The contribution of electrostatic interactions to the collapse of oligoglycine in water
Protein solubility and conformational stability are a result of a balance of interactions both within a protein and between protein and solvent. The electrostatic solvation free energy of oligoglycines, models for the peptide backbone, becomes more favorable with an increasing length, yet longer pep...
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irk-123456789-1558072019-06-18T01:27:43Z The contribution of electrostatic interactions to the collapse of oligoglycine in water Karandur, D. Pettitt, B.M. Protein solubility and conformational stability are a result of a balance of interactions both within a protein and between protein and solvent. The electrostatic solvation free energy of oligoglycines, models for the peptide backbone, becomes more favorable with an increasing length, yet longer peptides collapse due to the formation of favorable intrapeptide interactions between CO dipoles, in some cases without hydrogen bonds. The strongly repulsive solvent cavity formation is balanced by van der Waals attractions and electrostatic contributions. In order to investigate the competition between solvent exclusion and charge interactions we simulate the collapse of a long oligoglycine comprised of 15 residues while scaling the charges on the peptide from zero to fully charged. We examine the effect this has on the conformational properties of the peptide. We also describe the approximate thermodynamic changes that occur during the scaling both in terms of intrapeptide potentials and peptide-water potentials, and estimate the electrostatic solvation free energy of the system. Розчиннiсть та конформацiйна стабiльнiсть протеїну є результатом балансу взаємодiй як в межах протеїну, так i мiж протеїном та розчинником. Вiльна енергiя електростатичної сольватацiї олiгоглiцинiв, моделей для хребта протеїну, стає бiльш вигiдною iз зростанням довжини, до того ж довшi пептиди колапсують через формування вигiдних внутрiпептидних взаємодiй мiж диполями CO, в деяких випадках без водневих зв’язкiв. Сильно вiдштовхувальне формування розчинникової порожнини збалансовується ван дер вальсiвським притяганням та електростатичними внесками. Для того, щоб дослiдити конкуренцiю мiж виключенням розчинника та зарядовими взаємодiями, ми моделюємо колапс довгого олiгоглiцину з 15-ма блоками при скейлiнгу зарядiв на пептидi вiд нуля до повного заряду. Ми вивчаємо, який ефект це має на конформацiйнi властивостi пептиду. Ми також описуємо приблизнi термодинамiчнi змiни, що вiдбуваються пiд час скейлiнгу як через iнтрапептиднi потенцiали, так i через потенцiали пептид-вода, i визначаємо вiльну енергiю електростатичної сольватацiї для системи. 2016 Article The contribution of electrostatic interactions to the collapse of oligoglycine in water / D. Karandur, B.M. Pettitt // Condensed Matter Physics. — 2016. — Т. 19, № 2. — С. 23802: 1–10. — Бібліогр.: 53 назв. — англ. 1607-324X PACS: 87.15.ap, 87.10.E-, 87.15.Cc DOI:10.5488/CMP.19.23802 arXiv:1603.07152 http://dspace.nbuv.gov.ua/handle/123456789/155807 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
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Protein solubility and conformational stability are a result of a balance of interactions both within a protein and between protein and solvent. The electrostatic solvation free energy of oligoglycines, models for the peptide backbone, becomes more favorable with an increasing length, yet longer peptides collapse due to the formation of favorable intrapeptide interactions between CO dipoles, in some cases without hydrogen bonds. The strongly repulsive solvent cavity formation is balanced by van der Waals attractions and electrostatic contributions. In order to investigate the competition between solvent exclusion and charge interactions we simulate the collapse of a long oligoglycine comprised of 15 residues while scaling the charges on the peptide from zero to fully charged. We examine the effect this has on the conformational properties of the peptide. We also describe the approximate thermodynamic changes that occur during the scaling both in terms of intrapeptide potentials and peptide-water potentials, and estimate the electrostatic solvation free energy of the system. |
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Article |
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Karandur, D. Pettitt, B.M. |
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Karandur, D. Pettitt, B.M. The contribution of electrostatic interactions to the collapse of oligoglycine in water Condensed Matter Physics |
