1. 2. Introduction to Rosetta and structural modeling

2. Short history – in the beginning…
Initial goal – find structure
given sequence.
Motivation – structure defines
function
Challenge – many degrees
of freedom.
Rosetta started as a program aimed at finding the structure of a protein given a sequence alone, ab-initio. Achieved for relatively small proteins.
Reliable fold identification for short proteins. Recently improved to yield high-resolution models (within 2A RMSD)

3. A short history of Rosetta
Success of ab initio protocol led to extension to
Protein design
Design of new fold: TOP7
Protein loop modeling; homology modeling
Protein-protein docking; protein interface design
Protein-ligand docking
Protein-DNA interactions; RNA modeling
Many more, e.g. solving the phase problem in Xray crystallography
ATCSFFGRKLL…..
ATCSFFGRKLL…..

4. The basic assumption in structure prediction
Native structure located in global minimum (free) energy conformation (GMEC)
A good Energy function can select the correct model among decoys
A good sampling technique can find the GMEC in the rugged landscape
Assumption is that there’s a very deep energy funnel and at its bottom the native conformation is found, so that the large energy gap will prevent protein escape to alternative conformations most of the time. Advantage is that even with errors in the energy function, the signal can still be identified.
GMEC E
Conformation space

5. How to approch such a problem
Sampling
Reduce system Degrees Of Freedom (DOF)
Assume ideal bond lengths
and angles
Rough sampling until reaching
near global minimum
Scoring function based in part on the Boltzman principle, correlating frequency to energy
Scoring
In these simulations we assume ideal bond lengths and bond angles, as seen in most crystal structures. This reduces much of the system DOFs, but still a lot remains, so Rosetta has additional “tricks”, e.g. more accurate, computationally expensive sampling only in low energy regions.

6. Two-Step Procedure Low-resolution step locates potential minima (fast)
Cluster analysis identifies broadest basins in landscape
High-resolution step can identify lowest energy minimum in the basins (slow) E
First step is performed in a smooth energy landscape, where a rough representation of the protein reduces dramatically the DOFs - allows identification of low energy basins. Next, a rugged space is used, where small changes lead to drastic changes in energy. In such a space there’s need for more gentle sampling.
Conformation space
GMEC

7. Low-Resolution Step Structure Representation:
Equilibrium bonds and angles (Engh & Huber 1991)
Centroid: average location of center of mass of side-chain
(Centroid | aa, f,)
No modeling of side chains
Fast
This step is aimed at identifying the approximate fold of the protein, without interaction details. All backbone atoms are represented, including their hydrogens, while side chains are replaced by spheres with the approximate size and properties of the side chain. Using statistical analysis, we can derive properties of the centroids (e.g. phe in beta strands – calculate location of side chain center of mass). Picture shows a structure at the end of this step.

8. Low-Resolution Scoring Function (e.g. score4)
Bayes Theorem:
P(str | seq) = P(str)*P(seq|str) / P(seq)
Independent components prevent
over-counting
structure
dependent
features
sequence-
dependent
features
Constant
(for structure prediction)
Scoring function is decomposable, with its terms independent of each other. In bayes theorem, if we want to identify the probability of a structure given a certain sequence, we can decompose it to:
[probability to get such a structure (comprised of terms such as the probability to get such compactness) * probability to get the sequence given a certain structure]/the probability to get a certain sequence (which in the case of structure prediction is 1).

9. Sequence-Dependent Components
Bayes Theorem:
P(str | seq) = P(str) * P(seq | str) / P(seq)
Score = Senv+ Spair + …
Terms where a probability is calculated are based on statistics of known, accurate structures
Environment term - Burial of a residue: count how many Cbeta atoms are found within 10A of its Cb. The term calculates the probability to find this amino acid given the degree of burial. Implicitly accounts for solvation - the hydrophobic residues have more neighbors in a well solvated structure.
Pair – the probability of finding two residues at some sequence separation at a given distance. This term is normalized by the probability of each of them being found in such a distance from any aa, because this information is already accounted for in the env term – this allows the terms to be independent. Implicitly accounts for electrostatics and disulfide bond formation – cysteines and opposite charges will be found together more often.
neighbors: Cb-Cb <10Ǻ
Rohl et al. (2004) Methods in Enzymology 383:66
Origin: Simons et al., JMB 1997; Simons et al., Proteins 1999

