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Doktorarbeit / Dissertation, 2011
166 Seiten, Note: 1,0
List of Figures
List of Tables
1.1 Islet Amyloid Polypeptide
1.1.1 Diabetes Mellitus Type II
1.1.2 Mutations and Homologues
1.1.3 IAPP Properties
184.108.40.206 IAPP Aggregation
1.2 Hydrational Water
1.4 Thesis Objectives
2.1 Molecular Dynamics Simulation Methods in a Nutshell
2.2 Preparation of Initial Conformations
2.2.1 In vacuo hIAPP Simulations
2.2.2 Solvated Uncapped hIAPP
2.2.3 Solvated Amide Capped hIAPP
2.3 Scaling Charges
2.4.1 Ramachandran Angles
2.4.2 Hydrogen Bond Definitions
2.4.3 Statistical Properties
220.127.116.11 Water box and Maximum Distance between Heavy Atoms
2.4.4 Data Crunching
18.104.22.168 Error Estimate
22.214.171.124 Savitzky-Golay Smoothing Filter
126.96.36.199 Scott’s Choice
188.8.131.52 Rounding Data - Taylor
2.5 Hydration Water
2.5.1 System Description
2.5.2 Water Shell Analysis Software
3 Preparation of the Initial Conformations
3.1 Random Conformations from Vacuum
3.1.1 Data Analysis
184.108.40.206 Initial Modeled α -Helix Conformation
220.127.116.11 Comparison of Independent Starting Conformations .
18.104.22.168 Independent Concatenated Data
3.2 Extended Trajectories
4 Water Percolation
4.1 Hydration Water Properties
4.2 Hydration Water Analysis
4.2.1 Temperature-Induced Percolation Transition of Hydration Water
4.2.2 Effect of the Spanning Water Network on Peptide Properties
4.2.3 Effect of Peptide Structure on the Spanning Network of Hydration Water
5 Comparing hIAPP and rIAPP in Liquid Water
5.1 Conformational Changes of Oxidized hIAPP at 330 K
5.1.1 Conformational Properties Rg, reted, and SASA of IAPP
5.2 Compact hIAPP Conformation at 330 K
5.2.1 Aromatic-Aromatic Interactions
5.2.2 Secondary Structure
22.214.171.124 Ramachandran Angles
5.2.3 Snapshots of IAPP
5.2.4 H-bond Patterns and Secondary Structure of Oxidized hIAPP at 330 K
5.2.5 System Perturbation
126.96.36.199 Thermal Induced “Unfolding”
188.8.131.52 In silico Point Mutations on Oxidized hIAPP at 330 K
5.3 Discussion and Conclusions
5.3.1 Compact, but not Entirely Disordered, Polypeptide
5.3.2 Effect of P28 on the C-Terminal Region
5.3.3 Effect of Aromatic Residues
5.3.4 Temperature Effect on Oxidized hIAPP
5.3.5 Effect of the Disulfide Bond
B Poster Presentations
C Starting and Final Conformations
2.1 Initial Conformations for MD Production Runs
2.2 Bland-Altman Plots at 350 K — Comparing Charges
2.3 Bland-Altman Plots at 350 K — Comparing Runs
2.4 Ramachandran Plots at 350 K — Helix Cutoffs
2.5 Ramachandran Plots at 350 K — β -strands Cutoffs
2.6 Ramachandran Plots at 350 K — poly(Pro) Cutoffs
2.7 Ramachandran Plots at 350 K — Charge Scaling
2.8 Radial Distribution of reted 29
2.9 Water Density Temperature Dependence
2.10 Comparing Lmax vs. Box Size for Independent Runs at 350 K
3.1 Time Dependence of Rg and reted at 350 K
3.2 Comparing Rg and reted for Independent Runs at 350 K
3.3 Curve Fitting Rg and reted Distributions at 350 K
3.4 Temperature Dependence of Rg and reted for All Concatenated Trajectories
3.5 Rg and reted Uncertainty for Concatenated Trajectories
3.6 Temperature Dependence of Rg and reted for Selected Concatenated Trajectories
3.7 Time Dependence of Rg and reted and Data Distribution from 290 K to 350 K
4.1 Probability Distribution of Smax/Nw and Hmax 56
4.2 Temperature Dependence of (Smax/Nw) av, SP, and Δ Hmax 56
4.3 Temperature Dependence of Δ(Smax/Nw) and Smean 57
4.4 Dependence of (Hmax) av on (Smax/Nw) av 58
4.5 Temperature Dependence of df 59
4.6 Oxygen-Oxygen Pair Correlation Function gOO 60
4.7 Temperature Dependence of Rg and SASA compared to SP 60
4.8 Temperature Dependence of Δ(nppH) and (Smax/Nw) av 61
4.9 Temperature Dependence of Helical Content and nppH;HelicalCooperativityat310 K and 330 K
4.10 Dependence of SP and (Smax/Nw) av on npp H 63
5.1 Time Dependence and Mean Values of Rg at 310 K and 330 K
5.2 Time Dependence and Mean Values of reted at 310 K and 330 K
5.3 Time Dependence and Value Distribution of SASA at 310 K
5.4 Time Dependence and Value Distribution of SASA at 330 K
5.5 Rg and SASA Correlation at 310K
5.6 Rg and SASA Correlation at 330K
5.7 Rg and nHB Correlation at 310K
5.8 Rg and nHB Correlation at 330K
5.9 Time Dependence of Y37/F15 and Y37/F23|L23 Distances and Secondary Structure at 310 K
5.10 Time Dependence of Y37/F15 and Y37/F23|L23 Distances and Secondary Structure at 330 K
5.11 Ramachandran Plots at 310 K
5.12 Ramachandran Plots at 330 K
5.13 Time dependence of secondary structure assigned by DSSPcont at 310 K
5.14 Time dependence of secondary structure assigned by DSSPcont at 330 K
5.15 Mean Helical Content at 310 K and 330 K as assigned by DSSPcont
5.16 Snapshots of Oxidized hIAPP and rIAPP at 330 K
5.17 Helical Content between Residues 8-22
5.18 Backbone-Backbone H-bond Matrices at 310 K
5.19 Backbone-Backbone H-bond Matrices at 330 K
5.20 Time Dependence of Rg and reted and Data Distribution for the Perturbed Systems
5.21 Mean Helical Content for the Perturbed Systems as assigned by DSSPcont
B.1 Poster — CBSB08, Jülich (2008)
B.2 Poster — Biophysical Society Meeting, Boston (2009) and “Amyloid 2009”, Halle (2009)
1.1 IAPP Primary Structures
1.2 Relative Frequencies of Amino Acid Replacements
2.1 Secondary Structure Assignment
2.2 Hydrogen Bonds in Biological Systems
2.3 Random-flight Chain Statistical Properties (n = 36, l = 0 . 38 nm)
2.4 Error Estimate Calculated by g_analyze
3.1 Radius of Gyration at 1 bar and 350 K
3.2 End-to-End Distance between C α at 1 bar and 350 K