| author_facet |
Karandur, D. Pettitt, B.M. |
| author_sort |
Karandur, D. |
| title |
The contribution of electrostatic interactions to the collapse of oligoglycine in water |
| title_short |
The contribution of electrostatic interactions to the collapse of oligoglycine in water |
| title_full |
The contribution of electrostatic interactions to the collapse of oligoglycine in water |
| title_fullStr |
The contribution of electrostatic interactions to the collapse of oligoglycine in water |
| title_full_unstemmed |
The contribution of electrostatic interactions to the collapse of oligoglycine in water |
| title_sort |
contribution of electrostatic interactions to the collapse of oligoglycine in water |
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Інститут фізики конденсованих систем НАН України |
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2016 |
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http://dspace.nbuv.gov.ua/handle/123456789/155807 |
| citation_txt |
The contribution of electrostatic interactions to the collapse of oligoglycine in water / D. Karandur, B.M. Pettitt // Condensed Matter Physics. — 2016. — Т. 19, № 2. — С. 23802: 1–10. — Бібліогр.: 53 назв. — англ. |
| series |
Condensed Matter Physics |
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2025-07-14T08:02:25Z |
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Condensed Matter Physics, 2016, Vol. 19, No 2, 23802: 1–10
DOI: 10.5488/CMP.19.23802
http://www.icmp.lviv.ua/journal
The contribution of electrostatic interactions to the
collapse of oligoglycine in water
D. Karandur1∗, B.M. Pettitt1,2†
1 Structural and Computational Biology and Molecular Biophysics, Baylor College of Medicine,
Houston, TX 77030, USA
2 Sealy Center for Structural Biology and Molecular Biophysics, Department of Biochemistry and Molecular
Biology, University of Texas Medical Branch, 301 University Blvd., Galveston, TX 77555-0304, USA
Received November 3, 2015, in final form January 11, 2016
Protein solubility and conformational stability are a result of a balance of interactions both within a protein and
between protein and solvent. The electrostatic solvation free energy of oligoglycines, models for the peptide
backbone, becomes more favorable with an increasing length, yet longer peptides collapse due to the formation
of favorable intrapeptide interactions between CO dipoles, in some cases without hydrogen bonds. The strongly
repulsive solvent cavity formation is balanced by van der Waals attractions and electrostatic contributions. In
order to investigate the competition between solvent exclusion and charge interactions we simulate the collapse
of a long oligoglycine comprised of 15 residues while scaling the charges on the peptide from zero to fully
charged. We examine the effect this has on the conformational properties of the peptide. We also describe the
approximate thermodynamic changes that occur during the scaling both in terms of intrapeptide potentials and
peptide-water potentials, and estimate the electrostatic solvation free energy of the system.
Key words: hydration free energy, oligoglycine collapse
PACS: 87.15.ap, 87.10.E-, 87.15.Cc
1. Introduction
The polypeptide chain of proteins collapse in aqueous solvent due to a complex interplay of cor-
relations or effective interactions within the protein, and between the protein and solvent. Salt effects
can stabilize the fold, or destabilize it, based on the overall electrostatics and the interplay with solvent
forces [1]. Similar mechanisms have been observed to cause changes in peptide and protein solubility as
well [2–4]. Electrostatically driven reordering is not restricted to the solvent about a protein or peptide
solute but has been observed in simulated aggregates of pentaglycines in water [5]. In intrinsically disor-
dered proteins, different arrangements of charged amino acids have been observed to lead to changes in
solubility and conformation [6, 7].
The transfer model can be used to qualitatively describe the changes in free energy when the solubil-
ity or structure of a protein changes with respect to a solvent [8]. Bolen and co-workers used a variant of
the transfer model to show that backbone-solvent interactions are a major contributor to the free energy
changes during protein folding [9, 10]. There remain issues which make a precise quantitative argument
for the contribution of the backbone versus side chains based on the transfer model difficult [10–13].