10. Structure-Dependent Components
P(str | seq) = P(str) * P(seq | str) / P(seq)
Score = … + Srg + Scb + Svdw + …
Rg – radius of gyration (root of summed squared distances of all Calpha atom pairs). Will be relatively small for a globular, well packed structure. Implicitly accounts for attraction – residues near in space, and solvation, which reduces value compared to a non solvated protein.
Cbeta – how compact the structure is compared to random burial of amino acids. Corrects for the lack of interactions with the surrounding waters that were excluded.
Repulsive component of VdW – Penalty for each pair of residues that are found in a distance that is smaller than their sum of VdW radii (representing for each atom the region not to be penetrated).

11. Structure-Dependent Components
P(str | seq) = P(str) * P(seq | str) / P(seq)
Score = … + Srama
….+…..+ 10
Rama - given an amino acid with some secondary structure, what are the odds of finding it in the this phi, psi bin (ranges of 10 degree intervals, because odds of having exact phi,psi value pair is ~0).

12. Low resolution step over!
The resulting kind of structure from the low resolution step… the backbone will still be free to move in the following step, in the vicinity of the achieved fold, since side chain modeling might influence it, but in a finer sampling method so we don’t stray too much from this achieved model.

13. High-Resolution Step Structure Representation: Slow, exact step
All-atom (including polar and non-polar hydrogens, but no water)
Side chains as rotamers from backbone-dependent library
Side chain conformation adjusted frequently
High resolution scoring function
e.g. score12; Talaris; …
Slow, exact step
Locates global energy minimum
Backbone changes in this step are moderate
For each basin of low energy in the low resolution step a more fine tuned, high resolution search is performed. A rotamer would be a combination of side chain dihedral angles (denoted chi1, chi2, etc.), which is commonly observed in proteins for a given amino acid.
Dunbrack 1997

14. High-Resolution Step: Rotamer Libraries
Side chains have preferred conformations
They are summarized in rotamer libraries
Select one rotamer for each position
Best conformation: lowest-energy combination of rotamers
Rotamer libraries are based on statistics of known structures. Side chain preferences stem from an attempt to minimize side chain-backbone steric hindrance. Each peak in the distribution will be represented by a rotamer.
Serine c1 preferences
t=180o
g+=+60o
g-=-60o

15. High-Resolution Step – Major Contributions
Burial of hydrophobic groups away from water
Void-free packing of buried groups and atoms
Buried polar atoms form intra-molecular hydrogen bonds
At the end of this step, structure should behave like a native one, e.g. no buried unsatisfied polar atoms (not making any polar interaction), have pockets where water can fit in but not voids smaller than a water molecule.

16. High-Resolution Scoring Function
(score 12)
Packing interactions
Score = SLJ(atr + rep) + ….
Lennard Jones equation describes VdW interactions between two atoms. There’s linearization of the equation in the region where repulsion is dominant, since models can only jump between discrete side chain rotamers – we can’t make the very small changes that will reduce the energy in case there’s a clash, so instead we just don’t penalize that clash dramatically.
Between 5-5.5A there’s another linearization up to 0, so we don’t calculate all the interactions with faraway atoms that barely influence each other.
Linearized repulsive part
Linearized attractive part
e: well depth from CHARMm19
rij
d=5.5

17. High-Resolution Scoring Function
Implicit solvation
Score = … + Ssolvation + ….
xij2
xji2
xij=(rij - Ri)/li
Excluded volume implicit solvation model: Penalizes buried polars
The idea is that for each atom there is a reference energy – its energy in case it was surrounded by water only, and from that we reduce the energy of each surrounding atom that replaces the water. The VdW interactions calculated before come at the price of losing the surrounding waters, so this term introduces this loss too, without actually modeling water molecules (which is computationally expensive)
solvation free energy density of i
polar
polar
Lazaridis & Karplus, Proteins 1999

18. Solvation energy polar polar
xij2
xji2
solvation free energy density of i
Excluded volume implicit solvation model: Penalizes buried polars
Solvation free energy density is assumed to be approximated by a Gaussian distribution
fi(r)4 p r2 = ai exp (-xi2)
xi= (r – Ri)/li
li= 3.5A (6.0A for de-ionized groups) correlation length (width of first, or 2 first solvation shells)
ai = 2 * D Gifree/(sqrt p * li)
proportionality coefficient

