Dissertation Adam

7/31/2019 Dissertation Adam

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UNIVERSITEIT VAN AMSTERDAM

A Coarse-Grained Model for Self-Assembling collagen-silk-like

block-copolymer

Bruno Barbosa Rodrigues

Advisor: Peter G. Bolhuis

Co-Advisor: Marieke Schor

July 2009


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Abstract

We present the results of the sequence design of the adapted off-lattice minimalist model based on

the original Head-Gordon (HG) for a monodisperse, biodegradable, biocompatible and hydrophilic

collagen-like sequence. This sequence is part of a block copolymer made of two hydrophilic collagen-

like blocks flanking a hydrophobic silk-like block. We start with atomistic simulations of short pep-

tides to extract the bond distances, bend and dihedral angles distributions to fit the coarse-grained

(CG) force field (FF) and adapt the HG model for this collagen-like sequence. Due to the high con-

centration of proline and charged groups at low pH in the sequence, different distributions were found

for the dihedral angles according to the relative position of proline in the chain. Thus, we extended

the original three-letters minimalist model combined with a previous adapted shifted and rescaled

non-bonded potential developed for the silk-block sequence. We compared the results of the radius

of gyration (Rg) for different number of residues with the experimental value measured for a 400

residues long sequence, coming up with a scaling law between the R g and the number of residues in

the collagen-like sequence. We concluded that the exponent is close to the Flory exponent.

Keywords: Collagen-silk-like block copolymers, protein fibers, Molecular Dynamics, Coarse-

Grained model.


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Contents

1 Introduction p. 1

2 Methods p. 4

3 Results p.13

4 Conclusions and Future Perspectives p.19

Acknowledgements p.20

Appendix A -- Dihedral Angles p.21

Bibliography p.23


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1 Introduction

Protein based block copolymers that form fibers upon a certain stimulus (e.g. change in pH)[16]

are potentially very useful as biocompatible nanomaterials. One example is a block copolymer made

of two hydrophilic collagen-like blocks flanking a hydrophobic silk-like block. The collagen block

is responsible for limiting the growth direction of the silk block and drives it to form fibers with

improved transversal strength. The sequence of the collagen block is chosen in a way that, unlike

the most common gelatin in nature that forms a gel in the presence of water, it remains soluble and

unstructured under various conditions of pH and temperature. Previously, a coarse grained model

of the very regular, highly structured silk-like block has been developed [14]. However, a different

strategy is needed to develop such a model for the unstructured collagen-like block.

In the first section of this chapter we give an overview on the biocompatible materials and their

applications; the second section is dedicated to the protein polymers; the two last sections are ded-

icated to introduce the computer simulation techniques as tools to understand and predict proteindynamics, the limitations and possible solutions, ending up with an overview of this work in the last

section.

1.1 Biocompatible Materials

Nature produces a wide range of different materials, but all of them for its own purposes, like

actin, which is the main constituent of cytoskeleton, or collagen, the major component of extracel-

lular matrix. Genes can encode identical amino acid sequences (also called primary structures) with

absolute control over molecular weight, composition, sequence, and stereochemistry. Control of this

protein production can lead us to build materials that could fit human desires[4] such as chemo-

mechanical fibers[5], tissue engineering [6, 7] and drug delivery [8, 9].

Biocompatible materials are synthetic or natural materials intended to interface with biological

systems in intimate contact with living tissue. One way to build such high value materials is via ge-

netic and protein engineering, both components of a new polymer chemistry that provide the tools for

producing macromolecular polyamide copolymers of diversity and precision far beyond the current

capabilities of synthetic polymer chemistry.


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1.2 Protein Polymers

Control and understanding of the behavior of biocompatible materials requires one to look deep

into the atomic compostion of those materials. The function of a protein is intrinsically connected to

its spatial conformation (or tertiary structure) and the process that drives the protein towards this stateis called protein folding.

Proteins can be designed as blocks of repetitive amino acid sequences, also called block copoly-

mers. This term was introduced by Capello in 1990s [2] who built diblock copolymers containing

silk-like and elastin-like amino acid sequences. From that time on, many other block copolymers

have been produced [3], coming from diblock to multiblock sequences. The self-assembly charac-

teristic of the proteins can be used to tune organization in the molecular level [10], wich can build

organized nanoscopic objects that end up in macroscopic materials with interesting properties.