Oligoglycine is a tested model of the protein backbone [14–17]. Previous work has shown that the
electrostatic solvation free energy for oligoglycines at infinite dilution becomes more favorable with an
increasing chain length [16] while an isolated peptide collapses as seen both experimentally [17] and in
simulation [14, 15] to interact with itself. We have previously shown that this collapse is due to a bal-
ance between non-hydrogen bonding dipolar correlations (so-called “CO-CO” interactions) and solvent
∗Present address: Howard Hughes Medical Institute at the University of California, Berkeley, CA 94720, USA
†E-mail: mpettitt@utmb.edu
© D. Karandur, B.M. Pettitt, 2016 23802-1
http://dx.doi.org/10.5488/CMP.19.23802
http://www.icmp.lviv.ua/journal
D. Karandur, B.M. Pettitt
cavity formation [18]. If we decompose the solvation free energy for peptides into the underlying force
field components of van der Waals (vdW) cavity formation and electrostatics recent results show that
the vdW free energy does not follow naive hydrophobicity arguments [19–21]. The cavity has a repulsive
component which is unfavorable but in many cases the vdW attractions more than compensate and pro-
duce an uncharged cavity which has a favorable free energy when the surface area is maximized as in
a strictly linear peptide without electrostatic contributions [20, 21]. However, when peptides of alanine
were allowed to conformationally relax the vdW attractions no longer outweighed the repulsive cavity
formation [20].
The vdW terms for such solutes with strong dipoles like glycine in a polar solvent like water are
relatively small. Using the common classical force field components, electrostatics contribute the most to
the solvation free energy [16]. Several methods to estimate the solvation free energy are in the literature
[22, 23]. Approximatemethods based onmean field approaches such as Poisson Boltzmann theory [24, 25]
and Generalized Born theory [26] are relatively inexpensive, but are based on the assumption that the
solvent is a dielectric continuum and responds linearly to solute electrostatics. While near linearity has
been observed for systems comprised of monovalent ions [27, 28], complex systems such as proteins have
complicated multipolar distributions and show marked deviations from linearity [29]. Furthermore, at
length scales equivalent to the size of water molecules, there is evidence that continuum models break
down [30]. Hybrid models, where the solute and a solvation shell are modelled explicitly while the rest
of the solvent is modelled by a continuum representation, overcome some of these issues [31–33]. More
accurate are methods such as thermodynamic integration and free energy perturbation calculations [34–
36] usingmolecular dynamics with explicit descriptions of solute and solvent atoms.While thesemethods
are much more expensive, requiring extensive sampling, they are, in principle, capable of being much
more accurate [29, 37].
Recent work considered the change in the vdW cavity free energy between extended and collapsed
conformations for oligoalanine [20] in relation to the changes in solvent exposed area and classical hy-
drophobicity [38]. Given the cavity contribution to oligoglycine [16], alanine [20] and other peptide/pro-
tein collapse in water, we wish to characterize the electrostatic contributions and show how they change
the conformational manifold. In order to consider the contribution of the electrostatic solvation free
energy to a flexible peptide we have chosen Gly15, to compare with the previous, related work [16]. Weperform a series of simulations scaling charges on the peptide from zero to fully charged.We examine the
effect that the scaling charges have on peptide conformation. We then examine other structural and ther-
modynamic changes both within the peptide and between the peptide and water as charges are turned
on. The next section describes the models and methods used. We then describe the results in terms of the
effects that the variations in potential have on the structure followed by a detailed examination of the
accompanying thermodynamic changes, and end with our conclusions.
2. Methods
An oligoglycine peptide 15 residues (Gly15) with capped ends was built with CHARMM [39], in the fullyextended state. The peptide was solvated with TIP3P water with VMD [40] such that there are at least 5
solvation shells about the extended peptide.
We will consider the amount of the charge potential added to the peptide solute as a scaling factor λ.
The electrostatic contribution to the solute-solvent potential,U elec(r ) is thus linearly scaled as λU elec(r ).
For a sufficient number of λ points and sampling at each point, this would constitute a free energy charg-
ing coordinate.