19. Hydrogen Bonding Energy
(Kortemme, Morozov & Baker 2003 JMB)
Score = …. + Shb(srbb+lrbb+sc) + …. ]
srbb: short range, backbone HB
lrbb: long range, backbone HB
sc: HB with side chain atom
Hbonds are scored separately for side chains and for the backbone with itself, between residues near or far in sequence. Bonds involving protein backbones indicate secondary structure. Backbone-sidechain hydrogen bonds are also split into short-range and long-range, but this time according to the physical distance between the hydrogen and the acceptor. This is because the angular distributions of side-chain–side-chain h-bonds differs for the two different distance ranges. Residues participating in backbone-backbone H-bonds are not allowed to participate in a backbone-sidechain hydrogen bond (there was a bias towards residues that can form both types).
White bars- standard potential.
Based on statistics from high-resolution structures in the PDB
Slide from Jeff Gray

20. High-Resolution Scoring Function
Rotamer preference
Score = … + Sdunbrack + ….
The probability of the side chain is calculated as [probability of seeing that conformation given a phi,psi value * probability of seeing an amino acid given that phi,psi]/probability of that aa.
Dunbrack, 1997

21. Scoring Function: Summary
One long, generic function ….
Score = Senv+ Spair + Srg + Scb + Svdw + Sss+ Ssheet+ Shs + Srama + Shb (srbb + lrbb) + docking_score + Sdisulf_cent+ Srs+ Sco + Scontact_prediction + Sdipolar+ Sprojection + Spc+ Stether+ Sfy+ Sw+ Ssymmetry + Ssplicemsd + …..
docking_score = Sd env+ Sd pair + Sd contact+ Sd vdw+ Sd site constr + Sd + Sfab score
Score = SLJ(atr + rep) + Ssolvation + Shb(srbb+lrbb+sc) + Sdunbrack + Spair – Sref + Sprob1b + Sintrares + Sgb_elec + Sgsolt + Sh2o(solv + hb) + S_plane

22. Scoring Function: Summary
One long, generic function …. A weighted sum of
different terms: knowledge based and physics based
Score12 = w1*SLJatr + w2*SLJrep + w3*Ssolvation + w4*Shb(srbb+lrbb+sc) + w5*Sdunbrack + w6*Spair – Sref
Eventually the overall score of the protein is the sum of these different considerations, weighted according to the desired impact of each term in our protocol. When running different protocols, sometimes a different weight set is chosen, for instance in docking the weight of terms related to the interaction between proteins is increased, while the terms affecting mainly the structure of each monomer are decreased.
How can it be improved ?
Feature Analysis Tool : improve parameters
OptE : optimize weights
Leaver-Fay, …, & Baker (2013) Methods in Enzymology 523:109

23. How are scoring terms optimized?
Nature uses one scoring function…
Aim: one generic function for different applications
Optimization of parameters:
Originally from small molecules (experiments & quantum mechanical calculations)
Today: use of protein structures solved at high-accuracy
Benchmarks:
Discriminate ground state from alternative conformations
Identify correct side chain conformation
Predict effect of stability of point mutations (DDG)
We would want to have one energy function for the different desired tasks. From each task, new global truths can be discovered to improve the generic score function.
Some parameters are optimized using potentials from quantum mechanical calculations. We complement these types of terms with observations from protein structures.
To optimize a proposed function there are benchmarks evaluating the success of the function:
take different structures solved by x-ray, perturb them to different non native conformations and optimize a scoring function until near-native conformations are preferred over the alternative conformations.
side chains are stripped from a correct backbone conformation and need to be remodeled. This is a subtask of the aforementioned task, required for its success.
dG is the change in free energy when a protein folds (compared to unfolded state). ddG is the energy difference between the dG of a WT protein to that of a mutant protein and it represents the energetic effect of the mutation. Predicting this requires small changes to the protein, so if this fails, larger structural perturbation will also not be successful.
Leaver-Fay, …, & Baker (2013) Methods in Enzymology 523:109

24. Feature Analysis : improve scoring term
e.g. HB distance H- Og in Ser & Thr
Aim: similar distributions in crystal structures and models
Leaver-Fay, …, & Baker (2013) Methods in Enzymology 523:109

