1. Two views of the protein folding puzzle
BIOMAT 2017, the 7-th international Symposium
Moscow, Russia, October 30 - November 3, 2017
Two views of the protein folding puzzle
Alexei V. Finkelstein,
A.Y. Badretdin, O.V. Galzitskaya, D.N. Ivankov, N.S. Bogatyreva, S.O. Garbuzynskiy
Institute of Protein Research, RAS, RF;
NCBI-NIH, USA;
BGP-CRG, IST, UPF, Spain

2. Protein folding problem:
unique protein chain
folds (HOW?) into
unique 3D structure

3. unique protein chain folds (HOW?) into unique 3D structure
Protein chain: a polypeptide
Protein chain sequence: unique
unique protein chain
folds (HOW?) into
unique 3D structure
Emil Fischer (1852 –1919)
Nobel Prize: 1902
Frederick Sanger (1918 –2013)
Nobel Prizes: 1958, 1980
3D protein structure
X-ray
3D protein structure
NMR
Max  Perutz (1914 –2002) 
Nobel Prize: 1962
Kurt Wüthrich, 1938
Nobel Prize: 2002

4. Folding in vivo: minutes or less
NOT ONLY IN VIVO:
Spontaneous
protein folding
(refolding)
in vitro
Unfolded chain Native structure
Christian Anfinsen
(1916 –1995)
Nobel Prize: 1972 
Bruce Merrifield
(1921 – 2006)
Nobel Prize: 1972  
Folding
of chemically
synthesized
ribonuclease А
Refolding
of natural
ribonuclease А
Folding in vivo: minutes or less
Folding (refolding) in vitro: hours, minutes or less
Refolding is most typical for water-soluble, globular,
non-modified single-domain proteins (or separate domains)

5. Co-translational folding in vivo protein folding in vitro –
and
protein folding in vitro –
TWO PROBLEMS OR ONE?

6. Cotranslational protein folding in vivo (at ribosome);
at least for a small protein
 as in vitro
15N, 13C NMR:
Cotranslational structure acquisition of nascent
polypeptides monitored by NMR spectroscopy.
Eichmann, …, Deuerling, PNAS 107, 9111 (2010)
“Polypeptides [at ribosome] remain unstructured during elongation but fold into a compact, native-like structure when the entire sequence is available”
Small ingle-domain water-soluble proteins
Monitoring cotranslational protein folding in
mammalian cells at codon resolution.
Hana, ...., Qian, PNAS 109, (2012)
FLUORESCENCE (FRET, PET)
Cotranslational protein folding on the ribosome monitored in real time.
Holtkamp, …, Rodnina, SCIENCE 350, 1104 (2015)
Unfinished chain  as “natively disordered”
In vitro folding is a good model of the in vivo folding!

7. Cyrus Levinthal 
(1922 –1990)

8. Special pathways??
Phillips (1965): hypothesis:
nucleus of folding is formed at the N-terminus
of protein chain, and the remaining chain wraps around it
FOR SINGLE DOMAIN PROTEINS: NO:
Goldenberg & Creighton, 1983:
circular permutants: NO special role of the N-terminus
_____________________________________________________
DO NOT CONFUSE:
folding from the N-terminus in a domain (which is NOT observed)
and
folding starts from the whole N-terminus domain (which IS observed)!

9. Two views on the protein
folding/unfolding
Oleg PTITSYN
( )
Stepwise hypothesis:
Piotr PRIVALOV,
1932
Experiment:
“all-or-none”
(no intermediates)
intermediates
U N
U N
BUT:
folding/unfolding
is reversible:
[Segawa, Sugihara, 1984]

10. Special intermediates??
Special pathways??
Stepwise protein self-organization [Ptitsyn, 1973]
Unfolded chain
Secondary structures
fluctuating around their
native positions in the chain
Native-like
secondary structures
& folding pattern
Native tertiary
structure

