperativity at
310 K and 330 K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
69
4.10 Dependence of SP and
(S
max
/N
w
)
av
on n
pp
H
. . . . . . . . . . . . . . . . . . . .
70
5.1 Time Dependence and Mean Values of R
g
at 310 K and 330 K . . . . . . . . . .
75
5.2 Time Dependence and Mean Values of r
eted
at 310 K and 330 K . . . . . . . . .
76
5.3 Time Dependence and Value Distribution of SASA at 310 K . . . . . . . . . . .
78
5.4 Time Dependence and Value Distribution of SASA at 330 K . . . . . . . . . . .
79
5.5 R
g
and SASA Correlation at 310 K . . . . . . . . . . . . . . . . . . . . . . . .
81
iii
LIST OF FIGURES
5.6 R
g
and SASA Correlation at 330 K . . . . . . . . . . . . . . . . . . . . . . . .
82
5.7 R
g
and n
HB
Correlation at 310 K . . . . . . . . . . . . . . . . . . . . . . . . . .
83
5.8 R
g
and n
HB
Correlation at 330 K . . . . . . . . . . . . . . . . . . . . . . . . . .
84
5.9 Time Dependence of Y37/F15 and Y37/F23|L23 Distances and Secondary Struc-
ture at 310 K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
87
5.10 Time Dependence of Y37/F15 and Y37/F23|L23 Distances and Secondary Struc-
ture at 330 K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
88
5.11 Ramachandran plots at 310 K . . . . . . . . . . . . . . . . . . . . . . . . . . .
89
5.12 Ramachandran plots at 330 K . . . . . . . . . . . . . . . . . . . . . . . . . . .
90
5.13 Time dependence of secondary structure assigned by DSSPcont at 310 K . . . .
92
5.14 Time dependence of secondary structure assigned by DSSPcont at 330 K . . . .
93
5.15 Mean Helical Content at 310 K and 330 K as assigned by DSSPcont . . . . . . .
94
5.16 Snapshots of Oxidized hIAPP and rIAPP at 330 K . . . . . . . . . . . . . . . .
97
5.17 Helical Content between Residues 822 . . . . . . . . . . . . . . . . . . . . . .
98
5.18 Backbone-Backbone H-bond Matrices at 310 K . . . . . . . . . . . . . . . . . .
99
5.19 Backbone-Backbone H-bond Matrices at 330 K . . . . . . . . . . . . . . . . . .
100
5.20 Time Dependence of R
g
and r
eted
and Data Distribution for the Perturbed Systems 103
5.21 Mean Helical Content for the Perturbed Systems as assigned by DSSPcont . . .
104
B.1 Poster -- CBSB08, Jülich (2008) . . . . . . . . . . . . . . . . . . . . . . . . .
119
B.2 Poster -- Biophysical Society Meeting, Boston (2009) and "Amyloid 2009," Halle
(2009) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
121
iv
List of Tables
1.1 IAPP Primary Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
1.2 Relative Frequencies of Amino Acid Replacements
. . . . . . . . . . . . . . .
6
2.1 Secondary Structure Assignment . . . . . . . . . . . . . . . . . . . . . . . . .
29
2.2 Hydrogen Bonds in Biological Systems . . . . . . . . . . . . . . . . . . . . . .
30
2.3 Random-flight Chain Statistical Properties (n
= 36, l = 0.38nm) . . . . . . . . .
32
2.4 Error Estimate Calculated by g_analyze . . . . . . . . . . . . . . . . . . . .
36
3.1 Radius of Gyration at 1 bar and 350 K . . . . . . . . . . . . . . . . . . . . . . .
46
3.2 End-to-End Distance between C
at 1 bar and 350 K . . . . . . . . . . . . . . .
46
3.3 Standard Deviation vs. Error Estimate
. . . . . . . . . . . . . . . . . . . . . .
47
3.4 Nonlinear Curve Least-Squares Fit . . . . . . . . . . . . . . . . . . . . . . . .
49
3.5 End-to-End Distance from Fitting . . . . . . . . . . . . . . . . . . . . . . . . .
50
5.1 Conformational Properties r
eted
and R
g
at 1 bar and 310 K . . . . . . . . . . . .
77
5.2 Conformational Properties r
eted
and R
g
at 1 bar and 330 K . . . . . . . . . . . .
77
5.3 Helical Content assigned by
and angles at 1bar and at 310K and 330K . .
86
5.4 Helical Content assigned by DSSPcont at 1 bar and at 310 K and 330 K . . . . .
91
v
Summary
Conformational properties of the full-length human and rat islet amyloid polypeptide
137 (amyloidogenic hIAPP and non-amyloidogenic rIAPP, respectively) were stud-
ied at physiological temperatures by MD simulations both for the cysteine (reduced
IAPP) and cystine (oxidized IAPP) moieties. After performing a temperature scan from
250 K to 450 K at a 20 K interval, it was found that the two temperatures, 310 K and 330 K,
delimit the temperature at which the water percolation transition occurs and were thus
chosen for observing the conformational properties of IAPP where the biological activity
is highest. In fact, most living organisms have the highest biological activity in a tempera-
ture interval that corresponds to a percolation transition, which was calculated for hIAPP
at
320K and seems to be independent of the chemical composition of the IAPP variant.
At all temperatures studied, IAPP does not adopt a well-defined conformation and is
essentially random-coil in solution, although transient helices appear forming along the
peptide between residues 8 and 22, particularly in the reduced form. Above the water
percolation transition, the reduced hIAPP moiety presents a considerably diminished
helical content remaining unstructured, while the natural cystine moiety reaches a rather
compact state, presenting a radius of gyration that is almost 10 % smaller than what was
measured for the other variants, and is characterized by intrapeptide H-bonds that form
many
-bridges in the C-terminal region. This compact conformation presents a short
end-to-end distance and seems to form through the formation of
-sheet conformations
in the C-terminal region with a minimization of the Y/F distances in a two-step mecha-
nism: the first step taking place when the Y37/F23 distance is
1.1nm, with Y37/F15
subsequently reaching its minimum of
0.86nm. rIAPP, which does not aggregate, also
presents transient helical conformations. A particularly stable helix is located in proxim-
ity of the C-terminal region, starting from residues L27 and P28. These MD simulations
show that P28 in rIAPP influences the secondary structure of IAPP by stabilizing the pep-
tide in helical conformations. When this helix is not present, the peptide presents bends
or H-bonded turns at P28 that seem to inhibit the formation of the
-bridges seen in
hIAPP. Conversely, hIAPP is highly disordered in the C-terminal region, presenting tran-
sient isolated
-strand conformations, particularly at higher temperatures and when the
natural disulfide bond is present. Such conformational differences found in these simula-
tions could be responsible for the different aggregational propensities of the two different
homologues. In fact, the fragment 3037, identical in both homologues, is known to ag-
gregate in vitro, hence the overall sequence must be responsible for the amyloidogenicity
of hIAPP. The increased helicity in rIAPP induced by the serine-to-proline variation at
vii
Summary
residue 28 seems to be a plausible inhibitor of its aggregation. The specific position of
P28 could be more relevant for inhibiting the aggregation than the intrinsic properties of
proline alone; in fact, IAPP in cats, which have been observed to develop diabetes mel-
litus type II and present islet amyloid deposits, contains a proline residue at position 29.
Another characteristic of the above-mentioned compact state of monomeric oxidized
hIAPP is that a particularly reactive conformation found along the "folding" pathway is
stabilized by the presence of the disulfide bond. Such conformation presents a short end-
to-end distance, allowing the peptide to expose the amyloidogenic sequence N
22
FGAIL
27
to neighboring peptides. In the reduced hIAPP moiety, this state does not seem to form
for any significant amount of time, proven by the fluctuating end-to-end distance. The
mean end-to-end distance is smaller than the calculated value for a random-flight chain,
proving both the flexibility of hIAPP and the presence of interactions that bring the pep-
tide to compact conformations. Conversely, owing to the intrinsic rigidity of proline,
either rIAPP moiety seems to be too rigid to be able to fold to the short end-to-end
distance conformations observed for the oxidized hIAPP moiety, although there are in-
stances in which oxidized rIAPP reaches short end-to-end distances, corresponding to the
absence of helices in the P28 region. These conformations possibly occur thanks to the
disulfide bond/C-terminus interactions, as seen for hIAPP. Short Y37/L23 distances are
also observed in the same time frame of short end-to-end distances as seen with Y37/F23
distances in hIAPP, but since leucine is not aromatic, it is possible that the first step in
the "folding" process observed in hIAPP cannot occur in the wild-type rIAPP.
In silico mutations have been applied to the "folded" state obtained in the oxidized
hIAPP simulations at 330 K, in order to observe what kind of effect proline has on the
conformation. In particular, the S28P substitution induces the formation of a helix in
this region and disrupts the compact structure by separating the ends of this particularly
stable conformation; in fact, the wild-type oxidized homologue remains compact upon
heating up to 390 K.
Thus, in light of the results presented in this study, the collapsed state of the mono-
meric form was observed after the following three conditions had been met:
1. Presence of the disulfide bond: It was observed that the oxidized polypeptide was
more flexible than the reduced counterpart and the short end-to-end distance in IAPP
was stablized by its presence.
2. Absence of helical content in the C-terminus region: This allowed this region of the
polypeptide to be more flexibile and "fold." P28 seemed to stabilize the highly mobile
and unstructured portion of IAPP. Moreover, such helicity seemed to inhibit short
end-to-end distances.
3. Presence of aromatic residues: Interactions between aromatic residues, in particular
F23, seemingly stabilized one of the first steps in "folding."
Since these results have been obtained for the monomeric form, further studies are
necessary to determine whether these three structural characteristics are also relevant for
the aggregation propensity of IAPP.
viii
Chapter
1
Introduction
The word protein was coined by the Swedish scientist Jöns Berzelius in 1838 to describe
a certain class of molecules and their importance.