At constant pressure and temperature, the change in free energy of solvation with respect to adding
charges to the solute peptide,
∆G =
1∫
0
〈U elec〉λdλ, (1)
where 〈. . .〉λ denotes the configurational average at a particular value of λ.Here, we used six λ windows to scale the electrostatics: 0.0, 0.2, 0.4, 0.6, 0.8, 1.0. While the electro-
statics in some systems yields to linear response theory, a more complicated integrand with curvature
23802-2
The contribution of electrostatic interactions to the collapse of oligoglycine in water
means that more quadrature points may be required depending on the precision required. In addition,
sampling at each point for flexible systems is notoriously slow [20]. For these reasons, the use of equation
(1) here results in only a rough approximation. We wish to consider the competition between the cavity
formation and the charging on the conformational distribution. The range of λ points chosen will allow
us to consider the structural measures of the system between a purely uncharged but flexible vdW cavity
and the fully charged force field.
All the systems were minimized for 25 K steps with the peptide held fixed and then for 25 K steps
where all the molecules are allowed to move. They were then equilibrated for 2 ns in the N PT ensemble
(pressure = 1 atm, temperature = 300 K), followed by 1 ns in the NV T ensemble. Systems with λ = 0.0,
0.2, 0.4 and 0.6 were then run for 300 ns in the N PT ensemble. Systems with λ= 0.8 and 1.0 were run for
500 ns. The longer runs at these λ points allowed a more extensive sampling because the charged inter-
actions, both within the peptide and between the peptide and water, affect the conformational manifold
to a greater extent. The NAMD package was used to run the simulations [41] with the CHARMM27 force
field [42, 43] with a timestep of 1 fs. Particle Mesh Ewald with a grid size of 1 Å was used to calculate the
long-range electrostatics [44]. The RATTLE module was used to constrain all hydrogen bonds [45].
Components of the approximate free energy for our process corresponding to the response of other
terms in the potential energy model require doing integrals similar to the one presented above. We de-
composed the potential energy both within the peptide and between the peptide and water into standard
bonded (only intrapeptide) and non-bonded terms. The NAMD Energy plug-in was used to calculate these
terms [41]. Particle Mesh Ewald was not used during the calculation of these various potentials.
3. Results
3.1. Gly15 collapses in a charge-dependent manner
The peptide conformational distribution collapsed in a few nanoseconds at each λ. The systems ex-
plored different distributions with respect to λ, as will be described in detail below. In all the systems,
they explored a collapsed set of conformers versus a random chain. The systems rarely explored extended
conformations, usually for a few ns or less, before collapsing again. Figure 1 shows the distribution of the
radius of gyration in each of the different charge state windows. The system with all charges turned off,
i.e., where only vdW interactions both within the peptide and between the peptide and water are possi-
ble, shows the narrowest distribution. Since peptides normally strongly interact with water via dipolar
hydrogen bonds, turning the charges off prevents these interactions, allowing the peptide to collapse via
intrapeptide van der Waals interactions and via the cavity formation forces even though the intermolec-
ular vdW attractions oppose this [20].
Figure 1. (Color online) Probability distribution of radius of gyration of peptide for different λ windows.
The color scheme for each λ is described in the key.
23802-3
D. Karandur, B.M. Pettitt
Figure 2. Variation in the radius of gyration of peptide across time for different λ windows.
As charges are turned on, the distribution broadens, since the charge-charge peptide-water interac-
tions allow the peptide to explore a larger range of conformations. This is also reflected in the increase in
the mean radius of gyration with respect to an increasing charge. The radius of gyration also takes longer
to converge (figure 2). Thus, the higher λ value systems showmuchmore variation whereas the smaller λ
value systems apparently convergedwithin a 100 ns. Furthermore, the peptide in all the systems explored
the structural conformations of oligoglycine with different probabilities (figure 3). At lower λ values, the
peptide explores all the allowed regions of the Ramachandran space with almost similar probabilities,
but as the charges are turned on, the peptide becomes more constrained to the regions that are consis-
tent with that of glycines for this particular force field [43].