25. Feature Analysis : improve scoring term
e.g. HB distance H- Og in Ser & Thr
After correction: distribution in native & model structures overlap
Figure 6.3 H-bond length distributions for hydroxyl donors (SER/THR) to backbone oxygens. The thick curves are kernel density estimations from observed data normalized for equal volume per unit distance. The black curve in the background of each panel represents the Native sample source. (A) Boltzmann distribution for the length term in the Rosetta H-bond model with the Score12 and NewHB parameterizations. (B) Relaxed Natives with the Score12 energy function. The excessive peakiness is due to a discontinuity in the Score12 parametrization of the H-bond model. (C) Relaxed Natives with the NewHB energy function. (D) Relaxed Natives with the NewHB energy function and the Lennard–Jones minima between the acceptor and hydroxyl heavy atoms adjusted from 3.0 to 2.6 Å, and between the acceptor and the hydrogen atoms adjusted from 1.95 to 1.75 Å.
Aim: similar distributions in crystal structures and models
Leaver-Fay, …, & Baker (2013) Methods in Enzymology 523:109

26. OptE : optimize weights
Score12 = w1*SLJatr + w2*SLJrep + w3*Ssolvation + w4*Shb(srbb+lrbb+sc) + w5*Sdunbrack + w6*Spair – Sref
Maximum Likelihood Parameter Estimation
Benchmarks:
Discriminate ground state from alternative conformations
Identify correct side chain conformation
Sequence recovery in design: choose correct amino acid residue
Predict effect of stability of point mutations (DDG)
& more …
Aim: Best score for correct prediction
Leaver-Fay, …, & Baker (2013) Methods in Enzymology 523:109

27. Talaris-2013 scoring function
Parameter changes in some terms (e.g. improved geometries for h-bonds, disulfides;
new rotamer libraries).
better interpolation of
knowledge-based terms
Explicit Coulombic
electrostatic term with a
distance-dependent dielectric;
removal of the fa_pair term
rij
d=6.0
We use in the course a relatively old version of Rosetta, since it is considered stable. In the newer, recommended versions, there have been significant improvements to the scoring function. The most prominent change is the addition of an explicit electrostatic term (and the removal of the fa_pair term, which was supposed to implicitly consider electrostatics by the preference of charged residues to be near each other).
Leaver-Fay et al., Methods in Enzymology 2013
O’Meara et al., J. Chem. Theory Comput. 2015

28. Representations of protein structure: Cartesian and polar coordinates
PDB
x y z
ATOM N GLN A N
ATOM CA GLN A C
ATOM C GLN A C
ATOM O GLN A O
….. ….
Position PHI PSI OMEGA CHI1 CHI2 CHI3 CHI4 2 3 …. …

29. 2 ways to represent the protein structure
Cartesian coordinates (x,y,z; pdb format)
Polar coordinates (F-Y-W; equilibrium angles and bond lengths)
A protein is represented in the pdb as a set of atoms, each having their own x,y,z coordinates. Once we assume fixed bond lengths and bond angles, an alternative representation can store the first 3 atoms of the first residue as coordinates and then all other atoms will be represented only by their phi,psi angles relative to previous atoms.
ATOM N GLN A N
ATOM CA GLN A C
ATOM C GLN A C
ATOM O GLN A O
…..

30. The two representations in 2D
Cartesian representation:
points:
(0,0),(1,1),(1,2),(2,2),(3,3)
connections (of predefined length):
Internal coordinates:
bond lengths (predefined):
R=√2,1,1,√2
angles:
=450,90o,0o,45o x
(3,3) x √2
4-5 1
Same idea in 2D, for simplification
(1,2)
45o
(2,2)
3-4
2-3 1
90o
1-2
(1,1) √2
45o y y
(0,0)

31. The two representations in 2D
Constraint: keep bond length fixed upon movement
Cartesian representation
(0,0),(1,1),(1,2),(2,2),(3,3) 
(0,0),(1,1),(1,2),(2,2),(3,0)
Bond length changed!
Polar coordinates
450,90o,0o,45o 
450,90o,45o,45o
Bond length unchanged! x x
The advantage of polar coordinates representation over Cartesian coordinates is that any change in an angle does not change bond lengths and the structure is not distorted. √2 √3 y y