1,2
In fact, it derives from the Greek
word
proteØoc `of primary importance' which in turn derives from the word protoc
`first.'
3,4
After almost 150 years, one can read the opening sentence of the first chapter
of the book on the structure and molecular properties of proteins by Creighton
5
Virtually every property that characterizes a living organism is affected by
proteins.
Proteins: Structure and Molecular Properties, Creighton (1993)
and only wonder how much there still is to discover, in order to fully understand how
these organic molecules, constituting living organisms, function.
What is fascinating about proteins is the multitude of roles they have within living
organisms, from enzymatic catalysis to transport and storage, and from functions as
complex as biogenesis to being simply structural, just to mention a few primary func-
tions carried out by proteins. In other words, each cell carries out its activities through
the expression of its genes by means of its working molecules, i.e., the proteins. How
many proteins are encoded by a simple unicellular eukaryote like saccharomyces cere-
visiae? The predicted number expressed by this yeast genome is 6200 (as can be found
on Table 7.3 in Molecular Cell Biology by Lodish et al. (2000)).
*
But what is even more
astonishing is the fact that thousands of primary structures are linear chains consisting
of a combination of only twenty amino acids. A protein can thus be considered a word,
determined by a sequence of letters of the alphabet that has a meaning.
6
Once the sequence of amino acids has been found, the adventure begins! The reason
is that many times the function of the protein is still unknown. In fact, the primary struc-
ture of the object of this study, i.e., islet amyloid polypeptide (IAPP), is known, albeit its
biological function remains unclear. Moreover, the functionality of proteins and peptides
depends on the native conformation, which for IAPP is also still unknown.
IAPP seems to be involved in the regulation of the glucose metabolism, since it is co-
secreted with insulin from pancreatic
-cells. Its physiological role is unclear. Although
pancreatic amyloid deposits in the islets of Langerhans have been found in more than
*
The number of proteins encoded by the human genome is still under debate, ranging from 42 000 genes
to 65 00075 000 genes, as can be found on the Human Project Genome Information page
http://www.
ornl.gov/sci/techresources/Human_Genome/faq/genenumber.shtml
.
1
INTRODUCTION
1.1
95 % of the type II diabetes patients, the causal relationship between amyloid formation
and the disease is still largely unknown.
710
The conditions at which it aggregates are
also still unclear; in fact, the human IAPP (hIAPP) sequence in healthy individuals is
identical to that found in individuals who suffer from non-insulin-dependent diabetes.
On the other hand, other variants, presenting a sequence identity of at least 80 % such
as rodent IAPP (rIAPP), do not aggregate. Moreover, healthy hIAPP-transgenic mice,
which release hIAPP and insulin in a regulated manner, do not present any islet amyloid
deposits either. Hence, the primary structure of hIAPP alone is not sufficient to cause
amyloid formation. In fact, islet amyloid deposits were found only in mice that presented
dysfunctional
-cells. One of the characteristics of the deposits formed by amyloido-
genic precursor proteins, such as IAPP, is the proximity of the insoluble deposits to where
the protein is produced.
11
Owing to the complexity of living organisms and all the open questions surrounding
them, it would be impossible to determine the biological function of IAPP only through
MD simulations. In vitro experiments on hIAPP are particularly demanding, as it forms
insoluble aggregates within minutes, compared to other amyloidogenic peptides that take
1 to 3 days, like A
, responsible for the amyloid deposits in Alzheimer's Disease. The
difficulty lies in the identification of the intermediate states that occur when the peptide
undergoes a conformational transition from random coil to an aggregation-prone confor-
mation with increased hydrophobicity.
12
Therefore, in silico investigation of monomeric
IAPP conformations in liquid water at physiologically relevant temperatures is possible
and should, nevertheless, shed light on the initial steps of aggregation. In order to find
the proverbial needle in the haystack, a few points were considered to focus on putative
conformational properties that could be responsible for aggregation, i.e., proline. In fact,
Westermark et al. have shown that the S28-for-P28 substitution greatly inhibits aggrega-
tion.
13
Thus, an atomistic investigation by MD simulations could elucidate how different
rodent IAPP is from human IAPP and what characteristics could inhibit aggregation,
focusing in particular on, but not limited to, proline. In fact, Green et al. have shown
that certain mutations in rIAPP, where residues from the hIAPP sequence are substituted
into the rodent sequence, e.g., L23F, form fibrils in vitro.
14
Thus, a parallel comparison
between wild-type rIAPP and the in silico rIAPP(L23F) mutant could also give some
insight on conformational properties, which can be measured experimentally through
Fluorescence Resonance Energy Transfer (FRET).
The answer to the aggregation mystery seems to revolve around the nature of proline,
not present in hIAPP, and more precisely around the twenty-eighth residue in the IAPP
sequence. In fact, the position of P28 in the primary structure might be the residue that
inhibits the aggregation, since cats, which can also develop diabetes mellitus type II
accompanied by islet amyloid deposits,
12
present a proline residue in position 29 of the
IAPP sequence.
1.1 Islet Amyloid Polypeptide
1.1.1 Diabetes Mellitus Type II
Many degenerative diseases, such as Alzheimer's, Parkinson's, Creutzfeldt-Jakob, dia-
betes mellitus type II, and several other systematic amyloidoses are related to polypeptide
2
1.1
ISLET AMYLOID POLYPEPTIDE
aggregation. Human amyloid polypeptide (hIAPP) forms pancreatic amyloid deposits
found in the islets of Langerhans in more than 95 % of the type II diabetes patients. The
causal relationship between amyloid formation and the disease, however, is still largely
unknown.
710
These deposits were discovered by Opie at the turn of the twentieth cen-
tury, when he observed hyalinosis in postmortem samples of pancreas of individuals
suffering from diabetes.
11
Diabetes mellitus type II (DM2, hereafter), or non-insulin-
dependent diabetes, is characterized by an increasing peripheral insulin resistance and
secretory dysfunction of
-cells.
7*
The
-cell dysfunction is not clear, but -cell mass
loss does occur. The progressive loss of function of the
-cells can be demonstrated
before the clinical pathology of hyperglycemia develops.
11
Diabetes mellitus type II has been found to develop spontaneously in cats and mon-
keys (non-human primates), not only in man. It is quite difficult to establish the relation-
ship between islet amyloid deposition and the three following characteristics of diabetes
mellitus type II: increased insulin resistance, onset of hyperglycemia, and
-cell dysfunc-
tion. Only through pancreatic biopsies would it be possible to monitor the amyloid forma-
tion in relation with the above-mentioned characteristics. Through autopsies, extensive
islet amyloid deposits have been found in patients who had severe islet dysfunction, i.e.,
patients who needed insulin replacement therapy, rather than diet or oral hypoglycemic
agents. Hence, the
-cells are insufficient and thus unable to supply an adequate amount
of insulin, although the sole cause does not seem to be islet amyloid. In fact, patients with
long duration of diabetes mellitus type II have been found to have from prevalence
<1%
up to 90 %, with up to 80 % islet mass occupied by amyloid.
The length of the disease is,
therefore, unrelated to the severity of it.
12
Moreover, healthy elderly subjects have been
found with islet deposits, as is the case for patients with benign insulinoma.
15
Sponta-
neously developing diabetes mellitus type II has been observed in cats and monkeys, and
through longitudinal and cross-sectional studies, it was shown that these models of dia-
betes present a physiologic syndrome similar to that seen in man, i.e., older age of onset,
obesity, impaired glucose tolerance progressing to hyperglycemia, and dependence upon
insulin therapy. While the development of the disease is associated with progressive islet
amyloid deposit, the same does not hold true for man; in fact, the degree of amyloidosis
after many years of DM2 is variable. Owing to the lengthy development of the disease,
occurring over years, further investigation through laboratory observations was needed.
Islet amyloid did not occur in transgenic mice and rats that express the human IAPP gene
alone; in fact, other conditions, including increased transgene expression and obesity,
brought about by high-fat feeding and genetically determined obesity, were necessary to
observe islet amyloid formation. Many features of DM2 in animals have been demon-
strated to be similar in man, but some are very different. Thus, the islet amyloidosis does
*
The IAPP release by
-cells in diabetes mellitus type I is basically none, as a result of -cell destruc-
tion by an autoimmune condition.
11
Amyloid deposits are insoluble proteinaceous accumulations formed by a precursor protein and are
normally proximal to the location of production and secretion of the protein. Moreover, each fibril is
similar and presents a highly ordered structure, consisting of
-sheets with H-bonding along the length
of the fibril and characterized by a "cross-
" X-ray diffraction pattern, even though the size, location,
and function of the approximately twenty amyloidogenic precursor proteins are quite different from one
another. Fibrils, if examined by electron microscopy, are non-branching structures of indeterminate length
having a diameter of 510 nm.
11
Prevalence indicates the percentage of islets affected, whereas severity is the percentage of islet area
occupied.
3
INTRODUCTION
1.1
not seem to be the primary causative factor for the onset of diabetes in man, as the results
from animal models might have suggested. In fact, more than 50 % of the subjects have
less than 20 % prevalence and less than 10 % severity, whereas cross-sectional data show
that macaca mulatta present 100 % prevalence with
>80% severity.
12
1.1.2 Mutations and Homologues
Not all mutations are deleterious and lead to the death of organisms; in fact, even a per-
fectly adapted protein undergoes mutations. It is part of evolution. Some mutations of
the nucleotide sequence are silent, when the codon mutates into a synonym codon, while
others are not. The former are called silent sites and the latter are called replacement
sites, as the amino acid is replaced by a different one, expressed by the newly mutated
nucleotide sequence. Such replacements can be deleterious, neutral, or advantageous.
