Supplementary Material
Predicting the side-chain dihedral angle
distributions of non-polar, aromatic, and polar
amino acids using hard sphere models
Alice Qinhua Zhoua,b,c, Corey S. O’Hernb,d, Lynne Regana,b, *
aDepartment of Molecular Biophysics & Biochemistry, Yale University, New Haven, CT,
USA
bIntegrated Graduate Program in Physical and Engineering Biology (IGPPEB), Yale
University, New Haven, CT, USA
cHoward Hughes Medical Institute International Research Fellow
dDepartments of Mechanical Engineering & Materials Science, Applied Physics, and
Physics, Graduate Program in Computational Biology and Bioinformatics, Yale
University, New Haven, CT, USA
*Corresponding author, Lynne.Regan@yale.edu
Table S1: Numbers of dipeptides and α-helical segments in the 1.7Å and 1.0Å Dunbrack
databases. “Helix” and “Sheet” refer to structures with φ and ψ angles within ±10◦ of the
canonical α-helix (φ = −57◦, ψ = −47◦) and β-sheet (φ = −119◦, ψ = 113◦) values,
respectively.
† Same as Ref. [1], where all dipeptides are extracted with φ and ψ angles changed to
canonical α-helix (φ = −57◦, ψ = −47◦) or β-sheet (φ = −119◦, ψ = 113◦) values.
[1] Zhou AQ, Caballero D, O’Hern CS, Regan L. New insights into the interdependence
between amino acid stereochemistry and protein structure. Biophys. J. 2013;105:2403–
2411.
Table S2: Definitions of the backbone and side-chain dihedral angles. All of the dihedral
angles listed range from 0◦ to 360◦, except: 1) χ for the aromatic residues (Phe, Tyr,
2
and Trp), which range from 0◦ to 180◦, and 2) φ and ψ, which range from −180◦ to 180◦.
◦ a
shows datasfor
Sedata
r with
backbone
dral angle
andangle
χ1 =s and
60 . χWe
show
hows
forhe
Slical
er with
helical dihe
backbone
dihes
dral
1 = 60 . We sho
stick repress
etick
ntation
ofsethisconformation
in Columnin
2 Column
and thepe
rcent
of thenumbe
r
repre
ntation of thisconformation
2 and
thepe
rcent of thenum
of Ser dipeptide
tructure
s (with
variation
bond length
andlebond
angle
combinaof Sersdipe
ptide
structure
s (within
variation
in bond
ngth and
bond
angle combi
tions) that tions)
allow this
in Columnin
3.Column
In thefourth
column, wes
how the
that conformation
allow this conformation
3. In thefourth
column,
weshow
i+ 1
1 i+1
1
Ser Helixdistributiondis
oftribution
distances
Oγi+–H
on Ni+ 1n
) atom
.
offor
disO
tance
Oγ –N
and(hydroge
Oγ –Hi+ 1n(hydroge
on Ni +pairs
) atom
pa
γ –Ns forand
χ =60°
The red line indicates the hard 50%
sphere limit (σij ), and th
1
66 d distances. Near 50%of Ser in hel
red indicate
66s disallowe
In the
sarea
econd
row, in
we show the limiting clash for Ser i
The red lineThe
indicat
t he
hard sphere
limitsphe
(σi j re
), and
t he
shaded
red es
line
indicate
s the hard
limitt hus
(σij ),
and
thus
the areapale
shaded in pale
Ser Sheet
Oγ –O
only
7%areallowe
d. Swe
imilarly,
a comparison o
red indicat es
ances.dNear
50%s.ofNe
Ser
helical
allowed.areallo
redisallowed
d indicatesdist
disallowe
distance
ar in
50%of
Sebackbone
rand
in he
licalare
backbone
d.
χ =60°
1
tion
with
on he
a ehe
lical
In t he second
row,
show
ingthe
clash
for Ser
inhβ-sheet
conformat
is conformation
7%is (Row 3) shows t
In the
sewe
cond
row,t he
welimit
show
limiting
clas
for
SerCys
in β-s
tion
conformation
is
saeve
limiting
– only
5% is allowed due to Sγ –
Oγ –O and only
7%and
areonly
allowed.
Similarly,d.a S
comparison
of more
Ser in on
helical
Oγ –O
7%areallowe
imilarly, a comparis
ofre
Sly
er conformain a helical
conforma-
t ion red
wit hline
Cys
onre
adhelical
conformat
(Row
t hat
t hows
hearea
larger
atpale
om
tion
with
Cys
on
a he
conformation
(Row
3)t he
s
the
large
r sulfur
atom
oxyge
nthat
in sulfur
S
er. in
Finally,
we compare
Row 3 and Row
The
indicat
es
t he
hard
sphere
limit
(σi3)
),shows
and
tthan
hus
shaded
j re
The
line
indicate
slical
theion
hard
sphe
limit
(σ
ij ), and thus the area shaded in pale
i+ 1
i + i1+ 1 clashes,
i+ 1
Cys
Helix
is
severely
limit
–lyonly
5%
is– allowed
due
t in
o
Shelical
–Ndue
and
is
seing
vesre
limiting
only
is
allowe
d
S
–N
–Hareallo
heve
s, ry low percent of bo
redmore
indicat
es
dist
ances.
50%5%
Ser
allowed.
γmation,
γ –H
γS
χare
=and
60◦Sγor
180◦clas
. A
redisallowed
dmore
indicate
dis
allowe
dNear
dis
tance
s.ofNe
ar
50%of
Sebackbone
rto
inwith
he
lical
we
d.
1 backbone
χ =60°
1 oxyge
◦
t han
oxygen
Ser.
Finally,
we
compare
Row
3 and
Row
CysS
in
helical
conforthan
nshow
inrow,
Se
r.