Figure 1.1: Triblock copolymers consisting of a hydrophobic pH-responsive, silk-like block flanked

by hydrophilic, non-responsive collagen blocks self-assembling into m long fibrils. The collagen

block limits the assembly direction of the silk block [11].

The system under study on this dissertation is a collagen-like polypeptide [12] that flanks a silk-

like sequence [13] which self-assembles into a roll forming stacks under low pH [14] (fig. 1.1).

The triblock was produced experimentally by gene encoding of the yeast Pichia pastoris [15, 16]. The

collagen-like part [12] has a hydrophilic sequence that, although the normal collagens that form gels,

it remains soluble under many conditions of pH and temperature. With this random characteristic, the

collagen-like part can drives the silk-block towards the growth direction forming biocompatible fibers

that can have improved their transversal strength upon a stimulus (e.g. a change in pH).

1.3 Computer Simulations

During the last two decades, computer simulations have gradually been recognized as giving

complementary information about the properties of such new materials or to understand conforma-tional transitions in proteins [17, 18]. While most of the relevant dynamics in proteins, like folding

processes, occur on time scale of miliseconds and involve large molecular aggregates, atomistic simu-


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lations can only address hundreds of nanoseconds in simulations for small proteins in explicit solvent,

which means at least four and one orders of magnitude lower in time and in degrees of freedom, re-

spectively.

In this framework, many techinques were developed to overcome the system size and simulation

time. Simplification of the system under study by integrating out details that are not actually important

to the overall result can lead us to address longer length and time scales. In this work we focused on

adapting the Head-Gordon (HG) [25, 26] model to apply for the collagen-like part of the collagen-

silk-collagen block-copolymer. With this improvement, it is possible to simulate big systems long

enough to predict the properties of the collagen-like block, and understand its role on driving the

growth direction of the silk-fiber.

1.4 Outline of this Dissertation

The HG, developed to study protein floding and aggregation, was adapted for the collagen-like

sequence in such a way that the dihedral angles are treated either with a cosine and a harmonic

expansion. The resulting fit of the parameters can be combined with previous results for the silk-

like block copolymer in order to enable a complete description of the collagen-silk-collagen block-

copolymer.

In Chapter 2 we describe the methods in molecular dynamics applied for the system under study,

as well as details concerned to the simulation procedure. We also introduce the adapted Head-Gordon

model to coarse-grain the polypetide lumping together an entire amino acid in one bead. In Chapter

3 we investigate the results of the atomistic as well as the coarse-grained simulations, present the

output distributions that were used to fit the adapted HG model and show the scaling law between

the radius of gyration and the number of residues, appearing to be in very good agreement with the

experimental value. Thus, in Chapter 4 we conclude the work and give the future perspectives.


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2 Methods

In this chapter we discuss the atomistic and CG Molecular Dynamics (MD) simulation te-

chiniques which were used to study the collagen-silk block-copolymers. We performed the atom-

istic simulations using GROMACS version 4.0 [30], which provided the distributions for the bond

distances, bend and dihedral angles between the three and four consecutive C atoms respectively.

With these parameters, we fitted the adapted HG model that permitted the achievement of longer time

and length scales. The CG simulations were performed with the CM3D code[31].

2.1 Molecular Dynamics

The key of MD simulations is to integrate Newtons Law of motion for the N interacting particles

md2ri

dt2=

j=iFri j (2.1)

with accuracy and in such a way that the pairwise additive interactions do not scale as N2. Speed

up of the evaluation of both short-range and long-range forces is possible and for that we have some

techniques. Following the standard procedure to calculate the force by the derivative of a potential,

we can integrate Newtons equation of motion and many algorithms are available. A very simple

is the leap-frog integrator [32, 33] which is a Verlet-like second-order algorithm that evaluates the

velocities at half-integer time steps and uses these velocities to compute the new positions:

r(t+t) = r(t) +tv(t+t/2) (2.2)

v(t+t/2) = v(tt/2) +tf(t)

m(2.3)

The more sofisticated Gear predictor-corrector algorithm falls into the general finite difference

pattern, where the estimate of the positions, velocities etc. at time t+t may be obtained by Taylor

expansion about time t. These values are estimated and do not represent the true trajectory. After

calculating the forces at the new position rp(t+ t), the trajectories are corrected and the predicted

step is fed with the new information to iterate the corrected trajectory and rc(t+t) is now a better

approximation to the true position.