32. Polar Cartesian coordinates
Convert r and q to x and y x y
√2,1,1,√2
450,90o,0o,45o
(0,0),(1,1),(1,2),(2,2),(3,3)
From wikipedia

33. Cartesianpolar coordinates
Convert x and y to r and q x y
(0,0),(1,1),(1,2),(2,2),(3,3)
√2,1,1,√2
450,90o,0o,45o

34. Moving to a 3D world Cartesian representation: Internal coordinates:
points: additional z-axis
(0,0,0),(1,1,0),(1,2,0),
(2,2,0),(3,3,0)
connections (predefined):
1-2,2-3,3-4,4-5
Internal coordinates:
bond lengths (predefined):
√2,1,1,√2
angles:
450,90o,0o,45o
dihedral angles:
1800,180o z y x
Proteins: bond lengths and angles fixed. Only dihedral angles are varied

35. 2 ways to represent the protein structure
Cartesian coordinates
(x,y,z; pdb format)
Intuitive – look at molecules in space
Easy calculation of energy score (based on atom-atom distances)
Difficult to change conformation of structure (while keeping bond length and bond angle unchanged)
Polar coordinates
(F-Y-W; equilibrium angles and bond lengths)
Compact (3 values/residue)
Easy changes of protein structure (turn around one or more dihedral angles)
Non-intuitive
Difficult to evaluate energy score (calculation of neighboring matrix complicated)
Another advantage for polar coordinates is that the representation is compact – need less information stored to know where each atom lies. The disadvantages of this representation are exactly the advantages of Cartesian representation.

36. Solution: toggle MOVE STRUCTURE - Polar coordinates:
Transform: calculate dihedral angles from coordinates
MOVE STRUCTURE - Polar coordinates:
introduce changes in structure by rotating around dihedral angle(s) (change F-Y values)
CALCULATE ENERGY - Cartesian coordinates:
Derive distance matrix (neighbor list) for energy score calculation
It is possible to enjoy the advantages of both representations. It is rather easy to convert one representation to the other. The workflow is as following:
Move structure in polar space (without distorting it)
Build Cartesian representation from the polar coordinates and calculate the energy (which heavily relies on atom distances - very simple in Cartesian space).
Build Polar coordinates representation and move the structure again, and so on.
Transform: build positions in space according to dihedral angles
PDB
x y z
ATOM N GLN A N
ATOM CA GLN A C
ATOM C GLN A C
ATOM O GLN A O
….. ….
Position PHI PSI OMEGA CHI1 CHI2 CHI3 CHI4 2 3 …. …
(0,0),(1,1),(1,2),(2,2),(3,3)
450,90o,0o,45o

37. Cartesian polar coordinates
How to calculate polar from Cartesian coordinates: example F: C’-N-Ca-C
define plane perpendicular to N-Ca (b2) vector
calculate projection of Ca-C (b3) and C’-N (b1) onto plane
calculate angle between projections
PDB
x y z …
ATOM C GLN A N
ATOM N GLY A C
ATOM CA GLY A C
ATOM O GLY A O
….. ….
Position PHI PSI OMEGA CHI1 CHI2 CHI3 CHI4
….. 33 34 …. …
(0,0),(1,1),(1,2),(2,2),(3,3)
450,90o,0o,45o

38. Polar Cartesian coordinates
Find x,y,z coordinates of C, based on atom positions of C’, N and Ca, and a given F value (F: C’-N-Ca-C)
create Ca-C vector:
size Ca-C=1.51A (equilibrium bond length)
angle N-Ca-C= 111o (equilibrium value for N-Ca-C angle)
rotate vector around N-Ca axis to obtain projections of Ca-C and N-C’ with desired F
PDB
x y z …
ATOM C GLN A N
ATOM N GLY A C
ATOM CA GLY A C
ATOM O GLY A O
….. ….
Position PHI PSI OMEGA CHI1 CHI2 CHI3 CHI4
….. 33 34 …. …
(0,0),(1,1),(1,2),(2,2),(3,3)
450,90o,0o,45o

39. Representation of protein structure1 2 3 4 5 6 7 8
3 backbone dihedral angles per residue
Build coordinates of structure starting from first atom, according to dihedral angles (and equilibrium bond length and angle) – Atom tree 1 2 3 4 5 6 7 8 7 8
In Rosetta there’s a dedicated object that stores the information to convert representations – the atom tree. When changing a dihedral angle between residue 6 and residue 7, there is no need to recalculate the Cartesian coordinates of all the previous residues, just the ones following the change (even if only one dihedral changed, all the following segment changes along with that rotation).
Sampling and minimization in TORSIONAL space:
change angle and rebuild, starting from changed angle
Based on slides by Chu Wang