3.3 Standard Deviation vs. Error Estimate
3.4 Nonlinear Curve Least-Squares Fit
3.5 End-to-End Distance from Fitting
5.1 Conformational Properties reted and Rg at 1 bar and 310 K
5.2 Conformational Properties reted and Rg at 1 bar and 330 K
5.3 Helical Content assigned by φ and ψ angles at 1 bar and at 310 K and 330 K
5.4 Helical Content assigned by DSSPcont at 1 bar and at 310 K and 330 K
If I’m writing this, that means that the journey has reached it’s destination. Needless to say, there were many bumps and detours along the way, but as any journeyman could say, “you know where you start off, but you’re never sure of where you’ll end up.”
First and foremost, I would like to thank Prof. Dr. Roland Winter for offering me such an interesting topic to study, Prof. Dr. Alfons Geiger and PD Dr. Claus Czeslik for accepting to judge the dissertation of the my work, and ZACG for financing the computer clusters Dr. Gurpreet Singh and I assembled and maintained during our Promotion at TU-Dortmund. Dr. Werner Horstmann for getting me a great desktop computer to crunch the data during my time at University. Andrea Kreusel, Bertina Schuppan, and Kirsten Skodzik for helping with forms, faxes, and phone calls, when my German was still inexistent. My German is definitely better now, but still not good enough to be able to write the Zusammenfassung without the help of Patrick Kibies and Elena Zwar, who translated the summary for me. Many colleagues helped me along the way; in particular Dr. Singh, since we were the only students on our floor who were engaged in this MD adventure surrounded by experimentalists. Nevertheless, many fruitful discussions were carried out with Dr. Rajesh Mishra, Dr. Michael Sulc, Dr. Christian Reichhart, and Dr. Roland Krivanek. In particular, Dr. Krivanek helped me get my feet wet with python scripting, and LATEX posters and presentations. I would like to thank Dr. Leo Breebaart for his incredible PhD thesis LATEX package available at http://www.kronto.org/. Dr. Daniel Seeliger for the wonderful PYMACS package. Dr. Thomas Zielonka at the ITMC, for the nice hospitality in hosting our computer clusters in a nice and cool environment. Prof. Dr. Stefan Kast for allowing me to use the cluster for my “last” calculations. Milan Saskovic for helping me on his free time to make my home more accessible. Former colleagues from the University of Bologna, Dr. Manuel Melle-Franco, Dr. Jan-Willem Handgraaf, and Dr. Jukka-Pekka Jalkanen. Franco Tampieri, an IT professional, who also found the time to help me out when we had some issues with the cluster. Many thanks to the administration of IMPRS-CB, namely Prof. Dr. Martin Engelhard, Dr. Jutta Rötter, Dr. Waltraud Hofmann-Goody, and Christa Hornemann. I apologize if I missed any of you!
A very special acknowledgment goes to Dr. Aliaksei Krukau, who gave me the hydration water analysis FORTRAN executable developed by Dr. Ivan Brovchenko and Dr. Alla Oleinikova, without whom (Dr. Brovchenko and Dr. Oleinikova) all the data and data analysis on the hydration shell presented in Chapter 4 would never have taken form.
I gratefully acknowledge financial support from federal state of NRW, and the IMPRS-CB in Dortmund.
I owe my deepest gratitude to my family, old and new, for the endless support, in particular, Mom, Liz & Nikki, Eve, Anto & Remo, and Siska & Steele.
Dortmund, March 24, 2011 Maximilian N. Andrews
Conformational properties of the full-length human and rat islet amyloid polypeptide 1-37 (amyloidogenic hIAPP and non-amyloidogenic rIAPP, respectively) were studied 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 therefore 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 temperature interval that corresponds to a percolation transition, which was calculated for hIAPP at ≈ 320 K 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 characterized by intrapeptide Hbonds that form many β -bridges in the C-terminal region. This compact conformation presents a short end-to-end distance and seems to form through the formation of β -sheet conformations in the C-terminal region with a minimization of the Y/F distances in a two-step mechanism: the first step taking place when the Y37/F23 distance is ≈ 1 . 1 nm, and subsequently Y37/F15 reaches its minimum of ≈ 0 . 86 nm. rIAPP, which does not aggregate, also presents transient helical conformations. A particularly stable helix is located in proximity 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 peptide 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 β -bridges seen in hIAPP. Conversely, hIAPP is highly disordered in the C-terminal region, presenting transient isolated β -strand conformations, particularly at higher temperatures and when the natural disulfide bond is present. Such conformational differences found in these simulations could be responsible for the different aggregational propensities of the two different homologues. In fact, the fragment 30-37, which is identical in both homologues, is known to aggregate 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 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 mellitus 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 N22 FGAIL27 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 that there are interactions that bring the peptide to compact conformations. Conversely, due 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 instances 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 wildtype oxidized homologue remains compact upon heating up to 390 K.