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2.2 Atomistic Models

As described in the previous section, the key point of MD simulations is to solve Newtons equa-

tions of motion. But usually, the systems are defined by the potential energy rather than the forces,

which can then be easily calculated by the negative gradient of the potential: F(ri j) =

V(ri j).For that, many potential energy functions were developed to simulate protein systems, the so-called

force-fields (FF) [35]. The basic idea of a FF relies on mapping all the possible physical interactions

in the system and put them into a potential, like presented in eqs. 2.4 to 2.9:

V = Vnoncov +Vcov = (VLJ+VC) + (Vbond +Vbend +Vdih) (2.4)

VLJ(ri j) = 4i jC(12)i j

i j

ri j 12

C(6)i j

i j

ri j 6

(2.5)VC(ri j) =

1

40

qiqj

rri j(2.6)

Vbond(ri j) =1

2k

(bond)i j

ri jbi j

2(2.7)

Vbend(i jk) =1

2kbendi jk

i jk

0i jk

2(2.8)

Vdih(ijkl ) =1

2[C1(1 + cos()) +C2(1 cos(2))

+ C3(1 + cos(3)) +C4(1 cos(4))] (2.9)

where the potential is divided in bonded (or covalent) and non-bonded (non-covalent). The non-

bonded interactions contain a repulsion term, a dispersion term, and a Coulomb term. The repulsion

and dispersion terms are combined in the Lennard-Jones (or 6-12 interaction). In addition, (partially)

charged atoms act through the Coulomb term. Bonded interactions are based on a fixed list of atoms.

They are not exclusively pair interactions, but include 3- and 4-body interactions as well. There are

bond stretching (2-body), bond angle (3-body), and dihedral angle (4-body) interactions given by eqs.

2.7, 2.8 and 2.9, respectively.

There are many FF codes available nowadays, the most common are: AMBER [36], CHARMM

[37], GROMOS [38] and OPLS-AA [39]. Their potential energy is parametrized against experiments

and ab initio quantum mechanical calculations.

2.2.1 Setup atomistic simulations

The Atomistic simulations can reveal several details of the system, as it treats both the proteinunder consideration and the water. However, it is very difficult to reach long time and length scales

within this framework. In this case, the atomistic simulations were carried out only to extract the pa-


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that time on many approaches emerged. The CG models evoluted towards different directions, that

differ basically in the relation between the complexity of the representation versus the complexity of

the parametrization. Harmonic models represent the system by beads (usually one per amino acid)

connected by elastic springs [21], and are used basically for the analysis of the principal modes [22],

requiring a previous knowledge of an equilibrium reference configuration. Go-like models [23] alsorequire an a priori knowledge of the native state and lack on representing the most intriguing fact of

protein folding: the dependence on the primary sequence. A lower level of reference dependence can

be found in the Head-Gordon model [25], which represents each amino acid as one bead. Two-bead

models [27] were developed adding a second bead on the centroid of the sidechain, increasing the

independence with a reference configuration but increasing the complexity of the energy terms and

inserting correlations on dihedral angles. Four-six bead models [28, 29] represent the sidechain as

one bead but explicitly consider the coordinates of the three heavy atoms of the backbone.

We chose the Head-Gordon (HG) [25] model to coarse-grain the collagen-like block, as it was

successfully applied to the silk-like sequence before [14]. In this model, in constrast with Go [23]

model, we do not need to know anything about the tertiary structure of the native state. However, we

need to face the more difficult aspect of the protein folding problem, namely its dependence on amino

acid sequence. The C atoms trace are taken to represent the protein backbone and the structural

details of amino acids and aqueous solvent are integrated out and replaced by effective bead-bead

interactions.

2.3.1 Head-Gordon Model

The original Head-Gordon (HG) model is an improvement of previous efforts of Thirumalai and

coworkers [53] that is more general to helical, sheet and / protein topologies. The 20-

letter amino acid sequence is converted to a three-letter code defined by the flavors: hydrophilic (L),

hydrophobic (B) and neutral (N). The idea of describing an amino acid as one bead can be visualized

in the figure below:

Figure 2.2: Schematic description of an amino acid as a bead in the CG model.