40. Representation of protein structure
Rosetta folding 1 2 3 4 5 6 7 8
3 backbone dihedral angles per residue
Sampling and minimization in TORSIONAL space
Sampling and minimization in RIGID-BODY space
The atom tree allows to change the representation for all the covalently connected residues, but when there are two bodies interacting (e.g. two different proteins or a protein and a ligand) there’s need to sample other degrees of freedom (movement along the x,y,z axes and 3 possible rotations).
Backbone dihedral
angles fixed (rigid-body) 4 3 1 2 8 7 5 6
Rosetta docking 4’ 3’ 1’ 2’ 8’ 7’ 5’ 6’
6 rigid-body DOFs --
3 translational vectors
3 rotational angles
How can those two types of degrees of freedom be combined?

41. Fold tree representation
Construct fold-trees to treat a variety of protein folding and docking problems.
Allows simultaneous optimization of rigid-body and backbone/sidechain torsional degrees of freedom.
Example:
fold-tree based docking
“peptide” edge – 3 backbone dihedral angles 4 3 1 2 8 7 5 6
“long-range” edge (Jump) – 6 rigid-body DOFs
The fold tree object is responsible for defining connectivity between residues in different entities. In the case of two interacting proteins, each polymeric connection within the monomers is represented by a peptide edge and there is one non polymeric connection, a jump edge, defining the orientation of one protein relative to the other. 4’ 3’ 1’ 2’ 8’ 7’ 5’ 6’ 4’ 3’ 1’ 2’ 8’ 7’ 5’ 6’
“peptide” edge – 3 backbone dihedral angles
Fold tree: Bradley and Baker, Proteins (2006)

42. Fold-trees for different modeling tasks
protein folding N C
Color – flexible bb
Gray – fixed bb
Flexible “peptide” edge
rigid “peptide” edge 1 1’
rigid “jump” 1 1’
flexible “jump”
N: N-terminal; C: C-terminal; X: chain break; O: root of the tree;

43. Fold-tree for loop modeling1 x 1’ 2 x 2’ C
If we have a protein fold we want to preserve but want to model two loops in it, we can define which residues will remain fixed – a rigid jump between the ends of the loop will define the continuation of the structure relative to the segment before the loop (so one dihedral change will not propagate along the structure), and the loop itself will be flexible. The problem in this situation is that for the residues x in the loop, there are instructions on how to be built from two routes in the tree and these instructions will conflict once the loop is moved. In other words, this representation does not allow any cycles to exist. Therefore, the solution is to add a cut point wherever there’s a cycle in the tree.
Color – flexible bb
Gray – fixed bb
Flexible “peptide” edge
rigid “peptide” edge 1 1’
rigid “jump” 1 1’
flexible “jump”
N: N-terminal; C: C-terminal; X: chain break; O: root of the tree;

44. Fold-trees for different modeling tasks1 C 1’
fully flexible docking N 1 1’ C 2 2’ x 3’ 3
docking w/ loop modeling
What complicates things is that this representation does not allow any cycle to avoid situations where a residue can be reached by two different routes in the tree and in fact has conflicting instructions on how to be buil N 1 C 1’
docking w/ hinge motion
Color – flexible bb
Gray – fixed bb
Flexible “peptide” edge
rigid “peptide” edge 1 1’
rigid “jump” 1 1’
flexible “jump”
N: N-terminal; C: C-terminal; X: chain break; O: root of the tree;

45. Fold-trees for different modeling tasks
Color – flexible bb
Gray – fixed bb
Pale – symmetry operation

46. Fold-trees for different modeling tasks
Color – flexible bb
Gray – fixed bb
Filled colored circles - flexible sc

47. Fold-trees for different modeling tasks
Color – flexible bb
Gray – fixed bb
Filled colored circles - flexible sc
empty colored circles – flexible amino acid: design

48. Fold-trees for different modeling tasks
Color – flexible bb
Gray – fixed bb
Filled colored circles - flexible sc
empty colored circles – flexible amino acid: design