Thus, in light of the results presented in this Thesis, the collapsed state of the monomeric form is observed when the following three events occur:
1. Presence of the disulfide bond, which was observed to be more flexible than the reduced counterpart and to stabilize the short end-to-end distance in IAPP.
2. Absence of helical content in the C-terminus region, in order to allow more flexibility to this region of the peptide for “folding”. P28 seems to stabilize the highly mobile and unstructured portion of IAPP. Moreover, such helicity seems to inhibit short end-to-end distances.
3. Presence of aromatic residues, in particular F23, which seems to stabilize 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.
Mittels MD-Simulation wurden Konformationseigenschaften des ungekürzten Insel-Amyloid-Polypeptids 1-37 (humanes amyloidogenes hIAPP und nicht amyloidogenes rIAPP der Ratte) bei physiologischen Temperaturen untersucht, beide sowohl mit Cystein- (reduziertes IAPP) als auch mit Cystinresten (oxidiertes IAPP). Bei der Durchführung von Messungen bei Temperaturen von 250 K bis 450 K in Intervallen von 20 K zeigte sich, dass der Perkolationsübergang des Wassers zwischen 310 K und 330 K stattfindet. Somit wurden diese Temperaturen ausgewählt, um die Konformationseigenschaften des IAPP bei seiner höchsten biologischen Aktivität zu studieren. Tatsächlich zeigen die meisten lebenden Organismen ihre höchste biologische Aktivität in einem Temperaturbereich, der dem eines Perkolationsübergangs entspricht. Für hIAPP ergab die Berechnung einen Wert von ≈ 320 K. Dieser Wert scheint unabhängig von der chemischen Zusammensetzung der IAPP-Variante zu sein. Bei allen untersuchten Temperaturen nimmt IAPP keine definierte Konformation ein, sondern liegt in Lösung im Wesentlichen als zufälliges Knäuel vor, obwohl sich vor allem in der reduzierten Form kurzlebige Helices zwischen den Aminosäureresten 8 und 12 zu bilden scheinen. Oberhalb des Perkolationsübergangs von Wasser zeigt das reduzierte und immer noch strukturlose hIAPP einen deutlich verminderten helikalen Anteil. Währenddessen erreicht der natürliche Cystinrest einen recht kompakten Zustand mit einem, gegenber den Messergebnissen der anderen Varianten, um nahezu 10 % verminderten Trägheitsradius. Dies wird durch die intrapeptidischen Wasserstoffbrückenbindungen, welche viele β -Brücken in der Region des C-Terminus bilden, hevorgerufen. Die kompakte Konformation weist einen geringen Abstand beider Termini auf und scheint sich durch die Ausbildung von β -Faltblattkonformationen in der C-terminalen Gegend mit einer Minimierung der Y/F-Abstände in einem zweischrittigen Mechanismus zu bilden. Der erste Schritt findet bei einem Y37/F23 Abstand von ≈ 1 . 1 nm statt, woraufhin Y37/F15 ihre minimale Distanz von ≈ 0 . 86 nm erreichen. Das nicht aggregierende rIAPP zeigt ebenfalls kurzlebige helikale Konformationen. Eine besonders stabile Helix befindet sich in der Nähe der C-terminalen Region, beginnend mit den Aminosäureresten L27 und P28. Diese MD-Simulationen zeigen, dass P28 in rIAPP die Sekundärstruktur von IAPP durch die Stabilisierung des Peptids in helikalen Konformationen beeinflusst. Wenn diese Helix nicht vorhanden ist, zeigt das Peptid Krümmungen oder Hverbrückte Schleifen bei P28, die die Bildung von β -Brücken, wie sie in hIAPP gefunden wurden, unterdrücken. Im Gegensatz dazu ist hIAPP in der C-terminalen Region deutlich ungeordneter und zeigt, besonders bei höheren Temperaturen und wenn die natürliche Disulfidbrücke vorhanden ist, kurzlebige isolierte β -Strand-Konformationen. Derartige konformationelle Unterschiede, wie sie in diesen Simulationen gefunden wurden, könnten für die unterschiedlichen Aggregationsneigungen der beiden Homologe verantwortlich sein. Tatsächlich ist bekannt, dass der bei beiden Homologen identische Abschnitt 30-37 in vitro aggregiert, daher muss die gesamte Sequenz für die Amyloidogenität des hIAPP ursächlich sein. Es erscheint plausibel, dass der durch den Ersatz von Serin durch Prolin an Aminosäurerest 28 hervorgerufene höhere Anteil helikaler Konformationen im rIAPP dessen Aggregation inhibiert. Die spezifische Position des P28 könnte hierbei wichtiger für die Inhibierung sein als die intrinsischen Eigenschaften des Prolins allein. Tatsächlich wurde im IAPP von Katzen, die einen Diabetes Mellitus Typ II entwickelt haben und Insel-Amyloid-Ablagerungen zeigen, ein Prolinrest an Position 29 gefunden. Weiterhin ist für den oben genannten kompakten Zustand des monomeren, oxidierten hIAPP charakteristisch, dass eine besonders reaktive Konformation, die während der Faltung gefunden wurde, durch Disulfidbrücken stabilisiert ist. Eine solche Konformation besitzt einen geringen Abstand beider Termini, was dazu führt, dass die amyloidogene Sequenz N22 FGAIL27 gegenüber benachbarten Peptiden exponiert ist. Im reduzierten hIAPP-Rest scheint sich dieser Zustand nicht für einen signifikanten Zeitraum zu bilden, was durch die fluktuierende Distanz der Endgruppen nachgewiesen wurde. Der mittlere Abstand zwischen den Termini ist kleiner als der aus dem Irrflugmodell bestimmte Wert. Dies zeigt die hohe Flexibilität des hIAPP und dass Interaktionen, die das Peptid in eine kompakte Form überführen, vorhanden sind. Im Gegensatz dazu scheinen beide Formen des rIAPP auf Grund der dem Prolin eigenen Starrheit zu unflexibel zu sein, um sich so zu falten, dass ein geringer Abstand zwischen den Termini, wie bei der oxidierten Form des hIAPP, zustande kommt. Allerdings sind auch Fälle beobachtet wurden, in denen oxidiertes rIAPP kurze Termini-Abstände erreicht. Dies stimmt mit der Abwesenheit von Helices in der P28-Region überein. Diese Konformationen treten möglicherweise dank der bei hIAPP beobachteten Interaktionen zwischen Disulfidbrücken und C-Terminus auf. Kurze Abstände zwischen Y37 und L23 werden im selben Zeitrahmen wie die geringen Abstände zwischen Y37 und F23 in hIAPP beobachtet. Allerdings ist es durch die Tatsache, dass Leucin nicht aromatisch ist, möglich, dass der erste Schritt des beim hIAPP beobachteten Faltungsprozesses im Wildtyp des rIAPP nicht stattfinden kann.