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The force field in the original HG model is defined as:

H =

1

2k(0)

2

+ A(1 + cos) +B(1 cos) +C(1 + cos3) +D1 + cos+

4 (2.10)+

i,ji+3

4HS1

ri j

12S2

ri j

6

where we have the bond angle between three consecutive beads with 0 =105 being the equilib-

rium angle and k =20H/rad2. The dihedral angle between four consecutive beads can assume

different conformations depending on the region to be described, with the constants A, B, C and D

defining the shape of the distribution. The LJ potential determines the attraction-repulsion between

the beads of size with the three flavors i and i separated by ri j: B-B interactions are attractive and

represented by S1 = S2 =1; S1 =1/3 and S2 =0 apply for L-L and L-B interactions; and N-L, N-B

and N-N interactions have the constants S1 =1 and S2 =0. In the original HG model the bond lengths

are constrained by the RATTLE algorithm [54]. The non-bonded potentials are plotted in the Figure

below:

Figure 2.3: Non-bonded potential between neutral, hydrophilic, hydrophobic and proline (treated as

neutral) amino acids.

2.4 Adapted HG model

Based on the original Head-Gordon model and the adapted version for the silk part [14] of

the block-copolymer, we developed a four-letters minimalist model for the collagen-like block: hy-

drophilic (L), hydrophobic (B), neutral (N) and proline (P), where we defined proline as a separated


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Figure 2.4: Full collagen sequence transcription from the 20-letters amino acid code to the adapted

four-letters minimalist HG code based on table 2.2.

flavour, due to its key role on the stiffness of the dihedral angles. In the table 2.2 below we show the

sequence mapping between 20-letter amino acid and adapted CG four letter code, which generates a

minimalist full sequence according to the fig. 2.4.

Name 20 4 Name 20 4

Glycine GLY / G N Aspargine ASN / N L

Alanine ALA / A B Proline PRO / P P

Glutamic Acid GLU / E L Glutamine GLN / Q L

Lysine LYS / K L Serine SER / S N

Table 2.2: Sequence mapping between 20-letter amino acid and adapted CG four letter code.

The FF also needs to be modified to cover the new changes in the dihedral angles, bond distances

(which are no longer constrained) and non-local interactions between beads. The new FF is given by

the equations 2.11, 2.12 and 2.13 below:

Hadap = b

1

2kb (bb0)

2 +

1

2k(0)

2

+

Vweak() +Vsti f f()

(2.11)

+ i,ji+3

4HS1

ri j 0

12S2

ri j0

6

Vweak() = h

6

k=0Akcosk()

(2.12)

Vsti f f() = B01

2hB1 (0)

2 (2.13)

where now the bond distances are explicitly described by the spring potential, as CM3D package used

for the CG simulations employs a reversible multiple time-step integrator, the stiffness is given by

kb = 33h and b0 = 3.84A consistent with the measured all-atom CC distance distributions. The

bond angles have the same treatment as in the original HG model, with the parameters given by k =

20h

and 0 = 105 extracted from the atomistic simulations. The parameters A

k, B0, B1 and 0 set

the dihedral angles between four subsequent C-atoms that show either periodic behaviour with two

minima (weak) or harmonic with one minima (stiff) depending on the four beads sequence, as the


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Figure 2.5: Shifting the Lennard-Jones potential has the effect of shortening the range of the potential.The position of the nearest neighbors and the second nearest neighbors between strands in the silk part

are given by the dashed vertical lines. In the traditional L-J potential the second nearest neighbours

still feel the interaction.

new flavor (proline) plays an important role on the stiffness of the dihedral angle. The L-J potential

is shifted and scaled in order to coincide with the previous model optimized for the slik-part [14],

where the scaled parameter sets the range of the interaction and 0 shifts the potential to match

the size of the bead, as can be seen in the fig. 2.5. The strength of the non-bonded interaction kLJ =

4h was previously optimized for the silk part by M. Schor [14] by comparing the potentials of meanforce (PMF) from steered MD (SMD) simulations of the atomistic and the coarse-grained model. The

PMFs from SMD were calculated following the method of Park and Schulten [63, 64].

Simulations with CM3D were carried out for different sequence sizes. We started with the 30

residues structure built in MolMol and kept the positions of the Catoms. From this basic structure

we built sequences of 45, 60, 75, 90, 120, 150 and 200 beads by sticking together the pieces of short

peptides. We used VMD to manipulate the PDB files of the different sizes of collagen-like sequence.