3.2. Potential average components with respect to charge
We decomposed the non-bonded potential averages as a function of λ into electrostatic and van der
Waals components for both intrapeptide and peptide-water potential energies. The results are shown in
figure 4. Both intrapeptide electrostatic and van der Waals potentials increase with an increasing λ, in-
dicating that as the charges are turned on, intrapeptide interactions become unfavorable [figures 4 (a)
(points in black) and 4 (b)]. We have previously observed that oligoglycine collapse is not stabilized by
intrapeptide H-bonds [15, 18], but by a large number of dipole-dipole or “CO-CO” interactions. However,
the unfavorable nature of the intrapeptide electrostatic potential as the charge increases requires more
analysis. We and others have previously observed that a strong positive correlation occurs between adja-
cent peptide dipoles at 3 Å, which is inherently present in all polypeptides [5, 18, 46]. We note that gamma
turns or C7 rings, which would have favorable near-neighbor dipoles, are extremely rare in proteins orpeptides in solution [47]. In the more probable orientations, the near-neighbor dipoles are more aligned
23802-4
The contribution of electrostatic interactions to the collapse of oligoglycine in water
λ = 0.0
-150 -100 -50 0 50 100 150φ(degrees) -150
-100
-50
0
50
100
150
ψ(degrees)
λ = 0.2
-150 -100 -50 0 50 100 150φ(degrees) -150
-100
-50
0
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150
ψ(degrees)
λ = 0.4
-150 -100 -50 0 50 100 150φ(degrees) -150
-100
-50
0
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ψ(degrees)
λ = 0.6
-150 -100 -50 0 50 100 150φ(degrees) -150
-100
-50
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150
ψ(degrees)
λ = 0.8
-150 -100 -50 0 50 100 150φ(degrees) -150
-100
-50
0
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150
ψ(degrees)
λ = 1.0
-150 -100 -50 0 50 100 150φ(degrees) -150
-100
-50
0
50
100
150
ψ(degrees)
(a) (b)
(c) (d)
(e) (f)
Figure 3. (Color online) Ramachandran plots of Gly15 with respect to λ.
−150
−100
−50
0
50
100
0.0 0.2 0.4 0.6 0.8 1.0
<
U
e
le
ct
ro
st
a
tic
>
(
kc
a
l/m
o
l)
λ
−35
−30
−25
−20
−15
−10
0.0 0.2 0.4 0.6 0.8 1.0
<
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vd
W
>
(
kc
a
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o
l)
λ
−40
−20
0
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0.0 0.2 0.4 0.6 0.8 1.0
<
U
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o
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−
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o
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>
(
kc
a
l/m
o
l)
λ
−300
−250
−200
−150
−100
−50
0
0.0 0.2 0.4 0.6 0.8 1.0
<
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e
le
ct
ro
st
a
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>
(
kc
a
l/m
o
l)
λ
−80
−75
−70
−65
−60
−55
−50
−45
−40
−35
0.0 0.2 0.4 0.6 0.8 1.0
<
U
vd
W
>
(
kc
a
l/m
o
l)
λ
−350
−300
−250
−200
−150
−100
−50
0
0.0 0.2 0.4 0.6 0.8 1.0
<
U
n
o
n
−
b
o
n
d
>
(
kc
a
l/m
o
l)
λ
(a) (b) (c)
(d) (e) (f)
Figure 4. (Color online) Average potential energy with respect to λ. (a) shows intrapeptide electrostatic
potential energy. The total electrostatic potentials are shown in black and electrostatic potentials when
excluding C · · ·C and O · · ·O interactions between atoms of adjacent CO dipoles are shown in red. (b)
shows intrapeptide van derWaals potentials. (c) shows total intrapeptide non-bonded potential. (d) shows
peptide-water electrostatic potentials, (e) shows peptide-water van der Waals potentials and (f) shows to-
tal peptide-water non-bonded potentials.
23802-5
D. Karandur, B.M. Pettitt
with each other and form locally strong but unfavorable interactions. We also note that the proximity of
the near-neighbor dipoles is a requirement of forming a covalently linked polypeptide, and so becomes a
source of frustration in the energy landscape [48].