Auf den gefalteten Zustand, der durch Simulation des oxidierten hIAPP bei 330 K erhalten wurde, wurden in silico Mutationen eingebaut, um zu beobachten, welchen Einfluss Prolin auf die Konformation ausübt. Insbesondere der S28P-Austausch scheit die Bildung einer Helix in dieser Region zu induzieren und die besonders stabile, kompakte Struktur durch Trennung der Termini zu zerstören: Tatsächlich bleibt der Wildtyp des oxidierten Homologen kompakt bis zu einer Temperatur von 390 K.
Somit scheinen, in Anbetracht der Ergebnisse dieser Arbeit, drei Charakteristika notwendig zu sein, damit die monomere Form des Polypeptids in einen kollabierten Zustand übergeht:
1. Anwesenheit einer Disulfidbrücke, die, wie beobachtet, flexibler als die reduzierte Entspre chung ist und den kurzen Abstand zwischen den Termini in IAPP stabilisiert.
2. Abwesenheit helikaler Anteile in der C-terminalen Region, um dieser Flexibilität für die Fal tung des Peptids zu verleihen. P28 scheint den hochbeweglichen und unstrukturierten Ab schnitt von IAPP zu stabilisieren. Ferner scheint derartige Helikalität kurze Abstände der Termini zu unterdrücken.
3. Anwesenheit aromatischer Reste, im Besonderen F23, welches einen der ersten Schritte im Faltungsprozess zu stabilisieren scheint.
Da diese Ergebnisse zur monomeren Form erhalten wurden, sind weitere Studien notwendig, um zu bestimmen, ob diese drei strukturellen Charakteristika auch für die Aggregationsneigungen des IAPP relevant sind.
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 ‘ ’, which means “of primary importance” and in turn derives from the word ‘ ’, which means “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 Creighton5 Virtually every property that characterizes a living organism is affected by proteins. Proteins: Structure and Molecular Properties, Creighton (1993) and can only wonder how much there still is to discover, in order to fully understand how these organic molecules, which constitute 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 functions which are 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 cerevisiae? 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 proteins are comprised of linear chains of only twenty amino acids, which can be considered a sequence of letters of the alphabet that form words.6
Once the sequence of amino acids has been found, the adventure begins! The reason being, that many times the function of the protein is still unknown. In fact, the primary structure 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 β -cells. Its physiological role is unclear. Although pancreatic amyloid deposits in the islets of Langerhans have been found in more than 95 % of the type II diabetes patients, the causal relationship between amyloid formation and the disease is still largely unknown.7 -10 The conditions at which it aggregates are also still unclear; in fact human IAPP (hIAPP) in healthy individuals and non-insulin-dependent diabetes subjects has the same sequence. On the other hand, other variants that have a sequence identity of at least 80 % such as rodent IAPP (rIAPP), do not aggregate. Moreover, healthy hIAPP transgenic in mice, which release hIAPP and insulin in a regulated manner, also do not present any islet amyloid deposits. Hence, the primary
*The number of proteins encoded by the human genome is still under debate, ranging from 42 000 genes to 65 00075000 genes, as can be found on the Human Project Genome Information page http://www.ornl.gov/sci/ techresources/Human_Genome/faq/genenumber.shtml.
structure of hIAPP alone is not sufficient to cause amyloid formation. In fact, islet amyloid deposits were found only in mice that presented dysfunctional β -cells. One of the characteristics of the deposits formed by amyloidogenic precursor proteins, such as IAPP, is the proximity of the insoluble deposits to where the protein is produced.11
Due to the complexity of living organisms and all the open questions that surround 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 β, which is responsible for the amyloid deposits in Alzheimer’s Disease. The difficulty is identifying intermediate states that occur when the peptide undergoes a conformational transition from random coil to an aggregation prone conformation 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 inhibits the aggregation greatly.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, which is not present in hIAPP, and more precisely 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.