16
When two proteins have a correlated evolution, they are called homologues. By com-
paring the homology between two proteins, one can see which residues are essential for
the proteins' proper function. If the residue occupies the same position, it is said to be
invariant and should remain in the same position for the protein to be functional, whereas
if it changes, it could be either conservatively substituted or hypervariable. The former
occurs when two amino acids presenting similar properties occupy the same position,
i.e., glutamate and aspartate, whereas the latter is more or less indifferent to the change
of a residue in a particular position.
17
Proline and glycine are often used in mutagenic studies in virtue of their backbone
conformational properties. Biological functions in vivo depend on the stability of the
folded conformation and can be lost through a mutation that destabilizes the active con-
formation. In other words, negative observations become significant. An inactive mutant
can thus be isolated for further mutagenic studies until the function returns. This process
allows the identification of the role of the original residue in the folded and functional
protein. This mutation can be random or site-specific. An example could be the substi-
tution of a proline, which presumably terminates a helix, with another residue that can
extend the helix. Not only can proline and glycine alter the conformational entropy of
the unfolded state, but so can a disulfide bond; the introduction or replacement of one of
these elements can perturb the stability of the folded state of the protein. In fact, glycine,
proline, and cystine are conserved residues. Large hydrophobic residues are also seldom
replaced, whereas acidic and hydrophilic residues are often replaced. Relative frequen-
cies of replacement of the residues that differ in the above-mentioned IAPP variants are
listed in Table 1.2 on page 6, whereas all twenty residues can be found in Figure 3.2 of
Ref. 5. Normally, most of the mutations do not affect the stability of the folded state
since natural selection has most probably already optimized the sequence.
5
In general, proteins can tolerate the mutation of a single residue without significantly
altering the native structure, but the functional properties are much more sensitive to
changes. A classical example of this is sickle-cell anemia, where the replacement of a
polar glutamate with a nonpolar valine leads to a completely different quaternary struc-
ture, producing devastating effects.
*
Conversely, myoglobin and hemoglobin have only
*
Actually, the hemoglobin present in the sickle-cell anemia (HbS) is a typical case of Darwinian exam-
ple, where even one single mutation has led to adaptation of organisms that compete in an environment.
In fact, Anthony Allison discovered that heterozygote HbS individuals resisted malaria.
17
4
1.1
ISLET AMYLOID POLYPEPTIDE
20 % of the same sequence, yet share large structural, evolutionary, and functional simi-
larities.
2
Thus, with this in mind, discovering which effect the 16 % divergence between
human and rodent sequences may have on the structural properties could be a rather
daunting task.
Interestingly enough, islet amyloid formation in diabetes mellitus type II cannot be
related directly to any post-translational modification of the peptide or gene mutations
that would confer increased amyloidogenicity to the peptide.
12
Although, a missense
mutation in the exon 3 of the IAPP gene, reported in 4
.1% of the Japanese patients
subject to diabetes mellitus type II, seems to lead to an earlier and more severe onset of
the disease. The S20G mutation
*
leads to an in vitro aggregation that allows twofold
amyloid at a rate threefold higher than human wild-type gene.
18
1.1.3 IAPP Properties
Islet amyloid polypeptide (IAPP) is a 37 amino acid peptide, secreted by
-cells, and
derives from the precursor proIAPP (89 amino acid peptide), through the same enzymes
that convert proinsulin to insulin,
i.e., prohormone convertase 1/3 and 2. Both the IAPP
and insulin transcription genes are regulated by glucose or differently regulated by Ca
2+
,
and the secretion of either peptide is closely regulated, i.e., the plasma level of IAPP is
115 % that of insulin.
11
The role of IAPP seems to be insulin inhibitor, as can be deduced
from experiments carried out on IAPP knockout mice. The basal level of circulating
glucose and insulin was normal, although males exhibited an increased insulin response
to glucose administration and a more rapid glucose disappearance in oral and intravenous
glucose tolerance tests. Moreover, body mass in males increased by 20 %, which could
be determined by increased insulin secretion or an effect of IAPP on food intake.
15
Human and rat/mouse sequences are compared directly in Table 1.1, with the conser-
vatively substituted residues in green and the hypervariable ones in red, whereas those
residues found in cat and monkey IAPP that differ from hIAPP are indicated in cyan,
if conservatively substituted, and magenta, if hypervariable. The two wild-type islet
polypeptide variants of human and rat/mouse are highly conserved, being 84 % of the
primary structure identical. With the exception of residue 18, the different residues are
localized between 20 and 29, which can be seen underlined in the hIAPP primary struc-
ture in Table 1.1. Thus, the remaining 16 % seem to determine the capability of the
peptide to aggregate through
-pleated sheet formation, which has been proven to be
amyloidogenic in human and in cat. The most noticeable difference between hIAPP
and rIAPP is the presence of proline in positions 25, 28, and 29 (Table 1.1, in red) in
*
The primary structure of hIAPP, along with other homologues, can be found in Table 1.1 on the next
page.
An interesting note on proinsulin, which may also relate to IAPP, can be made on propeptide size.
It can be considered the lower limit of the size of a peptide that can be synthesized on a ribosome and
translocated into the ER. Insulin is synthesized as a 110 amino acid peptide called preproinsulin. After
removing the signaling protein, it is converted to proinsulin; only during its storage is it cleaved into
three parts with the removal of the C-peptide. The two remaining chains, A and B, are connected by two
intrapeptide disulfide bonds formed before cleavage. Mature insulin, consisting of 55 amino acids, does
not reassemble efficiently without the C-peptide, while proinsulin can refold readily.
5
Hence, unfolding
and subsequent inability to refold may be a cause for IAPP aggregation; in fact, such hypothesis may also
be supported by the fact that full or partial unfolding, rather than misfolding, seems to be a key step in
amyloidogenic diseases.
19
5
INTRODUCTION
1.1
rIAPP, which most likely does not form
-sheets as a result of the presence of proline
residues, normally known as
-sheet breakers.
11
Moreover, residue 23 (also in red) in
rIAPP replaces an aromatic residue, phenylalanine, with an aliphatic group, leucine. The
other substitutions (in green) are not as drastic, but also present amyloidogenic properties.
Residues 18 are both basic, histidine in hIAPP and arginine in rIAPP, while residues 26
are both aliphatic, isoleucine in hIAPP and valine in rIAPP. Green et al. have shown that
even though rIAPP is not cytotoxic and does not form fibrils, key single substitutions
of the hIAPP into the rIAPP sequence, i.e., R18H, L23F, or V26I, could induce fibril
formation in rat IAPP, albeit with low yield.
14
Table 1.1: IAPP Primary Structures
1
10
20
30
human
KCNTATCAT QRLANFLV
H
S SNN
F
G
A
I
L
SS
TNVGSNTY-NH
2
rat/mouse KCNTATCAT QRLANFLV
R
S SNN
L
G
P
V
L
PP
TNVGSNTY-NH
2
cat
KCNTATCAT QRLANFL
IR
S SNN
L
GAILS
P
TNVGSNTY-NH
2
monkey
KCNTATCAT QRLANFLV
R
S SNNFG
T
ILSS TNVGS
D
TY-NH
2
Single point mutations in genes can change the amino acid that is expressed, and the
resulting relative values can be seen in Table 1.2, although it may not correspond to the
actual observed frequencies, where the values with significant discrepancies are written
in bold font. Some of the replacements occur often, e.g., Thr/Ala, others seldom, e.g.,
His/Arg. Replacements involving proline also do not occur much, although the ones that
are observed most, i.e., Pro/Ala and Pro/Ser, are those that are found in IAPP (proline
properties will be discussed in Section 1.1.3.2). Other residues that are observed more
than their expected value, e.g., Ile/Val, Asp/Asn, and Ser/Gly, are also present in IAPP.
Table 1.2: Relative Frequencies of Amino Acid Replacements
Observed Values
a
Expected Values
b
Histidine/Arginine
10
8
Isoleucine/Valine
66
18
Phenylalanine/Leucine
17
41
Proline/Alanine
35
36
Proline/Serine
27
24
Threonine/Alanine
59
39
Threonine/Proline
7
28
Aspartic Acid/Asparagine
53
19
Serine/Glycine
45
16
a
Observed replacements in 1572 examples of closely related proteins.
20
b
Expected replacements obtained from random single-nucleotide mutations.
The first five replacements seen in Table 1.2 occur in human, rat/mouse, monkey, and
cat, while the replacements from the sixth to the eighth occur only in monkey, and the last
one is relative to the Japanese human IAPP mutation that has been found in diabetic pa-
tients.
18
Although histidine and arginine are sometimes classified as basic amino acids,
1,2
6
1.1
ISLET AMYLOID POLYPEPTIDE
they have different characteristics, so it is not surprising that the relative frequencies with
which they replace each other are pretty low; in fact, arginine is almost entirely exposed,
i.e., only 1 % of the residues are buried by at least 95 %, while histidine is slightly less ex-
posed, i.e., 17 % of the observed proteins are buried by 95 % (Table 6.3, Ref. 5, page 231).
While lysine and arginine are positively charged in physiological conditions, histidine can
be positively or negatively charged, depending on the environment, in virtue of the imida-
zole ring and is, thus, a good metal binder and is often found in active sites of proteins.
1,2
In human and rat/mouse IAPP, histidine and arginine are the eighteenth residue in the pri-
mary structure, located in a region that presents a transient helix seemingly important for
biological function,
21
so it is possible to hypothesize that they also have similar behavior,
i.e., as basic residues. The phenylalanine/leucine replacement also does not occur much
in virtue of their different characteristics, although both are nonpolar/hydrophobic and
pack well in the interior of proteins, with residues buried in at least 45 % of the residues.