We now consider the rest of the electrostatics excluding the aspects of the CO-CO interaction surface
associated with the near-neighbor amide dipoles. In order to exclude this near-neighbour effect, we cal-
culated the intrapeptide potential while excluding C · · ·C and O · · ·O interactions between the atoms on
the adjacent CO dipole atom pairs. The results are shown in figure 4 (a) (points in red). These interactions
alone account for much of the positive component of the intrapeptide electrostatic potential. The entire
intramolecular electrostatic potential becomes favorable at higher λ values without the near-neighbor
repulsions.
The intrapeptide vdW potentials increase as the charges increase due to favorable electrostatic inter-
actions inducing the changes in peptide conformational manifold with stronger contacts. It is interesting
to note that while the electrostatic potentials show an increased variation about the mean with an in-
creasing λ, the vdW potential averages show the same spread irrespective of λ. This leads to the total
non-bonded contributions variances as well as means being dominated by the electrostatics.
As charges are turned on, the peptide-water electrostatic interactions become increasingly favorable
[figure 4 (d)], indicating the formation of favorable, dipolar, peptide-water interactions such as hydrogen
bonds. As these interactions become available to the systems, they tend to add stability to the extended
conformations that these systems explore. As noted above, these systems do not assume extended con-
formations with a high probability. As observed previously [29], the peptide-water potential shows devia-
tions from linearity in λ. The peptide-water vdW potential does not show as much variation with respect
to λ [figure 4 (e)]. Thus, the total non-bonded intrapeptide potential increases as charges are turned
on, whereas total non-bonded peptide-water potential energy becomes more favorable [figures 4 (c) and
4 (f)], and in opposition they induce the peptide to explore larger conformational states.
We also considered whether the structural changes induced by turning the charges on affected the
intrapeptide bonded potential energies (figure 5). Both the intrapeptide bond energy and the angle en-
ergy become slightly unfavorable from the induced strain as the charges are turned on. However, the
dihedral angle energy becomes a bit more favorable with an increasing λ [figure 5 (c)] indicating that
the peptide is assuming conformations that will stabilise it in charged environments. Apparently, the
more compact conformations that the peptides assume at lower λ values, are unfavorable in terms of the
dihedral potential.
16
18
20
22
24
26
28
30
0.0 0.2 0.4 0.6 0.8 1.0
<
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o
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λ
45
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<
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λ
46
44
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0.0 0.2 0.4 0.6 0.8 1.0
<
U
d
ih
e
d
ra
l>
(
k
c
a
l/
m
o
l)
λ
(a) (b) (c)
Figure 5. Potential energy with respect to λ for (a) intrapeptide bond potential energy, (b) intrapeptide
angle potential energy and (c) intrapeptide dihedral potential energy.
3.3. Approximate electrostatic contributions to free energy
The approximate electrostatic solvation free energy was estimated as described in the methods as
-66 kcal/mol. Previous calculations on short oligoglycines have estimated the electrostatic solvation free
energy of pentaglycines to be −42.53 kcal/mol for the extended form [16] and −37.3 kcal/mol for the
helical form [49]. Since the solvation free energy per peptide is additive with respect to the number of
residues, as was shown to be true for the extended and collapsed forms [20], the expected solvation
free energy contribution for Gly15 should be ∼−127 kcal/mol using the linear conformation estimate or
−112 kcal/mol using the helical. There is a significant variation in the average potentials at the higher
23802-6
The contribution of electrostatic interactions to the collapse of oligoglycine in water
λ values, with λ = 0.8 showing a standard deviation of ±35 kcal/mol and λ = 1.0 showing a standard
deviation of ±57 kcal/mol [figure 4 (d)]. Thus, the rough estimate of the current approximation suffers
from statistical uncertainty in the averages used.
3.4. Water distribution about peptide
In order to examine the consequences of the competition between the electrostatics and peptide-
water vdW potentials as reflected in the solvation in greater detail, we calculated the radial distribution
of water oxygen atoms about all peptide heavy atoms for all λwindows. The results are shown in figure 6.