Many degenerative diseases, like Alzheimer’s, Parkinson’s, Creutzfeldt-Jakob, diabetes mellitus type II, and several other systematic amyloidoses are related to polypeptide aggregation. Human amyloid polypeptide (hIAPP) forms pancreatic amyloid deposits, which are found in the islets of Langerhans in more than 95 % of the type II diabetes patients, although the causal relationship between amyloid formation and the disease is still largely unknown.7 -10 These deposits were discovered by Opie at the turn of the twentieth century, 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 β -cell.7 * The β -cell dysfunction is not clear, but β -cell mass loss does occur. The progressive loss of function of the β -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 monkeys (nonhuman primates), not only in man. It is quite difficult to establish the the relationship between islet amyloid deposition and the three following characteristics of diabetes mellitus type II: increased insulin resistance, onset of hyperglycemia, and β -cell dysfunction. Only through pancreatic biopsies, it would be possible to monitor the amyloid formation 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, there are insufficient β -cells to supply an adequate amount of insulin, but the sole cause doesn’t 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, therefore the length of the disease is 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 Spontaneously 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 diabetes 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. Further investigation through laboratory observations was needed, due to the length of the development of the disease, which occurs over years. Islet amyloid in transgenic mice and rats that express the human IAPP gene alone, did not occur. 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 demonstrated to be similar in man, but some are very different. Thus, the islet amyloidosis doesn’t 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, i.e., the percentage of islets affected, and less than 10 % severity, i.e., the percentage of islet area occupied, whereas cross-sectional data show that macaca mulatta present 100 % prevalence with > 80 % severity.12
Not all mutations are deleterious and lead to the death of organisms; in fact, even a perfectly adapted protein undergoes mutations. It’s part of evolution. Some mutations of the nucleotide sequence are silent, when the codon mutates into a synonym codon, while others aren’t. 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 correlated evolution, they are called homo- logues. By comparing the homology between to 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, while if it changes, it could be either conservatively substituted or hypervariable. The former occurs when two amino acids, which present similar properties, occupy the same position, i.e., glutamate and aspartate, while 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 due to 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 conformation. 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 substitution 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 the 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, while acidic and hydrophilic residues are often replaced. Relative frequencies of replacement of residues that differ between the various IAPP variants are listed in Table 1.2 on the facing page (all twenty residues can be found in Figure 3.2 of Ref. 5). Normally, most of the mutations do not effect 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 the sickle-cell anemia, where a polar glutamate has been substituted by a nonpolar valine produces devastating effects,* leading to a completely different quaternary structure. Conversely, myoglobin and hemoglobin have only 20 % of the same sequence, yet share large structural, evolutionary, and functional similarities.2 Thus, with this in mind, discovering which effect the 16 % divergence between human and rodent sequences has 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
Islet amyloid polypeptide (IAPP) is a 37 amino acid peptide, which is secreted by β -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 Ca2 +, and the secretion of either peptide is closely regulated, i.e., the plasma level of IAPP is 1-15 % 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 conservatively substituted residues in green and the hypervariable ones in red, while 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 and 84 % of the primary structure is the same. With the exception of residue 18, the different residues are localized between 20 and 29, which can be seen underlined in the hIAPP primary structure in Table 1.1. Thus, the remaining 16 % seems to determine the capability of the peptide to aggregate through β -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 rIAPP, which most likely doesn’t form β sheets due to the presence of proline, normally known as β -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, and 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
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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, and others seldom, e.g., His/Arg. Replacements involving proline also don’t 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 184.108.40.206). 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
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a Observed replacements in 1572 examples of closely related proteins.20
b Expected replacements obtained from random single-nucleotide mutations.
The first five replacements 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 patients.18 Although histidine and arginine are sometimes classified as basic amino acids,1,2 they have different characteristics, so it’s not surprising that the relative frequencies with which they replace each other is 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 exposed, 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, thanks to the imidazole ring, and thus is 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 primary structure, and is included in a region which presents a transient helix, which seems to be 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 doesn’t occur much due to their different characteristics, although they 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 as what is 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 α -helices thanks to the hydroxyl group in the side chain by forming H-bonds with backbone.5 In monkey IAPP, asparagine is substituted by aspartic acid, which have a high observed relative replacement value, and even though they are polar and can form H-bonds, the latter is normally negatively charged in solution, while the former is neutral.1,2 The interesting residue replacement in the primary structure is position twenty-five. First of all it is, along with residue twenty-eight, the only position that has a proline in the primary structure that doesn’t aggregate, i.e., cat IAPP presents a proline residue in position twenty-nine and is known to aggregate, and 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 1-20) of both hIAPP and rIAPP seem to have a modest helical propensity, while the remaining fraction of the peptide (residues 21-37) 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 20-29 in particular, are hypervariable, and therefore most probably don’t influence its biological function.
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 β -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 β -cell loss. It seems that a β -cell dysfunction is also necessary for the islet amyloid formation; namely improperly processed proIAPP, which has been found to form fibrils and has been found in DM2 islet amyloid deposits. This could take place due to 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 of 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, forming, therefore, a “nucleus” for fibril formation.* In fact, the basement membranes contain heparan sulfate proteoglycans (HSPG), which are 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 secondary 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, through a two-step conformational transition from a largely α -helical to a β -sheet conformation, the peptide forms ordered fibrillar structures.8
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 α -helical conformations, if not at the N-terminus. Nevertheless, single proline residues can fit in long α -helices by distorting the local helical geometry. The five-member ring that defines proline is relatively rigid and drastically limits the φ angle in the Ramachandran plot to ≈ − 60°, where φ is the rotation angle of the peptide unit around the N − C α bond. The secondary structures that are assumed by proline are poly(Pro)I, poly(Pro)II, and type I and type II β -turns. Proline residues prefer reverse turns (Ref. 5, Table 6.5, page 256), which are defined by four residues, of which two are not involved in β -sheets, with a 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 φ angles are − 83° and − 78° for forms I and II, respectively. Proline also plays an important role in structural fibrous 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 the 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, respectively to proline and other residues. The residue is also slightly distorted from planarity; in fact, Δ ω = − 20° to 10°, compared to ω = 0° and 180° for cis and trans conformations, respectively. The free-energy barrier associated to a cis-trans isomerization is 20 . 4 kcal mol − 1, making it a slow conversion, i.e., τ 1 / 2 ≈ 20 min, which is temperature dependent with the rate increasing by a factor
3 . 3 every 10 ◦ C within the normal range. The possibility of assuming a cis conformation that isn’t sterically hindered, also affects the conformational properties such as the radius of gyration and end-to-end distance, which will be illustrated in Section 2.4.3 on page 28.5
Another interesting characteristic of proline is its presence in rapid degradable proteins. Such proteins contain one or more “PEST” regions, which are segments of 12-60 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, and thus limits IAPP deposit in vivo is unknown, and could be something worthwhile investigating.