5
Before discussing the monkey mutations, a quick glance at serine/glycine shows that
there are indeed more replacements than those expected. Glycine is so different from all
other amino acids, as its side chain is simply H. Moreover, serine can also cap the ends
of
-helices thanks to the hydroxyl group in the side chain by forming H-bonds with
backbone.
5
A highly observed substitution occurs in monkey IAPP, where asparagine
is substituted by aspartic acid, and even though both residues are polar and can form
H-bonds, the latter is normally negatively charged in solution, whereas the former is neu-
tral.
1,2
The interesting residue replacement in the primary structure is the one occurring in
position twenty-five. First of all, it is the only position in the primary structure, along with
residue twenty-eight, in which proline inhibits aggregation, i.e., cat IAPP presents a pro-
line residue in position twenty-nine and is known to aggregate. Second, it has the highest
variance, as it presents an uncharged polar residue in monkey, i.e., threonine, proline in
rat/mouse, and an aliphatic residue in cat, i.e., alanine. The threonine/alanine replacement
value is very high, so one could hypothesize that the structural effect these residues have
on proteins is negligible, but since they are both present in the amyloidogenic moieties,
and not proline, the flexibility of the polypeptide may determine the amyloidogenicity.
The first fraction (residues 120) of both hIAPP and rIAPP seems to have a modest
helical propensity, whereas the remaining fraction of the peptide (residues 2137) seems
to be less structured. Moreover, such helicity seems to be required for the biologically
active state.
21
In fact, the first twenty residues are either invariant (Table 1.1, in black)
or conservatively substituted (Table 1.1, in green), which is also true for monkey and
cat IAPP (Table 1.1, cyan). Therefore, one may suppose this sequence is conservatively
substituted in order to function properly. On the other hand, the residues in the second
half of the peptide, residues 2029 in particular, are hypervariable and most probably do
not influence its biological function.
1.1.3.1 IAPP Aggregation
IAPP is the only peptide found in the amyloid deposits, which occur in the islet. The
amyloidogenic form is absolutely necessary for amyloid formation, but there are other
factors as well. IAPP is produced by the
-cells, which is the site that is most proximal
to the amyloid formation, and its overproduction is not the only condition that can lead
to islet amyloid deposit and, thus, to
-cell loss. It seems that a -cell dysfunction is
also necessary for the islet amyloid formation; namely, improperly processed proIAPP,
7
INTRODUCTION
1.1
found to form fibrils and present in DM2 islet amyloid deposits. This could occur as a
result of the disproportionate release of proinsulin relative to processed insulin. Since
this change is present in high-risk individuals prior to the development of the disease
and the PC 1/3 and PC2 proteolytic enzymes process both proinsulin and proIAPP, it
is possible that proIAPP is improperly converted to IAPP. Therefore, amyloidogenic
proIAPP may lead to deposits at the early phases of the islet amyloid deposit formation.
This processing, in order to be efficient, needs a tightly regulated environment; in fact,
optimal pH and calcium concentrations are necessary for processing proIAPP, as shown
by in vitro experiments.
11
DM2 fibrils are found almost exclusively at the extracellular
sites in the islets, with small deposits located adjacent to the basement membrane of islet
capillaries. The basement membrane could anchor aggregates of IAPP or proIAPP, form-
ing, therefore, a "nucleus" for fibril formation.
*
In fact, the basement membranes contain
heparan sulfate proteoglycans (HSPG), involved in synthetic IAPP fibrillogenesis, and
proIAPP has a consensus sequence for HSPG.
12
Jha et al. have shown that proIAPP
exhibits a much higher amyloidogenic propensity in the presence of negatively charged
membranes than in bulk solvent. However, hIAPP is still much more amyloidogenic than
proIAPP. Morphological changes have been observed, although differences in the sec-
ondary structures of the aggregated species of hIAPP and proIAPP at the lipid interface
are small. Unlike hIAPP, proIAPP forms essentially oligomeric-like structures at the lipid
interface.
9
Other studies have also shown morphological changes when IAPP interacts
with negatively charged membranes; in fact, Lopes et al. show that the N-terminal part
of hIAPP interacts strongly with the negatively charged lipid interface, and the peptide
forms ordered fibrillar structures through a two-step conformational transition from a
largely
-helical to a -sheet conformation.
8
1.1.3.2 Proline
Proline is a special amino acid, as the side chain is bonded to the nitrogen of the amino
group forming an imino acid. This tertiary nitrogen cannot form hydrogen bonds, given
the absence of N
-H, and is incompatible with -helical conformations, if not at the
N-terminus. Nevertheless, single proline residues can fit in long
-helices by distorting
the local helical geometry. The five-member ring that defines proline is relatively rigid
and drastically limits the
angle in the Ramachandran plot to - 60°, where is the
rotation angle of the peptide unit around the N
-C
bond. The secondary structures
assumed by proline are poly(Pro)I, poly(Pro)II, and type I and type II
-turns. Proline
residues prefer reverse turns (Ref. 5, Table 6.5, page 256), defined by four residues, of
which two are not involved in
-sheets, with an H-bond between residues i and i+3,
and proline occupying position i+1. Poly(Pro)I and poly(Pro)II are determined by the
conformation of proline, as it can be in either cis, in form I, and trans, in form II; both of
which depend on the solvent, with form II predominating in water, acetic acid, and benzyl
alcohol, and form I predominating in propanol and butanol. Conformational changes
have been observed to occur upon solvent change. The
angles are -83° and -78° for
forms I and II, respectively. Proline also plays an important role in structural fibrous
*
Nucleation seems to occur through a two-step mechanism, with the nucleation, or seed-forming step,
followed by an exponential phase of fibril formation. The cytotoxicity of the amyloid deposits seems to
be caused by the initial aggregation steps. Interestingly enough, the cytotoxicity of IAPP is inhibited by
Congo Red, while the fibrillogenesis is not.
11
8
1.2
HYDRATION WATER
proteins, like collagen, as it can impart rigidity and stability to the structure. Collagen is
characterized by a triple helix similar to poly(Pro)II, with a glycine every three residues,
i.e., (
-Gly-Xaa-Yaa-)
n
, with a preponderance of hydroxyproline (Hyp) as Xaa or
Yaa, where Hyp forms H-bonds between the hydroxyl group and the amide group of the
glycine backbone.
5
Unlike other amino acids, the peptide unit of proline does not have a partial double
bond character to it; in fact, the residue preceding proline is more likely to be in a cis
conformation than other residues, i.e., a 4:1 ratio favoring the trans conformation, as
opposed to 1000:1, when comparing proline to other residues, respectively. The resi-
due is also slightly distorted from planarity; in fact,
= -20° to 10°, compared to
= 0° and 180° for cis and trans conformations, respectively. The free-energy barrier
associated to a cis-trans isomerization is 20
.4kcalmol
-1
, making it a slow conversion,
i.e.,
1
/2
20min, which is temperature dependent with the rate increasing by a factor of
3
.3 every 10
C within the normal range. The possibility of assuming a cis conformation
not sterically hindered also affects the conformational properties such as the radius of
gyration and end-to-end distance, illustrated in Section 2.4.3 on page 31.
5
Another interesting characteristic of proline is its presence in rapid degradable pro-
teins. Such proteins contain one or more "PEST" regions, which are segments of 1260
residues, in primary structures rich in proline, glutamic acid, serine, and threonine.
5
Whether the high amount of proline residues facilitates the degradation of rIAPP in any
way, compared to the serine residues in hIAPP, resulting therefore in a limited in vivo
IAPP deposit, is unknown and could be worth investigating.
1.2 Hydration Water
Is there a possible explanation as to why the experimentally measured lag time of hIAPP
aggregation drops drastically at approximately 320 K, as shown by Kayed et al.?
10
Is
it a coincidence that another amyloidogenic peptide, like A
42,
22
also undergoes a
conformational transition at a very close temperature?
There are definitely still many questions evolving around biomolecules and their
activity. Pioneering studies by Careri et al. have shown that biomolecules regain their
biological activity upon recovering the minimum amount of surrounding water molecules
that form an infinite hydration network from an ensemble of small water clusters. This
threshold is where water undergoes a quasi-2D percolation transition. One layer of wa-
ter, or a "monolayer," is sufficient for activity of the biomolecule and is referred to as
hydration water. These water molecules are connected by H-bonds of two different types:
those that span the system, and those that do not. In other words, the H-bonds of the
spanning network wrap the biomolecule completely, without covering it entirely, as there
can be water molecules or small clusters of water molecules that are not connected by
H-bonds to this network. At low temperature, the dimensionality of network of H-bonded
water molecules is quasi-2D, and this network of H-bonds envelopes the biomolecule.
Upon heating, this H-bond network of the water molecules decreases until breaking into
an ensemble of small clusters.
*
The process that can describe this is a quasi-2D percola-
*
A clarifying image of the breakage of the H-bond network can be that of a ball in a net. If the net is
intact, the ball moves when one of the knots of the net is pulled, as the H-bond network would behave at
lower temperature, i.e., by "pulling" one water molecule everything follows. If the net is weak, pulling
9
INTRODUCTION
1.4
tion transition. Moreover, this transition occurs at biologically relevant temperatures.
23
(Ref. 23, 24, and the references therein, include a complete overview of the percolation
transition of hydration water in biosystems.)
Studying the conformational changes of the peptide above and below the percola-
tion transition could shed some light on why faster aggregation was measured by Kayed
et al.
10
1.3 Overview
In aqueous solution, hIAPP has been shown to have an essentially disordered conforma-
tion as seen in far UV-CD.