Then the sequences were put in a cubic box (as the CG simulation employs implicit solvent, the shapeof the box is not relevant)with periodic boundary conditions in all x, y and z directions. The time step

used is 2fs.

We started relaxing the protein at low temperature. The first simulation was carried out with

velocities given by a Boltzmann distribution, at 30K for 1ns in a NVT ensemble with Nose-Hoover

chain with 4 units and time step of 1.6ps. Then we performed further 1ns simulations based on

previous velocities and positions and raising gradually the temperature up to 60K, 100K, 200K and,

finally, 300K. Then we equilibrated the system for 1ns in 300K and started a 50ns simulation to

sample the averages. The 1ns simulations were carried out in a local machine and took no more than

30 minutes at most for the 200 residues sequence. For the 50ns long we simulated on LISA cluster


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with 1 processor 2 Intel Xeon 3.4GHz and took at most 20 hours for the longest sequence (200 beads).

2.5 Order Parameters

The configuration space is very high-dimensional and a visualization of its direct quantities is

meaningless. To overcome this problem, we need to project the phase space in one-dimensional

representations. They can monitor the (un)folding transitions, characterize native and unfolded states

and some of them can directly be compared to experimental measurements.

Since a protein chain is not a regular object and because it is subject to dynamic structural equi-

librium that involves motion, it is necessary to consider a statistical measure of a chain size. Then the

end-to-end distance is a key description for the statistical behavior of the chain.

A commonly used order parameter is the Root Mean Square Deviation (RMSD) from a refer-

ence structure, usually obtained experimentally by X-ray or NMR. RMSD was calculated minimizing

under rotations and translations and is defined as:

RMSD =

1

M

N

i=1

mi|ri rre fi |

2

12

(2.14)

A second order moment about the mean chain position is the radius of gyration. It describes the

overall spread of the molecule and it is defined as the root mean square distance of the collection ofatoms from their common centre of gravity:

Rg =

1

M

N

i=1

mi|ri rcm|2

12

(2.15)

where rcm denotes the position of center of mass of the protein. This measure gives a valuable way to

compare our CG method with the experimental data available for the collagen-like system.

Root Mean Square Fluctuation (RMSF) is a measure of the deviation between the position ofparticle i and some reference position.

RMSF =1

T

T

tj=1

ri(tj) ri

2(2.16)

where T is the time over which one wants to average, and ri is the reference position of particle i.

Typically this reference position will be the time-averaged position of the same particle i, ie. ri. Note

that, instead of averaging over the particles (as in RMSD), RMSF averages over the simulation time,

giving a value for each particle i, usually the C atoms.


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3 Results

The results of the MD simulations described in the chapter 2 are presented here. We analyse the

bond distances, bend and dihedral angles and order parameters obtained from the Atomistic simu-

lations and use them to fit the CG adapted model for the collagen-like block copolymer. Thus, we

present the improved CG model and compare the results with the previous atomistic simulations.

Lastly, we summarize the results obtained from the adapted model analysing the order parameters.

3.1 Atomistic Simulations

Atomistic simulations of the short peptides provided enough information about bonds, bends and

dihedral distributions, while the 30 residues collagen-like simulation revealed several details about

the dynamics of the protein. Bond distance distributions (see fig. 3.1 (left)), strongly peaked around

3.84 0.12A representing the distance between C- atoms of subsequent amino acids, justify theuse of a stiff harmonic potential for the bonds. Also based on the distributions calculated from the

atomistic simulations, the rather narrow flexibility of the bend angles (see fig. 3.1 (right)) justifies the

same treatment as in the original HG model. The dihedral angles between four subsequent C-atoms

show periodic behaviour with two minima (flexible) or harmonic with one minima (stiff) leading to

an expansion of the model in such a way that these details can be taken into account.

Figure 3.1: Bond distances (left) and bend angles (right) distributions obtained from an all-atomsimulation of the short peptide A1.


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Analyzing the dihedral distributions shown in the fig. 3.2, we can see three examples of rather

different potentials that were fitted either with cosine expansion or harmonic potentials depending on

the position of proline in the dihedral angle.