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 β 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 water, or a “monolayer”, is sufficient for activity of the biomolecule, and is referred to as hydrational water. These water molecules are connected by H-bonds of two different types, those that span the system, and those that don’t. 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 percolation 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 percolation transition could shed some light on why faster aggregation was measured by Kayed et al.10
In aqueous solution, hIAPP has been shown to have an essentially disordered conformation as seen in far UV-CD.10,25 -28 However, it may also assume compact structures27 and a transient sampling of α -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 . 6 Å, 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 structures; in fact, rIAPP adopts structures which are similar to hIAPP prefibrillar states.27 Other studies reveal sampling of α -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 α helical propensity from residues 5-19 and their temperature coefficients indicate such a region from residues 7-22.
The 20-29 decapeptides of the different homologues were studied in detail with regards to their aggregation propensity, and it was shown that the S28-to-P28 substitution strongly reduced the amyloidogenicity.13 Normally, proline residues are both β -sheet and α -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 30-37, which is 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 β -sheets.36
The most astonishing fact regarding amyloidogenesis is the fact that many precursor proteins, about twenty, differ not only in primary structure and size, but also in location. The main objective of this thesis is to observe two very similar polypeptide sequences, being 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 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 GROMACS37 -39 trajectory files. A description of this program has been illustrated in Chapter 2. Certain parameters, i.e., definitions of H-bonds, which are so important for the protein aggregation, and Ramachandran angles for the secondary structure, that have been defined in Chapter. 2, were obtained through trial and error as explained in Chapter 3.
Due to the difficulty in preparing the initial conformation for an unstructured biomolecule, a detailed description how the system was prepared can be found in Chapter 3. A very helpful tool for the investigation of the proper temperature range and thus to local-ize a temperature induced conformational change is the analysis of the percolation transition of the hydrational water that surrounds the peptide. Theories on percolation on infinite systems have been developed, but the actual determination of the percolation threshold, especially for fi-nite systems, required extensive study. This tedious work was based on determining which of the many properties of a biomolecule should be measured for locating the percolation transi-tion. Amongst the various properties that are monitored, the prefered properties are the spanning probability and fractal dimension of the largest cluster. Similar calculations performed on other biomolecules/polypeptides22,40 -42 have also been performed on IAPP, where the break occurs at ≈ 320 K via a quasi-2D percolation 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 K44 can be found in Appendix C.
The Molecular Dynamics Simulation Method is definitely a very powerful tool for investigating 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 = m a. 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 = −k x. Second, that the potential is obtained through pair-wise vector summation. The relationship between scalar potential and a conservative force, as seen in the following equation
illustration not visible in this excerpt
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 δt, lead to new positions. 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 thermodynamical 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 occurs for hydrogen bound to heavy atoms, like oxygen, so the maximum time step is ≈ 0 . 5 fs. In order to consume less computational time, it is possible by applying constrained dynamics, which allow the time step to increase, because the faster vibrations, like those which involve H 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 performed to reproduce thermodynamical properties using computer simulation techniques, and may include vibrational frequencies, other than parameters to reproduce conformational 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 for reproducing a certain property, and are therefore limited to their target of application. An generic functional form can be seen as follows:
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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, which is most often expressed in the common 6 / 12 Lennard-Jones form, and electrostatic potential, which is 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 log N).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, which is a three point simple 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 an 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 Simulations can be summarized by stating that since the motion is continuous, it can be used as a bridge between structures and macroscopic kinetic data, although it is expensive to execute and yields a short time span, requiring a high CPU usage.2
The polypeptide was modeled with MOLDEN v.4.446 in an α -helical conformation and subsequently modified with SWISS-PDB VIEWER v.3.7sp547 through the rotation around a few bonds to enable the creation of the cystine moiety by bringing the two thiol groups of C2 and C7 within 10 % of the equilibrium bond length, (2 . 048 ± 0 . 026) Å.48 SWISS-PDB VIEWER was also used to create an extended conformation of the polypeptide by dragging the Ramachandran angles to accepted values near − 180° for φ (less than − 130°) and 180° for ψ (greater than 140°). These structures were simulated with the Molecular Dynamics suite GROMACS v.3.3.137 -39 using the OPLS-AA/L force field (with 2001 amino acid dihedrals).49,50
The two hIAPP moieties’ molecular weights are 3906 . 33 Da and 3908 . 35 Da, respectively 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 equi- librium Ka 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 − p Ka = log[His] / [HisH+] at pH 7.4 and p Ka = 6 . 04,51 the concentration ratio is 22.9, which yields a net charge of 0 . 0436 e. This p Ka 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 ϵ 2, as it is the most favorable hydrogen bonding conformation.5 As seen in Section 2.1, MD simulations cannot describe bond cleavage, and therefore ionization states in are fixed at the beginning of the simulation. In other words, the protonation state of the residues is kept constant, rather than pH.52 *
Both the α -helical and fully extended (β -strand) conformations of either moiety were minimized with the L-BFGS algorithm†53 and then with the Polak-Ribiere conjugate gradient 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 . 9 nm 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 an additional 1 ns was performed 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 interactions between the termini. The mean values of end-to-end distance between the C α atoms of the first and last residues, referred to as reted, is (0 . 62 ± 0 . 14) nm or less in the four simulations in vacuo of 1 ns each. This structural parameter seems to be the only one which 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 200 ns production run performed at 450 K 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 Lmax, and the radius of gyration, Rg, 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 Rg and reted, in fact, the dielectric screening of the medium reduces the long-range Coulomb interactions, allowing the peptide more movement.