10,2528
However, it may also assume compact structures
27
and a transient sampling of
-helical conformations has been observed;
21,29
the former
has been proven through FRET, and the latter, through NMR spectroscopic studies. The
Förster distance between tyrosine and phenylalanine measured for hIAPP in the lag phase
of the aggregation process is 12
.6Å, which, if compared to the values obtained through
a random walk model,
30
i.e., 30 Å for Y37/F23 and 40 Å for Y37/F15, clearly reveals a
structure that is more compact than what is expected for a fully unfolded peptide. The
two homologues, human and rat IAPP, when free in solution, show comparable struc-
tures; in fact, rIAPP adopts structures similar to hIAPP prefibrillar states.
27
Other studies
reveal sampling of
-helical conformations in the central region of the peptide for about
40 % of its length, starting approximately after the tight disulfide bond. In fact, the NMR
chemical shifts indicate
-helical propensity from residues 519 and their temperature
coefficients indicate such a region from residues 722.
The 2029 decapeptides of the different homologues were studied in detail with re-
gards to their aggregation propensity, showing that the S28-to-P28 substitution strongly
reduced the amyloidogenicity.
13
Normally, proline residues are both
-sheet and -helix
breakers, but if present as the first element in the helix, they may act as an N-capping
residue and can also stabilize helices, even at higher temperatures.
31,32
Other residue
substitutions, e.g., rIAPP(L23F), seem to promote aggregation in rIAPP, albeit in low
yield.
14
In fact, the fragment 3037, identical in both homologues, aggregates in vitro.
Hence, it is probably the overall sequence that influences the amyloidogenicity of IAPP.
33
The disulfide bond between residues C2 and C7 also plays an important role. In fact, it
has been found experimentally that the presence of this disulfide bond in the peptide also
changes the kinetics of aggregation, making the reaction much faster and allowing it to
form fibers by secondary nucleation, leaving the structure of the IAPP fiber core intact.
34
Moreover, the disulfide of the cystine seems to stabilize the short end-to-end distance in
the oxidized moiety of hIAPP,
35
allowing the formation of aggregation-prone
-sheets.
36
1.4 Objectives
The most astonishing aspect regarding amyloidogenesis is that many precursor proteins,
about twenty, differ not only in primary structure and size, but also in location. The main
objective of this study was to observe two very similar polypeptide sequences, being
one knot could cause the net to break leaving the ball where it is, or even breaking away from the net itself,
i.e., only a water molecule or a small cluster would follow when "pulling" a water molecule.
10
1.4
OBJECTIVES
84 % conserved, and pinpoint the different conformational properties of the monomer
that may induce or hinder peptide aggregation.
Finding conformational differences of the two monomeric polypeptide homologues
in solution could shed light on the underlying mechanism of the aggregation pathway of
hIAPP and was thus the focus of this work using MD simulations. The properties studied
in this work were the interaction of the aromatic residues of hIAPP and rIAPP, including
the mutated in silico variant rIAPP(L23F), the influence of the presence, or absence, of
the disulfide bond in both homologues, and the effect of proline, in particular residue 28,
on the secondary structure of IAPP. These results are presented in Chapter 5, with an
outlook on future work on IAPP presented in Chapter 6.
The conformational properties have been calculated by an ad hoc python program
that analyzes GROMACS
3739
trajectory files. An overview of this program can be found
in Chapter 2. Certain parameters, i.e., definitions of H-bonds, which are so important
for protein aggregation, and Ramachandran angles for the secondary structure, defined
in Chapter 2, were obtained through trial and error, as explained in Chapter 3.
Owing to the difficulty in preparing an initial conformation for an unstructured bio-
molecule, a detailed description of how the system was prepared can be found in Chap-
ter 3.
A very helpful tool for the investigation of the proper temperature range to be used is
the analysis of the percolation transition of the hydration water surrounding the peptide,
localizing therefore a temperature-induced conformational change. Theories on percola-
tion on infinite systems have been developed, but the actual determination of the percola-
tion threshold, especially for finite systems, required extensive study. This tedious work
was based on determining which of the many properties of a biomolecule should be mea-
sured for locating the percolation transition. Amongst the various monitored properties,
the preferred properties are the spanning probability and fractal dimension of the largest
cluster. Similar calculations performed on other biomolecules/polypeptides
22,4042
have
also been performed on IAPP, where the break occurs at
320K via a quasi-2D percola-
tion transition.
43
A more statistically relevant calculation has since been performed and
will be presented in Chapter 4.
For convenience, Ref. 43 is available in Appendix A, with the poster presentations
in Appendix B, and the initial and final conformations of the oxidized hIAPP moiety at
330 K
44
are available on request.
11
Chapter
2
Methods
2.1 Molecular Dynamics Simulation Methods in a Nutshell
The Molecular Dynamics Simulation Method is definitely a very powerful tool for inves-
tigating molecular conformations and many other properties. The principles behind it are
quite simple and can be explained by Newton's law of motion, with trajectories obtained
by solving the renown second law, F
= ma. In order to apply these laws, there are a
few assumptions to be made. The first being, that the motion of electrons are ignored,
allowing the system to be treated through classical physics. An obvious limitation in this
method is the inability to describe bond cleavage. The bonds are thus treated as springs,
described by potentials as simple as Hooke's law for a harmonic oscillator, i.e., F
= -kx.
Second, that the potential is obtained through pair-wise vector summation. The relation-
ship between scalar potential and a conservative force, as seen in the following equation
F
= -V(r),
(2.1)
allows a generation of trajectories from a distribution of particles, where the potential
is obtained by a pair-wise vector sum between the particles that comprise the system.
Hence, from distributions of particles, it is possible to obtain potentials, from which
forces can be obtained, and thus accelerations, which after a time
t, lead to new po-
sitions. This cycle is then repeated, and repeated, and repeated. Each new position is
obtained through integration of the acceleration with respect to time, by means of finite
difference methods, with the Verlet Algorithm being the most used. The MD simulation
is deterministic in a way that the past has an influence on the future of the system, also
because the kinetic energy is also taken into account to determine the total energy of the
system. This deterministic aspect is useful for determining conformational properties of
flexible molecules. Normally, MD simulations can sample NVE ensembles, where N, the
number of particles in the system, V, the volume, and E, the energy, are all kept constant.
Modifications can be made in order to sample from other ensembles, for example the
isobaric-isothermal ensemble, where pressure and temperature are kept constant instead
of volume and energy, as seen in the microcanonical ensemble (NVE). The thermody-
namical properties are calculated through an average by the number of time steps.
2,45
Unfortunately, this holds true only if the time interval is small enough for the force to
be constant, and normally this is true when it is smaller than the fastest vibration, which
13
METHODS
2.2
occurs for hydrogen bound to heavy atoms, like oxygen, so the maximum time step is
0.5fs. In order to consume less computational time, it is possible to apply constrained
dynamics, allowing the time step to increase, because the faster vibrations, like those
which involve hydrogen bonded to heavy atoms, are "frozen out" by constraining the
bond length to the equilibrium length. The suggested time step, when the molecules are
flexible, with rigid bonds, allowing translation, rotation, and torsion is 2 fs.
2,45
Force fields are the sum of functional forms and parameters. Parametrization is per-
formed to reproduce thermodynamical properties using computer simulation techniques
and may include vibrational frequencies, other than parameters to reproduce conforma-
tional properties, with the aid of cross-terms. The OPLS force field, i.e., optimized
parameters for liquid simulations, has been obtained this way. Unfortunately, there are
no absolute force fields, as they have been obtained through a parametrization in order to
reproduce a certain property, limiting, therefore, their target of application. An generic
functional form can be seen as follows:
V
= V
bonds
+V
angles
+V
torsion
+V
Lennard
-Jones
+V
Coulomb
,
(2.2)
where the first three terms are interactions between bonded atoms, i.e., bond length,
bond angle, and torsion angle potentials, respectively, while the last two are relative
to nonbonded interactions, i.e., van der Waals potential, most often expressed in the
common 6
/12 Lennard-Jones form, and electrostatic potential, approximated by the
Coulomb's law, respectively. Actually, there is also a fourth term between bonded atoms
related to out-of-plane bending, but this is used to enforce planarity and/or chirality to the
modeled molecule by the use of dummy atoms and not always necessary. The last terms
are usually the ones that require more time to calculate when obtaining the potential
during a simulation step. A possible method to treat long-range interactions, without
having to perform a cutoff, is the Ewald Method, which was derived from crystallography
due to the periodicity of ions in the unit cells of crystal structures. In order to apply this
method for biomolecules, a periodic boundary condition is required, as the charges are
placed on a lattice and considered to have infinitely many images in space. The smooth
particle-mesh Ewald method allows to lower the aforementioned bottleneck for
O(N
2
)
to
O(N logN).
2,45
Water models are many and can be classified in three main types: simple interaction-
points with rigid molecules, flexible molecules, and finally models that take polarization
effects into account. SPC/E is the updated model of the SPC, a three-center simple point
model with charges exactly balanced on H and O. The van der Waals interactions are
calculated with a Lennard-Jones function between the oxygen atoms only.
2,45
And last but not least, the initial conformation of the sample is very important for
the outcome of the experiment, in particular the removal of "hot spots," in which the
system presents high-energy interactions that can cause instability in the system. The
system must therefore be adequately minimized by means of minimization algorithms.
45
Chapter 3 is entirely dedicated to the preparation of the initial conformation of IAPP.
The pros and cons of Molecular Dynamics Simulation Methods can be summarized
by stating that since the motion is continuous, it can be used as a bridge between struc-
tures and macroscopic kinetic data, although it is expensive to execute and yields a short
time span, requiring a high CPU usage.
2
14
2.2
PREPARATION OF INITIAL CONFORMATIONS
2.2 Preparation of Initial Conformations
The polypeptide was initially modeled with MOLDEN v.4.4
46
in an
-helical conforma-
tion. In order to create the cystine moiety, it was necessary to bring the two thiol groups
of C2 and C7 within 10 % of the equilibrium bond length,
(2.048 ± 0.026)Å.