Figure 3.2: Negative Logarithm of the dihedrals distibutions of the sequences LNPL (left), PNLP

(center) and LLNL (right) obtained from an all-atom simulation of the short peptides in the minimalistfour-letters description. We can easily see how the distribution changes according to the relative

position of the Proline amino acid in the sequence.

After obtaining all the required parameters for the CG model, we present the results for

the 30 residues peptide which was simulated for 60ns to have a reference system and com-

pare with the new minimalist model. This sequence was simulated under the same procedure

adopted for the small pieces of the collagen-like sequence. We chose an intermediate sequence

|GNEGQPGQPGQNGQPGEPGSNGPQGSQGNP|to sample as many different amino acids as possible and cal-

culated the order parameters (see fig. 3.3) for the RMSD, Rg and RMSF.

Figure 3.3: RMSD (left), Rg (center) and RMSF (right) calculated for a 60ns simulation of the 30

residues sequence. It can be observed that RMSD reaches a plateau after 45ns and also R g does not

change its value, but instead remains flat during the whole simulation. The xaxis in the RMSF

graphic represents the C atoms and it can be seen that none of the atoms is more likely to find a

more stable position related to the others.


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Figure 3.4: Comparison between the Atomistic short peptides and 30 residues CG simulations for

the negative logarithm of the dihedrals distibutions of the sequences LNPL (left), PNLP (center) and

LLNL (right). It is observed that the fitting for PNLP and LNPL sequences are good enough but the

agreement for the LLNL potential seems to show some histeric hindrance, or maybe the phase space

was not sampled enough.

3.3 Analysis of the collagen-like block

The analysis of all the dihedral angles in the atomistic simulations showed a strong sequence-

dependence of the distributions, leading us to adapt the original Head-Gordon model to achieve a

more accurate description of our collagen-like proteins. From our simulations, we concluded that

the high concentration of proline randomly spread in the sequence plays an important role on the

stiffness of the dihedral angles between four consecutive C and therefore proline must be taken

into account as a separated flavour. In this way, we characterized the dihedrals distributions using

four flavours: hydrophilic (L), hydrophobic (B), neutral (N) and proline (P). The relation between the

amino acids present in the collagen-like and their four letters minimalist codes are given in Table 2.2.

After taking the negative logarithm of the dihedral distributions, we fitted them either with cosine

expansion (6k=0Akcos

k()

) or parabolic function (B012B1 (0)

2) according to the position of

the proline. The results of the observations of the dihedrals stiffness can be summarized in the table

below, whegre the distributions were divided in groups according to their main characteristcs. The

first group, where the proline is not present, shows a flexible and smooth logarithmic distribution

of the dihedral angles. The second group has a proline at the third position, and it is observed that it

makes the dihedral angles stiff and the logarithmic distribution is therefore very stiff with one minima.

The third group has a proline at the second position and, despite of its stiffness, it still can be fitted

by a cosine expansion. The fourth and last group has proline in one or both flanks, and it makes the

dihedral angles very flexible and the distribution is, therefore, smooth.

Analyzing the table 3.1 and the figs. 3.4 above, it is possible to infer some conclusions about the

role that Proline plays in the dihedrals distributions:

1. Proline makes the dihedral angles stiffer when it is on the second or third position from the first


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3.4 Dependence of the Rg with the number of residues

We then calculated the radius of gyration from the output of a CG simulation runned in CM 3D

for many collagen sizes and plotted in fig. 3.6 a logarithm scale curve for Rg as a function of the

number of residues. There is a very good agreement with the experimental value for 400 residueswithin the statistical error, which serves to validate the adapted HG model for the collagen-part block-

copolymer. Calculating the slope of the curve, we can see the dependence of the radius of gyration

with the number of molecules to be Rg = 1.391(N)0.528 in good agreement with the Florys exponent

(0.583) [62] in a good solvent (which means that the particles affectively repel each other), where N

denotes the number of residues.

Figure 3.6: Logarithm dependence between the radius of gyration (in nm) and the number of residues

on the collagen-like sequence. The simulation values are plotted with the experimental result for 400

residues sequence and fitted with a linear function.


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4 Conclusions and Future Perspectives

Finally, we can conclude that the adapted HG model developed for the collagen-like protein

can predict the experimentally observed order parameter value. Therefore, as stated in the begin,

it is confirmed that the high concentrations of proline and the charged/hydrophilic residues in the

sequence play an important role on avoiding the structure to folds into any specific state, but instead

retains its randomness. The radius of gyration has a very good agreement with experiments, behaving

in a logarithmic dependence with the number of residues and providing a good value for the Flory

expoenent.