MD simulations have been carried out on four additional conformations per hIAPP moiety§ obtained in vacuo, along with the above-mentioned initial α -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 conformations 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 . 5 fs) using Berendsen thermostat.56 Also a short NPT density pre-equilibration of 100 ps using Berendsen thermostat and pressure coupling56 was carried out before running the equilibration and production runs, using Parrinello-Rahman pressure coupling61,62 and the Nosé-Hoover thermostat,58,59 with time constant for both couplings set at 2 . 0 ps, 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 simulation at constant pressure. The preferred choice is the Berendsen thermostat, as this particular thermostat scales the velocities, thus bringing the temperature quickly to equilibrated 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 barostat61,62 needs to be applied.
Constraints were applied to the water molecules by using the SETTLE63 algorithm, while for the peptide SHAKE64 was applied to bonds involving hydrogen. Long-range electrostatic interactions were treated using smooth particle-mesh Ewald,55,65 with short-range interaction cutoffs set at 0 . 9 nm. 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 α -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.
The protonation states are the same as described in Section 2.2.2, with the exception of the Cterminus 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 production isobaric-isothermal MD simulation 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 which were obtained after an arbitrary pre-equilibration time of at least 50 ns and that presented a C α RMSD of at least 1 . 23 nm from the initial modeled α -helix, as can be seen in Figure 2.1. These initial pre-equilibration 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 minimization and equilibration of the system, the following 500 ns NPT production runs, in which data were collected every 2 . 0 ps, were performed using the Nosé-Hoover thermostat58,59 and the Parrinello-Rahman pressure coupling61,62 with coupling times of 2 . 0 ps. In order 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 SETTLE63 algorithm, while for the peptide SHAKE64 was applied to covalent bonds involving hydrogen. Long-range electrostatic interactions were treated using smooth particle-mesh Ewald,55,65 with short-range interaction cutoffs set at 0 . 9 nm. Periodic boundary conditions were set in all three directions, with no interaction between adjacent images as the box size set at 7 nm and the maximum distance between heavy atoms, Lmax, being no larger than 5 . 5 nm.
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 angle, torsion angles, and the Coulomb and
(a) Red. hIAPP 310 K - initial vs α-helix
(b) Red. hIAPP 310 K - after 10 ns vs α-helix
(c) Ox. hIAPP 310 K - initial vs α-helix
Figure 2.1: Comparing hIAPP initial conformations. The white ribbons show the initial α-helical conformation which was simulated at 350 K as described in Section 2.2, while the magenta ribbons show the random conformation obtained after hundreds of nanoseconds, which were used as initial conformations for the 500 ns production run at 310 K and 330 K analyzed in Chapter 5. van der Waals interactions between atom pairs describe the potential energy of the system.2 The Coulomb term is therefore 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 Lysozyme66 and A β 4267 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, qot,wasscaleddown to neutrality, qst,bysubtractingthepartialscaledcharge, qi,withtheappropriatesigngivenbythe ratio qt/|qt| from the initial partial charge, qoi,ascanbeseeninthefollowingequations:
illustration not visible in this excerpt
where the partial charge needed for the charge scaling calculation, qpi,isobtainedbymultiplying the total charge by the contribution of each atom i to the absolute total charge given by the ratio ∑ n
qoi/ i =1 |qi|,ascanbeseeninthefollowingequation:
illustration not visible in this excerpt
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, due to the difficulty in parametrizing the backbone φ and ψ 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 original unscaled charges, should be negligible compared to the forces involved with the nonbonded interactions governing the secondary structure. In fact, considering a Bland-Altman plot72 of the Coulomb potential comparing first the effect of different charges on the same structure, and then between independent runs with the different neutralizing 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 mM sodium chloride concentration to neutralize the charge (NACL), which is obtained by adding 33 chloride anions and 31 sodium cations randomly.
illustration not visible in this excerpt
The Bland-Altman plot72 is normally used in medicine to test the reliability of new clinical measurements compared to old ones. Calculating the correlation coefficient is not enough, as it may be misleading; in fact, two methods that have been studied to measure 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 correlation coefficient, rxy, in Figure 2.2 is between 0 . 97 to 0 . 99, but that isn’t surprising, since the electrostatic potential is calculated for the trajectory with the same (VS) charges used for the 30 ns MD simulation runs, then the potential is recalculated with the other charges (VO), 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 between two charges qi and qj separated by a distance rij, is given by the following equation:
illustration not visible in this excerpt
where f is the electric conversion factor equal to 138 . 935 485 kJ mol [Abbildung in dieser Leseprobe nicht enthalten]>.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., [Abbildung in dieser Leseprobe nicht enthalten] , while the ordinates show the difference between them, Δ VS,O = VS − VO.* If the data were truly independent, the difference between the two sets would be zero, which is not the case. The data has 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 σ (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 Δ VS,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 preceding 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, VD, compared to opposite partial charges distributed on the SPME grid, VG, and neutralizing charges given by an NaCl solution at physiological ionic strength 150mM, VP. As can be seen in the left panels in Figure 2.3, the correlation between the electrostatic potential of parallel runs is uncorrelated, with rxy between 0 . 35 and − 0 . 17, so the Bland-Altman plots in the left panels, should also be uncorrelated. Unfortunately, only comparison of the neutralizing methods with the original charges are uncorrelated, as seen in Figures 2.3e and 2.3f, where the relative difference between VG and VP 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 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
illustration not visible in this excerpt
(e) Ox. hIAPP Bland-Altman Plot for NACL
(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 right panels the Bland-Altman72 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 mM ionic force for (e) oxidized and (f) reduced hIAPP. the charge of each individual group. The atoms still belong to charge groups, but the groups may deviate from neutrality due to 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 φ and ψ 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 angles 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. Plotting the regions relative to α -helix, β -strands, and poly(L-proline), and a cutoff region 60° × 60°, comprising the regions in the Ramachandran plot which 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 which 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 more than another than to the peaks, 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 β -strands than the other runs, the contribution to the secondary structures for the independent 30 ns trajectories doesn’t differ significantly. If the φ and ψ 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 φ and ψ of the three runs diverge slightly in some runs, with some of the points which drift 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, amongst which the cutoff, and cannot be solely attributed to the charge scaling. In fact, the standard deviation of the mean, which indicates 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°. 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 α and H α, which results in a slightly larger dipole (3 . 98 D vs. 3 . 5 D). The neutralizing charge is distributed throughout the entire peptide, so either two charge distributions for the peptide bond is not zero, making the calculation of the dipole pointless for comparison since it depends on the Cartesian coordinates of the atoms.* A systematic error in the calculation of the dipole of the peptide bond could influence the overall secondary structure, but it seems that there is no significant difference between the characteristic Ramachandran plots for helical and extended conformations seen in Figure 2.7 on page 24. Due to this uncertainty in the calculation of the dipole, scaled charges shouldn’t be used to calculate IR-spectra, since it depends on the variation of the dipole moment,2 but it should be irrelevant for MD simulations.