47
This sec-
ond step was possible after the rotation around a few arbitrary bonds with SWISS-PDB
VIEWER v.3.7sp5.
48
Such program was also used to create an extended conformation of
the polypeptide by dragging the Ramachandran angles to accepted values near
-180° for
(less than -130°) and 180° for (greater than 140°). These structures were simulated
with the Molecular Dynamics suite GROMACS v.3.3.1
3739
using the OPLS-AA/L force
field (with 2001 amino acid dihedrals).
49,50
The two hIAPP moieties' molecular weights are 3906
.33Da and 3908.35Da, respec-
tively 535 atoms for the cystine moiety and 537 atoms for the cysteine moiety. All the
residues, including the termini, have been set at the standard ionization state at a pH
of 7
.4 at 25
C of the individual residues, yielding a net charge of 2 e for the uncapped
C-terminus moiety. If the equilibrium K
a
of the ionizable side chains are considered, the
only one which might have a partial charge in aqueous solution is histidine; in fact, if
given the Henderson-Hasselbach equation pH
- pK
a
= log[His]/[HisH
+
] at pH 7.4 and
pK
a
= 6.04,
51
the concentration ratio is 22.9, which yields a net charge of 0
.0436e. This
pK
a
is relative to an amino acid in solution, therefore the protonation state can change
according to the conformation of the peptide, but it is possible to approximate it to a
single protonated state, where the hydrogen atom is located on N
2, as it is the most
favorable hydrogen bonding conformation.
5
As seen in Section 2.1, MD simulations
cannot describe bond cleavage; therefore, ionization states are determined and fixed at
the beginning of the simulation. In other words, the protonation state of the residues is
kept constant, rather than pH.
52*
2.2.1 In vacuo hIAPP Simulations
Both the
-helical and fully extended (-strand) conformations of either moiety were
minimized with the L-BFGS algorithm
53
and then with the Polak-Ribiere conjugate gra-
dient algorithm
54
with a F
max
tolerance of 100 kJ mol
-1
, followed by an MD simulation
in NVT ensemble of 100 ps in vacuo at 1000 K, with a time step of 2 fs, a 0
.9nm cutoff for
short-range interactions, smooth particle-mesh Ewald (SPME)
55
to treat the long-range
Coulombic interactions, and Berendsen thermostat.
56
The following production phase,
needed to sample random configurations to determine a suitable starting structure,
57
was
performed for an additional 1 ns at the same conditions, albeit using the Nosé-Hoover
thermostat.
58,59
The polypeptide collapses within 20 ps of equilibration to minimize the charge-charge
*
At the time of the presentation of Ref. 52 by Donnini et al., histidine protonation states were still
work in progress.
Limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm by Nocedal.
Two methods were used, since the L-BFGS implementation in GROMACS v.3.3.1 is bugged and does
not allow the use of SPME for long-range interactions. First L-BFGS was used with a switch potential,
then when minimizing by means of other algorithms, i.e., CG, or SD for the solvated system, as well as the
other simulations, the SPME method was used. The insertion of a disulfide bridge for such a small loop is
strenuous on the bond and torsion angles of a peptide and therefore requires a sturdy energy minimization.
15
METHODS
2.2
interactions between the termini. The mean values of end-to-end distance between the
C
atoms of the first and last residues, referred to as r
eted
, are
(0.62 ± 0.14)nm or less in
the four 1 ns in vacuo simulations. This seems to be the only structural parameter that is
strongly influenced by the charge-charge interaction in vacuo, compared to the value of
at least
(1.22 ± 0.07)nm obtained through a 200ns production run performed at 450K in
SPC/E water.
60
The lack of charge screening in vacuo is seen also by the fact that mean
values of the maximum distance between heavy atoms, referred to as L
max
, and the radius
of gyration, R
g
, are comparable, but slightly smaller than the ones obtained through the
solvated run at 450 K. The same holds true for the standard deviation of the mean of R
g
and r
eted
; in fact, the dielectric screening of the medium reduces the long-range Coulomb
interactions, allowing the peptide more movement.
2.2.2 Solvated Uncapped hIAPP
MD simulations have been carried out on four additional conformations
*
per hIAPP moi-
ety obtained in vacuo, along with the above-mentioned initial
-helical conformation as
described in Section 2.2. The trajectories on these solvated peptides were compared in
order to ensure an unbiased starting conformation to use for the production phase (see
Section 2.2.3) and are studied in detail in Chapter 3.
The peptides were solvated using equilibrated SPC/E water.
60
The initial confor-
mations were appropriately minimized and subsequently temperature pre-equilibrated
by a short 50 ps NVT run with restraints on the solute and short time steps (0
.5fs) us-
ing Berendsen thermostat.
56
Also a short NPT density pre-equilibration of 100 ps using
Berendsen thermostat and pressure coupling
56
was carried out before running the equil-
ibration and production runs, using Parrinello-Rahman pressure coupling
61,62
and the
Nosé-Hoover thermostat,
58,59
with time constant for both couplings set at 2
.0ps, and a
time step of 2 fs collecting data every 2 ps. It is standard procedure to equilibrate the
system through a two-step equilibration, first at constant volume followed by a simu-
lation at constant pressure. The preferred choice is the Berendsen thermostat, as this
particular thermostat scales the velocities, thus bringing the temperature quickly to equi-
librated values.
If a real NVT ensemble is needed, correct fluctuations are obtained by
applying the Nosé-Hoover thermostat.
58,59
The same holds true for pressure coupling,
i.e., if thermodynamic properties need to be calculated through MD simulations, the
Parrinello-Rahman barostat
61,62
needs to be applied.
Constraints were applied to the water molecules by using the SETTLE
63
algorithm,
while SHAKE
64
was applied to covalent bonds of the peptide involving hydrogen. Long-
range electrostatic interactions were treated using smooth particle-mesh Ewald,
55,65
with
short-range interaction cutoffs set at 0
.9nm. Periodic boundary conditions were set in all
three directions, with the box size set at 6 nm for the random conformations taken from
Section 2.2.1 and 7 nm for the
-helical conformation taken as reference.
The system charge was neutralized by scaling the partial charges on the peptide to
neutrality as described in Section 2.3.
*
Details on how these initial conformations were chosen are discussed in Section 3.1.1.2.
An interesting tutorial can be found at
http://www.bevanlab.biochem.vt.edu/
Pages/Personal/justin/gmx-tutorials/lysozyme/index.html
.
16
2.3
SCALING CHARGES
2.2.3 Solvated Amide Capped hIAPP
The protonation states are the same as described in Section 2.2.2, with the exception of
the C-terminus being amide capped, yielding a net charge of 3 e for hIAPP and 4 e for
rIAPP. In order to neutralize the system in solution, the total charge on the biopolymer
was also scaled down to neutrality by distributing an equal and opposite charge on the
peptide itself, as seen for the uncapped polypeptide.
The isobaric-isothermal MD simulation production runs of 500 ns for each moiety
were performed at 1 bar at 310 K and 330 K. These runs were performed on random
starting conformations, i.e., conformations that were obtained after an arbitrary pre-
equilibration time of at least 50 ns and that presented a C
RMSD of at least 1.23nm
from the initial modeled
-helix, as can be seen in Figure 2.1. These initial pre-equilibra-
tion data were discarded to ensure a completely random starting conformation due to the
long autocorrelation times of H-bonds and secondary structure at the lower temperatures.
The peptides were solvated using equilibrated SPC/E water.
60
After proper minimiza-
tion and equilibration of the system, the following 500 ns NPT production runs, in which
data were collected every 2
.0ps, were performed using the Nosé-Hoover thermostat
58,59
and the Parrinello-Rahman pressure coupling
61,62
with coupling times of 2
.0ps. In or-
der to avoid "hot solvent and cold solute," the solvent and solute were coupled to two
different thermostats and barostats. Constraints were applied to the water molecules by
using the SETTLE
63
algorithm, while SHAKE
64
was applied to the covalent bonds of
the peptide involving hydrogen. Long-range electrostatic interactions were treated using
smooth particle-mesh Ewald,
55,65
with short-range interaction cutoffs set at 0
.9nm. Pe-
riodic boundary conditions were set in all three directions, with no interaction between
adjacent images as the box size was set at 7 nm with the maximum distance between
heavy atoms, L
max
, being no larger than 5
.5nm.
2.3 Scaling Charges
One of the underlying principles of force fields is that the effective energy potentials are
additive, i.e., interaction between atoms are described by a functional form, which is
the sum of local terms, between bonded atoms, and nonlocal terms, between nonbonded
atoms, as described by Eq. (2.2). Deviations from the equilibrium bond length, bond an-
gle, torsion angles, and the Coulomb and van der Waals interactions between atom pairs
describe the potential energy of the system.
2
Therefore, the Coulomb term is calculated
independently from the other terms, allowing the possibility of slightly modifying the
partial charges on the peptide without drastically perturbing the other terms that describe
the potential energy of the system.
Oleinikova et al. and Brovchenko et al. in studies on the hydration shell of Lyso-
zyme
66
and A
42
67
neutralized the charge of the system by scaling the charges, so the
same method was chosen in order to compare the results of the hydration shell analysis of
these systems without introducing unknowns to the system, such as counter ions, which
could noticeably affect the hydration water. In order to neutralize the system in solution,
the total charge of the polypeptide, q
o
t
, was scaled down to neutrality, q
s
t
, by subtracting
the partial scaled charge, q
p
i
, with the appropriate sign given by the ratio q
t
/|q
t
| from the
17
METHODS
2.3
(a) Red. hIAPP 310 K initial vs
-helix
(b) Red. hIAPP 310 K after 10 ns vs
-helix
(c) Ox. hIAPP 310 K initial vs
-helix
Figure 2.1: Comparing hIAPP initial conformations. The white ribbons show the initial
-helical
conformation that was simulated at 350 K as described in Section 2.2, while the magenta rib-
bons show the random conformation obtained after hundreds of nanoseconds, used as initial
conformations for the 500 ns production run at 310 K and 330 K analyzed in Chapter 5.