Finally,
wecompareRo
w
3
and
Row
Cys
in
a
he
conforIn
t he
second
row,
t he
limit
ing
clash
for Ser
in4:
islicalwith
5%
Ininthe
sewe
cond
we
show
the
limiting
clas
hβ-sheet
for
er aconformat
in4:
β-s
he
e
tion
conformation
combinations
are
compatible
χis
1 = 60 , whereas virt
◦
◦
mation,
with
=◦ .60
180
.S
A
very low
pe
nt
of
bond
leconformangth
and
angle
mat
ion,
witonly
h γχ–O
=and
60
orχ180
A◦ or
very
low
percent
ofabond
and
angle
17%areallowe
Oγ –O
and
are
allowed.
Similarly,
comparison
of rce
Serlengt
ahhelical
17%
O
only
d.a
imilarly,
comparis
on
of
S◦erbond
in
a he
licalbond
conformawith
χin
1 = 180 .
◦
◦
combinations
are
compatible
with
χ3)
60
, whe
virtually
100%
are
are
compat
withe
hlical
χ 1 ion
=conformation
60
, whereas
virt
100%
aresulfur
compat
1=
tcombinat
ion wit hions
Cys
onwith
a helical
conformat
(Row
shows
tually
hat
tas
he
larger
atible
om
tion
Cysible
on
a
(Row
3)re
s
hows
that
the
large
r scompatible
ulfur atom
5.2.3 Val and Thr
◦
◦Cys
i+ 1
i + i1+ 1 clashes, i + 1
with
χ1Helix
=eing
180
witmore
h χ 1 severely
= 180
. limit
is
5% is– allowed
t o Sγ d
–Ndue
andSγS–N
is more
s
ve
re–ly.only
limiting
only 5%due
is allowe
to
Sγ –H clashes,
γ –H and
5.2.4
Le
u
and
Ile
χ =180°
1 oxyge
t han oxygenthan
in Ser.
Finally,
n in Se
we
r. compare
Finally, wecompareRo
Row 3 and Row
w 4:
3 and
CysRow
in a 4:
helical
Cys in
confora helical confor98%
5.2.3
5.2.3 Val and
ThrVal and Thr
◦
◦
with
=◦ .60
180
. A
very low
percelengt
nt ofhbond
lengthangle
and bond angle
mat
wit mation,
h
χ 1Ile
= Le
60
orχ180
A◦ or
very
low
percent
of bond
and bond
1Ile
5.2.4
u and
5.2.4ion,Leu
and
◦
◦
combinations
are compatible
with
χ1 = 60virt
, whe
reas
virtually
100%ible
are compatible
combinat ions
are compat ible
wit h χ 1 = 60
, whereas
ually
100%
are compat
◦ χ
of the steric clashes in Ser and Cys dipeptide mimetics.
with
180◦ .
wit h χ 1 = Figure
180
. S1:
1 =Illustration
Row 1: Ser in an α-helical backbone conformation with side-chain dihedral angle χ1=60◦.
5.2.3
Val inand
Thr
5.2.3 ValRow
and
Thr
2:
Ser
a β-sheet
backbone conformation with side-chain dihedral angle χ =60◦;
1
an Ile
α-helical backbone conformation with side-chain dihedral angle
5.2.4
Leuinand
5.2.4 LeuRow
and 3:
IleCys
◦
χ =60 ; Row 4: Cys in an α-helical backbone conformation with side-chain dihedral
1
angle χ1=180◦. Column 1: Specified backbone conformation and χ1 value in each row.
Column 2: Stick representation of Ser and Cys dipeptide mimetics in backbone and
side-chain conformations specified in Column 1. Column 3: The separation distributions
between key atom pairs (in Å). The red vertical line indicates contact between the pair of
atoms. The area shaded in pale red highlights sterically disallowed atomic separations.
Column 4: The percentage of Ser residues in the 1.7Å database for which the
highlighted atom pairs in Column 3 possess separations that are sterically allowed in the
specified conformation (Column 1).
67
67
67
Figure S2: Error bars for the side-chain dihedral angle distributions for Ser and
Cys dipeptide mimetics: Comparison of the observed (red lines) and calculated (blue
lines) probability distributions P(χ1) of the side-chain dihedral angle χ1 for Ser and Cys in
dipeptide mimetics with backbone dihedral angles φ and ψ within ±10° of canonical αhelix (φ=−57°, ψ=−47°) and β-sheet (φ=−119°, ψ=113°) values. To estimate the error
bars, we break the set of structures for a given residue type into groups, where from
each group we can obtain a reasonably smooth distribution Pi(χ1), where i=1,...,Ng and
Ng is the number of groups. The numbers of structures in each group of observed and
calculated for Cys and Ser are 50 and 10, respectively. The average P(χ1) is defined as
𝑁𝑔
1
𝑃(𝜒1 ) = ∑𝑖=1
𝑃𝑖 (𝜒1 ) with error bars given by the error in the mean σ(χ1)/(Ng)1/2, where
𝑁𝑔
σ(χ1) is the standard deviation in each bin. The probabilities are normalized such that ∫
P(χ1) dχ1=1.
c
h
i1
0
.1
0
.0
5
c
h
i2
0
0
.2
0
.1
c
h
i3
0
0
.0
3
0
.0
2
0
.0
1
0
0
6
0
1
2
0
1
8
0
2
4
0
3
0
0
3
6
0
Figure R1: (left) Stick representation of the Met dipeptide. (right) Predicted probability
distributions for χ1 , χ2, and χ3 from the hard-sphere plus stereochemical constraint model
for Met dipeptides with two hydrogen atoms artificially placed in an sp3 configuration on
the sulfur atom. The probabilities are normalized such that ∫ P(χn) dχn=1.