Albeit these 30 ns MD simulation runs at 350 K and 1 bar (NPT) are relatively short for statistical purposes, it is possible to conclude that the difference in secondary structure maxima may or may not be induced by the scaling of the charges, but it is certain that the fluctuation of the system is preponderant over any slight effect the scaling of the charges may induce. In fact, such scattering is in line with the scattering of different independent simulation runs.
These data were obtained with uncapped IAPP fearing that the systematic error introduced was larger than with the amide capped system, since this polypeptide is much smaller than Lysozyme as
illustration not visible in this excerpt
Figure 2.3: Each subfigure shows the correlation between two data sets in the left panels and in right panels the Bland-Altman72 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 mM ionic force for (e) oxidized and (f) reduced hIAPP.
studied by Oleinikova et al.,66 but the formation of salt bridges tend to bias the trajectories causing short distances between charged groups, whether they are the charged termini end-to-end distances or the charged carboxyl group and R18 in rIAPP. Hence, subsequent runs with amide capped Ctermini were performed, where the partial charges for hIAPP are scaled by 2 . 2 % and 3 . 0 % for rIAPP. A first approximation of the error on the electrostatic potential for the capped rIAPP, which presents a charge of 4 e, is 4 . 2 % (as seen in Footnote † on page 16),70 but as seen for the uncapped hIAPP, it might also be as small as the percentage of the charge scaling, i.e., 2 . 2 % and 3 . 0 % for hIAPP and rIAPP, respectively. Moreover, A β 42, which is a 42 residue 627 atom polypeptide bearing a similar size of IAPP, has also been scaled to neutrality from 3 e without apparent effects on the force field to reproduce system properties.67
(a) Ox. hIAPP Ramachandran Plot 60° × 60° at 350 K (b) Ox. hIAPP Ramachandran Plot 80° × 80° at 350 K
(c) Red. hIAPP Ramachandran Plot 60° × 60° at 350 K (d) Red. hIAPP Ramachandran Plot 80° × 80° at 350 K
Figure 2.4: (a)-(b) Oxidized and (c)-(d) reduced hIAPP Ramachandran plots relative to the helical region enclosed by the dashed red line, − 100° ≤ φ ≤ − 40° and 10° ≤ ψ ≤ − 50° , for (a) and (c), and − 110° ≤ φ ≤ − 30° and 20° ≤ ψ ≤ − 60° , for (b) and (d) for NACL, SPME, and SCAL runs. The circles indicate the mean value of the φ and ψ angles for the data within the dashed red square, with the area of each circle proportional to the contribution of each trajectory to the data distribution. The error bars indicate the standard deviation of the mean.
illustration not visible in this excerpt
Figure 2.5: (a)-(b) Oxidized and (c)-(d) reduced hIAPP Ramachandran plots relative to the isolated β- strand region enclosed by the dashed red line, − 175° ≤ φ ≤ − 115° and 125° ≤ ψ ≤ 185° , for (a) and (c), and − 185° ≤ φ ≤ − 105° and 115° ≤ ψ ≤ 195° for (b) and (d) for NACL, SPME, and SCAL runs. The circles indicate the mean value of the φ and ψ angles for the data within the dashed red square, with the area of each circle proportional to the contribution of each trajectory to the data distribution. The error bars indicate the standard deviation of the mean.
illustration not visible in this excerpt
Figure 2.6: (a)-(b) Oxidized and (c)-(d) reduced hIAPP Ramachandran plots relative to the poly(Pro) II region enclosed by the dashed red line, − 115° ≤ φ ≤ − 55° and 105° ≤ ψ ≤ 165° , for (a) and (c), and − 105° ≤ φ ≤ − 45° and 95° ≤ ψ ≤ 175° , for (b) and (d) for NACL, SPME, and SCAL runs. The circles indicate the mean value of the φ and ψ angles for the data within the dashed red square, with the area of each circle proportional to the contribution of each trajectory to the data distribution. The error bars indicate the standard deviation of the mean.
illustration not visible in this excerpt
Figure 2.7: Ramachandran plots for the oxidized hIAPP (a) SCAL, (c) SPME, and (e) NACL runs, and for the reduced hIAPP runs (b) SCAL, (d) SPME, and (f) NACL. The green circles indicate the theoretical values calculated for rigid spheres and van der Waals radii.74,75 The occurrences have been normalized and are relative to the highest peak found in (b).
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