The contact peak shifts in all the curves are a reflection of interatomic interactions. The induced structure
is reminiscent of the charging process in other polar fluids [50–52]. At lowerλ values, these small distance
peaks appear as shoulders on the curve, but as charges are increased, they become more pronounced
and even split into two peaks at λ = 1.0 due to the formation of peptide-water hydrogen bonds. Beyond
∼ 6 Å, the curve depicts water distribution with respect to the conformationally averaged peptide. At
λ = 0.0, only van der Waals interactions occur between peptide and water molecules (as well as within
the peptide). Thus, the location of the first peak reflects the effective vdW distance, i.e., the formation of
the solvent cavity. As charges are turned on, water forms the expected electrostatic interactions with the
peptide that allows the aspects of the cavity size to decrease, lowering the distance at which the first peak
occurs as λ values increase. We also see the effect of the increase in the radius of gyration as the charge
increases in the tails of the distributions of the radius of gyration.
Figure 6. (Color online) Radial distribution of water oxygens about non-hydrogen peptide atoms for the
different λ windows. The color scheme for each λ is described in the key.
4. Discussion
The peptide-water electrostatic potential becomes increasingly favorable as charges are turned on.
The approximate electrostatic solvation free energy for Gly15 is quite favorable, as has been observed forother, shorter oligoglycines [16, 49]. However, in spite of the large favorable solvation free energy, oligo-
glycines collapse due to the formation of favorable intrapeptide interactions. Here, oligoglycine in each
λ window collapsed versus a random chain, with the most compact manifold of structures occurring at
λ= 0.0. As λ increases, the peptide explores larger conformations as it forms favorable electrostatic inter-
actions with water and has both short-ranged internal repulsions and longer-ranged hydrogen bonding
opportunities. Few intramolecular H-bonds result, however, typically less than 3 for Gly15.From polymer theory, the degree of collapse can be quantified by the following relationship:
Rg = aNν, (2)
23802-7
D. Karandur, B.M. Pettitt
where Rg is the radius of gyration, a is the length of a monomer unit (3 Å in peptides, obtained from the
oligoglycine peptide in the fully extended state), N is the number of monomer units (15 in this case) and
ν is a scaling exponent [53]. For a polymer in a “good” solvent ν � 0.6, for a polymer in a “poor” solvent
ν � 0.3 and in a solvent where the polymer is expected to behave like an ideal linear chain, ν= 0.5. The
rare conformationswith the largestRgwere observedwhenλ= 1.0. ThemeanRg forλ= 1.0 is 6.5 Å— the
Rg which is expected in a relatively poor solvent (see figure 7). Thus, while the peptide forms interactionswith water as charges are turned on, and the peptide-water interaction potential becomes increasingly
favorable, the peptide does not form kinetically stable extended conformations, but only briefly explores
these conformations before collapsing again due to the balance of forces.
0.16
0.2
0.24
0.28
0.32
0.36
0.0 0.2 0.4 0.6 0.8 1.0
ν
λ
Figure 7. The radius of gyration exponent ν with respect to λ. The error bars demonstrate the variability
of Rg.
While peptides collapse due to cavity forces and favorable intrapeptide vdW interactions when the
charges are turned off, these interactions become less dominant as charges are turned on. Some of the
change in vdW interactions is due to the inevitable tension between the vdW repulsions and the elec-
trostatic attractions. The decreasing favorability of the total intrapeptide potential with an increasing λ
is caused in part by a repulsion between the oxygen atoms from adjacent CO-CO dipoles oriented par-
allel to each other as observed previously [18]. When these interactions are discounted, electrostatic in-
trapeptide interactions become favorable and compete with peptide-water interactions to stabilize the
collapsed conformations. Since intrapeptide H-bonds have been observed with low probability in oligo-
glycines [5, 15, 18], these interactions are primarily non-hydrogen bonded interactions between amide
dipoles, or the so-called CO-CO interactions. The configurationally averaged interactions between the CO-
CO pairs are favorable after removing the constrained neighbor oxygen repulsions. Furthermore, it has
been observed during simulations of aggregation of pentaglycines that while the intrapeptide electro-
static potential was positive during aggregation, the interpeptide electrostatic potential was negative and
decreased continuously during aggregation [5]. The intrapeptide potential in a pentaglycine would come
primarily from the neighbouring CO dipoles whereas the interpeptide potential comes from CO dipoles
forming favourable interactions.