18
2.3
SCALING CHARGES
initial partial charge, q
o
i
, as can be seen in the following equations:
q
o
t
=
n
i
=1
q
o
i
= +2e,
(2.3)
q
s
t
=
n
i
=1
q
s
i
= 0,
(2.4)
q
s
i
= q
o
i
-
q
t
|q
t
|
|q
p
i
|,
(2.5)
where the partial charge needed for the charge scaling calculation, q
p
i
, is obtained by
multiplying the total charge by the contribution of each atom
i to the absolute total
charge given by the ratio q
o
i
/
n
i
=1
|q
o
i
|, as can be seen in the following equation:
q
p
i
= q
t
q
o
i
n
i
=1
|q
o
i
|
.
(2.6)
The scaled partial charges on each atom differ less than 1
.5% from the starting value,
respectively 1
.48% for the cystine moiety and 1.47% for the cysteine moiety,
*
which
leads to an error of less than 3 %.
,
Moreover, the error that may be introduced by the
use of scaled charges is still negligible considering the limitations force fields have in
reproducing secondary structures, because of the difficulty in parametrizing the back-
bone
and dihedral terms.
71
The overall charge of the polypeptide chains is positive,
therefore the scaling of the charges makes the negative charges slightly more negative,
and the positive charges, a little less positive. Same charge repulsive interactions will be
higher in the case of negative charges and lower for positive charges. It is highly unlikely
that the secondary structure may be influenced by such a slight change in electrostatic
potential, since the difference in interaction between scaled charges, relative to the orig-
inal unscaled charges, should be negligible compared to the forces involved with the
nonbonded interactions governing the secondary structure. In fact, considering a Bland-
Altman plot
72
of the Coulomb potential comparing first the effect of different charges
on the same structure, and then between independent runs with the different neutraliz-
ing methods, it seems the uncertainty introduced is negligible. The system charge was
neutralized in the three following ways: scaled charges as previously described (SCAL);
a neutralizing charge distributed on the smooth particle-mesh Ewald grid (SPME);
55,65
and a 150 m
M
sodium chloride concentration to neutralize the charge (NACL), obtained
by adding 33 chloride anions and 31 sodium cations randomly.
The Bland-Altman plot
72
is normally used in medicine to test the reliability of new
clinical measurements compared to old ones. Calculating the correlation coefficient is
*
Moreover, none of these charges pass the limit of qmax, which is used to define the hydrophobicity
in g_sas,
68
so the determination of the solvent accessible surface area is not biased (see GROMACS
manual for details).
69
The electrostatic potential between two charges q
i
and q
j
separated by a distance r
i j
is given by the
following relation:
V
i j
=
q
i
q
j
4
0
r
i j
, with the error given by
V
i j
V
i j
=
q
i
q
i
2
+
q
j
q
j
2
+
r
i j
r
i j
2
q
i
q
i
+
q
j
q
j
+
r
i j
r
i j
.
70
It is possible to run the simulation without scaling the charges and including a reaction field in the
Coulomb potential term or by introducing a neutralizing charge on the SPME grid, but it was preferred to
scale the charges since the effects it would have on the water model used are still unclear.
19
METHODS
2.3
not enough, as it may be misleading; in fact, two methods that have been studied to mea-
sure the same quantity should be highly correlated. Thus, two independent methods are
compared by graphical interpretation of the difference of the measured quantities plotted
against the average between the two, as can be seen in the right panels of Figures 2.2 and
2.3, where the left panels show the correlation between the same sets of data. The correla-
tion coefficient,
r
xy
, in Figure 2.2 is between 0
.97 to 0.99, but that is not surprising, since
the electrostatic potential is calculated for the trajectory with the same (V
S
) charges used
for the 30 ns MD simulation runs, then the potential is recalculated with the other charges
(V
O
), e.g., for the scaled charges run (SCAL) the electrostatic potential is first calculated
with the scaled charges (same charges of the simulation, indicated with
S), then with the
original unscaled charges (other charges, indicated with O). The electrostatic potential be-
tween two charges
q
i
and q
j
separated by a distance r
i j
is given by the following equation:
V
i j
= f
q
i
q
j
r
i j
,
(2.7)
where f is the electric conversion factor equal to 138
.935485kJmol
-1
nm e
-2
.
69
The
data on the abscissae in the right panels of Figure 2.2 are the mean value between the two
different electrostatic potentials just mentioned, i.e., ¯
V
S
,O
=
V
S
+V
O
2
, while the ordinates
show the difference between them,
V
S
,O
= V
S
-V
O
.
*
If the data were truly independent,
the difference between the two sets would be zero, which is not the case. The data have
a systematic error, and this is a way to quantify it. As can be seen by the distribution of
the data and the confidence level of 95 %, or
±1.96 (shown in Figures 2.2a and 2.2b),
the data seem to be normally distributed, with 94
.2% and 95.3% data within the 95%
confidence level, for the oxidized and reduced hIAPP respectively. The relative mean
value of the difference of electrostatic potential percentage is
-1.13% for the cystine
moiety and
-1.05% for the cysteine moiety. The other trajectories, i.e., the SPME and
NACL, which have been calculated with the original OPLS-AA partial charges,
49,50
when substituted with the scaled charges, give an even smaller absolute value of
V
S
,O
,
as can be seen in Figures 2.2c through 2.2f.
It is obvious that a systematic error has been introduced, but the question is how large?
The initial estimate was maximum 3 %, around 2 % if calculated by the square root of
the sum of the squares of the relative errors (as seen in Footnote on the previous page).
The absolute value of the relative error on the calculated electrostatic potential with two
different charge sets on the same conformations is less than 1
.13%. The next step is to
look at the effect the scaled charges have on the electrostatic potential,
V
D
, compared
to opposite partial charges distributed on the SPME grid,
V
G
, and neutralizing charges
given by an NaCl solution at physiological ionic strength 150 m
M
, V
P
. As can be seen in
the left panels in Figure 2.3, the correlation between the electrostatic potential of parallel
runs is uncorrelated, with r
xy
between 0
.35 and -0.17, so the Bland-Altman plots in the
left panels should also be uncorrelated. Unfortunately, only comparison of the neutraliz-
ing methods with the original charges are uncorrelated, as seen in Figures 2.3e and 2.3f,
where the relative difference between V
G
and V
P
is
-0.2% and 0.1%, respectively for
oxidized and reduced hIAPP. The scaled charges seem to overestimate the electrostatic
potential. In fact, just like in Figures 2.2a and 2.2b, ¯
d in Figures 2.3a through 2.3d ranges
*
In order to make it easier to quantify the differences,
V
S
,O
, are divided by the mean values, ¯
V
S
,O
, and
multiplied by 100.
20
2.3
SCALING CHARGES
-
82 -81 -80 -79 -78 -77
V
S
/ kJ mol
-1
-82
-81
-80
-79
-78
-77
V
O
/k
Jm
o
l
-
1
r
xy
= 0.99
-
82 -80 -78
¯
V
S
,O
/ kJ mol
-1
-4.5
-4.0
-3.5
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0
.0
0
.5
1
.0
1
.5
2
.0
2
.5
3
.0
3
.5
4
.0
4
.5
V
S,
O
/
¯ V
S,
O
×
10
-
2
¯
d = 1.13
= 0.08
cl
1
.96
= 94.2%
(a) Ox. hIAPP Bland-Altman Plot for SCAL
-
82 -81 -80 -79 -78 -77
V
S
/ kJ mol
-1
-82
-81
-80
-79
-78
-77
V
O
/k
Jm
o
l
-
1
r
xy
= 0.98
-
82 -80 -78
¯
V
S
,O
/ kJ mol
-1
-4.5
-4.0
-3.5
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0
.0
0
.5
1
.0
1
.5
2
.0
2
.5
3
.0
3
.5
4
.0
4
.5
V
S,
O
/
¯ V
S,
O
×
10
-
2
¯
d = 1.05
= 0.13
cl
1
.96
= 95.3%
(b) Red. hIAPP Bland-Altman Plot for SCAL
-
82 -81 -80 -79 -78 -77
V
S
/ kJ mol
-1
-82
-81
-80
-79
-78
-77
V
O
/k
Jm
o
l
-
1
r
xy
= 0.97
-
82 -80 -78
¯
V
S
,O
/ kJ mol
-1
-4.5
-4.0
-3.5
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0
.0
0
.5
1
.0
1
.5
2
.0
2
.5
3
.0
3
.5
4
.0
4
.5
V
S,
O
/
¯ V
S,
O
×
10
-
2
¯
d =
-0.85
= 0.15
cl
1
.96
= 95.9%
(c) Ox. hIAPP Bland-Altman Plot for SPME
-
82 -81 -80 -79 -78 -77
V
S
/ kJ mol
-1
-82
-81
-80
-79
-78
-77
V
O
/k
Jm
o
l
-
1
r
xy
= 0.97
-
82 -80 -78
¯
V
S
,O
/ kJ mol
-1
-4.5
-4.0
-3.5
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0
.0
0
.5
1
.0
1
.5
2
.0
2
.5
3
.0
3
.5
4
.0
4
.5
V
S,
O
/
¯ V
S,
O
×
10
-
2
¯
d =
-0.84
= 0.11
cl
1
.96
= 95.1%
(d) Red. hIAPP Bland-Altman Plot for SPME
-
82 -81 -80 -79 -78 -77
V
S
/ kJ mol
-1
-82
-81
-80
-79
-78
-77
V
O
/k
Jm
o
l
-
1
r
xy
= 0.98
-
82 -80 -78
¯
V
S
,O
/ kJ mol
-1
-4.5
-4.0
-3.5
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0
.0
0
.5
1
.0
1
.5
2
.0
2
.5
3
.0
3
.5
4
.0
4
.5
V
S,
O
/
¯ V
S,
O
×
10
-
2
¯
d =
-0.89
= 0.13
cl
1
.96
= 96.1%
(e) Ox. hIAPP Bland-Altman Plot for NACL
-
82 -81 -80 -79 -78 -77
V
S
/ kJ mol
-1
-82
-81
-80
-79
-78
-77
V
O
/k
Jm
o
l
-
1
r
xy
= 0.98
-
82 -80 -78
¯
V
S
,O
/ kJ mol
-1
-4.5
-4.0
-3.5
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0
.0
0
.5
1
.0
1
.5
2
.0
2
.5
3
.0
3
.5
4
.0
4
.5
V
S,
O
/
¯ V
S,
O
×
10
-
2
¯
d =
-0.88
= 0.11
cl
1
.96
= 94.7%
(f) Red. hIAPP Bland-Altman Plot for NACL
Figure 2.2: Each subfigure shows the correlation between two data sets in the left panels and
in the right panels the Bland-Altman plot
72
of the same sets. The occurrence of the data is
represented by a reverse spectral color code (ROYGBIV), where the most occurring events are
violet and red the least, with black being 100 % and gray 0 %. Scaled charges for (a) oxidized
and (b) reduced hIAPP. Neutralizing charge distributed on SPME grid for (c) oxidized and (d)
reduced hIAPP. Physiological 150 m
M
ionic force for (e) oxidized and (f) reduced hIAPP.