In the future, this adapted collagen-like CG model will be combined with the adaped CG model

previously developed for the silk-part to be applied for the whole collagen-silk-collagen block copoly-

mer. Thus, it will enable us to study the effect of the collagen-like on silk-like block folding and

self-assembling.


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Acknowledgements

Many people contributed to the accomplishment of this work. I pay here special attention to some

of them, not neccerily the most important, but the ones who were essential, in precise moments, to

consolidate this achievement.

First of all I thank God, for having given me the ability to learn and understand, always supplying

me with vitality to face the challenges and keeping up achieving my goals, never allowing me to

surrender, but instead keeping me humble.

I thank my supervisor Peter Bolhuis, for giving me the opportunity to start this Msc. project at the

University of Amsterdam. I also thank Marieke Schor, who co-supervised me during the project, and

made my life much easier with your expertise on protein folding and coarse-grained simulation. I also

thank the Molsim group, Bernd, Francesco, Anna, Grisell, Murat, Wolfgang, Rosanne and Zerihum,

my friend, with whom I had a great time in the course of this project. I also acknowledge Sara cluster

for the computer power provided for the simulations.

I also thank my friends in Amsterdam Pedro, Dimas, Max, Igor, Raquel, Vinicius, Girry, Anthony,

Adrien, and many other students, thanks you all for the great time we had here in Amsterdam. To

my friends in Lyon Roberto, Diego, Rodrigo, Franck, Dorian, Jakub, Alex, Aion, Jana, that made that

short stay in France one of the best periods in my life.

I would like to thank the coordinators of the AtoSim Programme for accepting my application to

this course and Erasmus Mundus for the scholarship.

Finally, to all of them who contributed directly or indirectly to the accomplishment of this project.

Thank you very much!


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APPENDIX A -- Dihedral Angles

Here we present all the dihedral angles distributions analized in the collagen-like sequence as

well as the fitting parameters. It can be observed that some of them have almost the same behavior

and can be tabulated in four categories defined by the position of the proline. These groups are shown

in the table 3.1. All the sequences are listed in the figures subsequent, with the fitting parameters atthe captions.

Figure A.1: The fitting coefficients are NNLN: A0=-3.34, A1=1.51, A2=2.19, A3=-1.22, A4=-3.34,

A5=-0.69; LLNL: A0=-3.31, A1=-1.99, A2=-0.64, A3=2.17, A4=-0.14, A5=-0.69; NLLN: A0=-4.25,

A1=0.69, A2=2.27, A3=-0.29, A4=-1.32, A5=0.36.

Figure A.2: The fitting coefficients are BNNL: A0=-3.98, A1=0.63, A2=-0.42, A3=-1.98, A4=0.70,

A5=0.89; NLNB: A0=-1.61, A1=-0.33, A2=-4.59, A3=2.08, A4=1.73, A5=-0.81; PBNL: A0=-2.68,

A1=0.08, A2=1.72, A3=0.55, A4=0.33, A5=-0.11.


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Figure A.3: The fitting coefficients are LNPL - NNPL: B0=-5.81, B1=0.051, 0=-50.24; NNPN:

B0=-6.73, B1=0.23, 0=-109.86; NBPN: B0=-6.54, B1=0.28, 0=-115.27.

Figure A.4: The fitting coefficients are BPNL: A0=-2.34, A1=-2.73, A2=-1.08, A3=10.75, A4=-12.81,

A5=5.07; LPNL - LPNN: A0=-2.33, A1=-0.23, A2=-2.84, A3=-0.02; LNLP: A0=-3.73, A1=-2.24,

A2=1.02, A3=1.02, A4=-1.41, A5=2.03.

Figure A.5: The fitting coefficients are NLNP: A0=-4.59, A1=-1.02, A2=2.63, A3=-0.18, A4=-0.43,

A5=0.91; LLNP: A0=-1.61, A1=-0.33, A2=-4.59, A3=2.08, A4=1.73, A5=-0.81; PNLP: A0=-3.72,

A1=-2.25, A2=1.02, A3=1.01, A4=-1.41, A5=2.03.


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