5. Conclusions
In this study, we simulated the Gly15 in water while varying the peptide charge. Peptides in all thechargewindows collapsed, evenwith the strongly favorable electrostatic solvation free energy. The extent
of collapse depended on the charge, with peptides having lower charge collapsing to a greater extent due
to favorable intrapeptide vdW interactions. However, when charges are turned on, the peptides formed
favorable intrapeptide interactions, especially when the interactions between oxygen atoms of adjacent
CO dipoles were discounted, which overcame the large electrostatic solvation free energy of the system.
We have previously shown that while H-bonds are absent in collapsed oligoglycines, the interactions
between CO dipoles helped stabilize the collapsed state [18].
23802-8
The contribution of electrostatic interactions to the collapse of oligoglycine in water
Acknowledgements
The Robert A. Welch Foundation (H-0037), the National Science Foundation (CHE-1152876) and the
National Institutes of Health (GM-037657) are thanked for partial support of this work. This research was
performed in part using the Keenland and Stampede systems, part of the National Science Foundation
XSEDE resources.
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Внесок електростатичних взаємодiй у колапс
олiгоглiцину у водi
Д. Карандур1, Б.М. Петтiтт1,2
1 Структурна i обчислювальна бiологiя та молекулярна бiофiзика, Коледж медицини Бейлора,
Г’юстон, Техас 77030, США
2 Центр Сейлi структурної бiологiї i молекулярної бiофiзики, Факультет бiохiмiї i молекулярної бiологiї,
Медичне вiддiлення Унiверситету Техасу, Унiверситетський бульвар, 301, Ґалвестон,
Техас 77555-0304, США
Розчиннiсть та конформацiйна стабiльнiсть протеїну є результатом балансу взаємодiй як в межах про-
теїну, так i мiж протеїном та розчинником. Вiльна енергiя електростатичної сольватацiї олiгоглiцинiв,
моделей для хребта протеїну, стає бiльш вигiдною iз зростанням довжини, до того ж довшi пептиди ко-
лапсують через формування вигiдних внутрiпептидних взаємодiй мiж диполями CO, в деяких випадках
без водневих зв’язкiв. Сильно вiдштовхувальне формування розчинникової порожнини збалансовується
ван дер вальсiвським притяганням та електростатичними внесками. Для того, щоб дослiдити конкурен-
цiюмiж виключенням розчинника та зарядовими взаємодiями,ми моделюємо колапс довгого олiгоглiци-
ну з 15-ма блоками при скейлiнгу зарядiв на пептидi вiд нуля до повного заряду.Ми вивчаємо, який ефект
це має на конформацiйнi властивостi пептиду. Ми також описуємо приблизнi термодинамiчнi змiни, що
вiдбуваються пiд час скейлiнгу як через iнтрапептиднi потенцiали, так i через потенцiали пептид-вода, i
визначаємо вiльну енергiю електростатичної сольватацiї для системи.
Ключовi слова: вiльна енергiя гiдратацiї, колапс олiгоглiцину
23802-10
http://dx.doi.org/10.1016/0076-6879(86)27006-8
http://dx.doi.org/10.1002/jcc.21287
http://dx.doi.org/10.1016/0263-7855(96)00018-5
http://dx.doi.org/10.1002/jcc.20289
http://dx.doi.org/10.1021/jp973084f
http://dx.doi.org/10.1002/jcc.20065
http://dx.doi.org/10.1063/1.464397
http://dx.doi.org/10.1016/0021-9991(83)90014-1
http://dx.doi.org/10.1038/nchembio.406
http://dx.doi.org/10.1016/0009-2614(85)85509-3
http://dx.doi.org/10.1073/pnas.84.21.7524
http://dx.doi.org/10.1021/jp052403x
http://dx.doi.org/10.1063/1.443606
http://dx.doi.org/10.1063/1.443972
http://dx.doi.org/10.1063/1.444719
Introduction
Methods
Results
Gly15 collapses in a charge-dependent manner
Potential average components with respect to charge
Approximate electrostatic contributions to free energy
Water distribution about peptide
Discussion
Conclusions
|