21
METHODS
2.3
from 0
.9% to 1.4%. This is possibly due to the fact that the unscaled charges belong to
neutral charge groups, which are no longer neutral after charge scaling. As stated in the
manual, if, for example, an atom-atom interaction calculated with O of a water molecule
is calculated without the neutralizing charges of the other atoms in the charge group, e.g.,
the two H atoms, a large dipole can be induced in the system.
69
Therefore, in order to
avoid this problem, the atom-atom interactions are calculated with all the atoms included
in a charge group. In the case of the scaled charges, the overall charge of the peptide is
neutral; not the charge of each individual group. The atoms still belong to charge groups,
but the groups may deviate from neutrality because of the scaling of the charge, thus
introducing a systematic error.
Therefore, the scaling of the charges can influence the electrostatic potential, which
in turn could bias the 1-4 interactions that define the
and torsion angles, which
define the secondary structure. As a first estimate, an error of 1
.4% in the electrostatic
potential, as estimated in Figure 2.3, could correspond to a 5° error in the dihedral an-
gles on the Ramachandran plot, if there were no other forces or barriers involved. This
should not be the case, since most torsional terms in OPLS-AA force fields are calculated
from ab initio calculations on models using an HF/6-31G* basis set
73
and, thus, should
not be influenced by the scaling of the charges. This was investigated by plotting the
regions relative to
-helix, -strands, and poly(L-proline), and a cutoff region 60°×60°,
comprising the regions in the Ramachandran plot that contain the maximum peaks of
the corresponding areas relative to the considered secondary structures, as can be seen
delimited by the dashed red squares in the images on the left of Figures 2.4 to 2.6 and
given in detail in Section 2.4.1. The mean values of the data that determine these peaks
are at maximum within 5°; moreover, all the mean values lie within the contour that
defines the highest content of the secondary structure in consideration. The peaks of
these Ramachandran plots are given by the sum of all three runs, with the areas of each
marker that determine the contribution of each run to the peak within the red square.
None of the charge-neutralizing methods seems to contribute to the peaks more than
another, if not the salt solution of reduced hIAPP, NACL in Figure 2.5c. In fact, with
the exception of Figure 2.7f, in which there seems to be a more significant content of
-strands than in the other runs, the contribution to the secondary structures for the inde-
pendent 30 ns trajectories does not differ significantly. If the
and angle acceptance
for these secondary structures is increased by 10° in all directions delimiting a cutoff
region of 80°
×80° (right plots of Figures 2.4 to 2.6), the mean values of and of
the three runs diverge slightly in some runs, with some of the points drifting out of the
contour with the maximum occurrence, as can be noticeably seen between Figures 2.5c
and 2.5d. Hence, this divergence of the mean points depends on many factors, among
them the cutoff, and cannot be solely attributed to the charge scaling. In fact, the standard
deviation of the mean, indicating the fluctuation of the system while the conformations
project their movement on this plane, is normally 15° when considering the 60°
×60°
cutoff and reaches values of 20° for the extended cutoff. Another possible control to
verify the influence of the charge scaling could have been calculating the dipole moment
of the peptide bond H
-N-C-
-O, but unfortunately the GROMACS charge groups differ
from this, including also the C
and H, which results in a slightly larger dipole (3.98D
vs. 3
.5D). The neutralizing charge is distributed throughout the entire peptide, so neither
charge distribution for the peptide bond is zero, making the calculation of the dipole
22
2.3
SCALING CHARGES
-
82 -81 -80 -79 -78 -77
V
D
/ kJ mol
-1
-82
-81
-80
-79
-78
-77
V
G
/k
Jm
o
l
-
1
r
xy
= 0.35
-
82 -80 -78
¯
V
D
,G
/ kJ mol
-1
-4.5
-4.0
-3.5
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0
.0
0
.5
1
.0
1
.5
2
.0
2
.5
3
.0
3
.5
4
.0
4
.5
V
D
,G
/
¯ V
D
,G
×
10
-
2
¯
d = 1.4
= 0.7
cl
1
.96
= 94.8%
(a) Ox. hIAPP Bland-Altman Plot V
D
vs. V
G
-
82 -81 -80 -79 -78 -77
V
D
/ kJ mol
-1
-82
-81
-80
-79
-78
-77
V
G
/k
Jm
o
l
-
1
r
xy
= -0.07
-
82 -80 -78
¯
V
D
,G
/ kJ mol
-1
-4.5
-4.0
-3.5
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0
.0
0
.5
1
.0
1
.5
2
.0
2
.5
3
.0
3
.5
4
.0
4
.5
V
D
,G
/
¯ V
D
,G
×
10
-
2
¯
d = 0.9
= 0.8
cl
1
.96
= 96.2%
(b) Red. hIAPP Bland-Altman Plot V
D
vs. V
G
-
82 -81 -80 -79 -78 -77
V
D
/ kJ mol
-1
-82
-81
-80
-79
-78
-77
V
P
/k
Jm
o
l
-
1
r
xy
= -0.06
-
82 -80 -78
¯
V
D
,P
/ kJ mol
-1
-4.5
-4.0
-3.5
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0
.0
0
.5
1
.0
1
.5
2
.0
2
.5
3
.0
3
.5
4
.0
4
.5
V
D
,P
/
¯ V
D
,P
×
10
-
2
¯
d = 1.2
= 0.9
cl
1
.96
= 95.4%
(c) Ox. hIAPP Bland-Altman Plot V
D
vs. V
P
-
82 -81 -80 -79 -78 -77
V
D
/ kJ mol
-1
-82
-81
-80
-79
-78
-77
V
P
/k
Jm
o
l
-
1
r
xy
= -0.17
-
82 -80 -78
¯
V
D
,P
/ kJ mol
-1
-4.5
-4.0
-3.5
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0
.0
0
.5
1
.0
1
.5
2
.0
2
.5
3
.0
3
.5
4
.0
4
.5
V
D
,P
/
¯ V
D
,P
×
10
-
2
¯
d = 1.0
= 0.9
cl
1
.96
= 95.8%
(d) Red. hIAPP Bland-Altman Plot V
D
vs. V
P
-
82 -81 -80 -79 -78 -77
V
G
/ kJ mol
-1
-82
-81
-80
-79
-78
-77
V
P
/k
Jm
o
l
-
1
r
xy
= -0.06
-
82 -80 -78
¯
V
G
,P
/ kJ mol
-1
-4.5
-4.0
-3.5
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0
.0
0
.5
1
.0
1
.5
2
.0
2
.5
3
.0
3
.5
4
.0
4
.5
V
G
,P
/
¯ V
G
,P
×
10
-
2
¯
d =
-0.2
= 0.9
cl
1
.96
= 95.5%
(e) Ox. hIAPP Bland-Altman Plot V
P
vs. V
G
-
82 -81 -80 -79 -78 -77
V
G
/ kJ mol
-1
-82
-81
-80
-79
-78
-77
V
P
/k
Jm
o
l
-
1
r
xy
= 0.04
-
82 -80 -78
¯
V
G
,P
/ kJ mol
-1
-4.5
-4.0
-3.5
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0
.0
0
.5
1
.0
1
.5
2
.0
2
.5
3
.0
3
.5
4
.0
4
.5
V
G
,P
/
¯ V
G
,P
×
10
-
2
¯
d = 0.1
= 0.7
cl
1
.96
= 95.5%
(f) Red. hIAPP Bland-Altman Plot V
P
vs. V
G
Figure 2.3: Each subfigure shows the correlation between two data sets in the left panels and
in the right panels the Bland-Altman
72
plot of the same sets. The occurrence of the data is
represented by a reverse spectral color code (ROYGBIV), where the most occurring events are
violet and red the least, with black being 100 % and gray 0 %. Scaled charges for (a) oxidized
and (b) reduced hIAPP. Neutralizing charge distributed on SPME grid for (c) oxidized and (d)
reduced hIAPP. Physiological 150 m
M
ionic force for (e) oxidized and (f) reduced hIAPP.
23
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Details
- Quote paper
- , 2014, Molecular Dynamics of Monomeric IAPP in Solution: A Study of IAPP in Water at the Percolation Transition, Hamburg, Bedey Media GmbH, https://www.anchor-publishing.com/document/312779
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