11. Special intermediates??
Special pathways??
Stepwise protein self-organization [Ptitsyn, 1973]
Unfolded chain
Secondary structures
fluctuating around their
native positions in the chain
Native-like
secondary structures
& folding pattern
Native tertiary
structure
Stability increase
Now: observed:
“Pre-molten globule”
Now: observed:
“Molten globule”

12. Special intermediates??
Special pathways??
Stepwise protein self-organization [Ptitsyn, 1973]
Unfolded chain
Secondary structures
fluctuating around their
native positions in the chain
Native-like
secondary structures
& folding pattern
Native tertiary
structure
Stability increase
Now: observed:
“Pre-molten globule”
Now: observed:
“Molten globule”
BUT:
- This works only when stability increases from stage to stage

13. Special intermediates??
Special pathways??
Stepwise protein self-organization [Ptitsyn, 1973]
Unfolded chain
Secondary structures
fluctuating around their
native positions in the chain
Native-like
secondary structures
& folding pattern
Native tertiary
structure
Stability increase
Now: observed:
“Pre-molten globule”
Now: observed:
“Molten globule”
BUT:
- This works only when stability increases from stage to stage
- Many proteins fold without observable intermediates

14. Special intermediates??
Special pathways??
Stepwise protein self-organization [Ptitsyn, 1973]
Unfolded chain
Secondary structures
fluctuating around their
native positions in the chain
Native-like
secondary structures
& folding pattern
Native tertiary
structure
Stability increase
Now: observed:
“Pre-molten globule”
Now: observed:
“Molten globule”
BUT:
- This works only when stability increases from stage to stage
- Many proteins fold without observable intermediates
- Does not predict dependence of the folding rate on protein size

15. And:
Maybe, the “Levinthal’s paradox” is not a paradox at all?

16. ? … any tilt of the E-surface solves the “Levinthal’s paradox” ?
model
? … any tilt of the
E-surface solves
the “Levinthal’s
paradox” ?
Bryngelson, Wolynes,
1989

17. ? … any tilt of the E-surface solves the “Levinthal’s paradox” (!?)?
model
? … any tilt of the
E-surface solves
the “Levinthal’s
paradox” (!?)?
Bryngelson, Wolynes,
1989

18. ? … any tilt of the E-surface solves the “Levinthal’s paradox” (!?)?
Bryngelson, Wolynes,
1989

19. ? … any tilt of the E-surface solves the “Levinthal’s paradox” ?
Bryngelson, Wolynes,
1989

20. volcano is high in the absence of phase separation
? … any tilt of the
E-surface solves
the “Levinthal’s
paradox” ?
Bryngelson, Wolynes,
1989
volcano is high
(~100 kT0 for 100 res.)
in the absence of
phase separation

21. “all-or-none”
310
320

22. volcano Question: maybe, the “Levinthal’s paradox”
is not a paradox at all?
Answer: Levinthal’s paradox
still exists, because the barrier
prevents the “downhill” folding!
volcano

24. # 
BARRIER

26. # Knots: insignificant: < ~2L/100-fold slowing MD: Phase separation
Shaw, 2010
Knots: insignificant:
< ~2L/100-fold slowing

28. __

29. SAMPLING:
Levinthal: all conformations
We: all compact
structures only

33. Sampling: ~ LN: <L/N>15 a.a.per secondary structure
The main reason for decrease of the conformation space at the level of secondary structures:
their number N is much smaller than the number L of a.a. residues 1 L
<L/N>15 a.a.per secondary structure

34. L2/3 ~L
34.5
3-L/ps
100
500
100

35. ~L L2/3 34.5 “Simple” folds (weak entangling) observed “simple” 100
500
100

36. Conclusions:
Exhaustive sampling
at the level of
amino acid residues
IS IMPOSSIBLE
secondary structure
elements
IS POSSIBLE at N<100
The Lewinthal’s paradox is solved at the level of combinatorics, without
energetics
L amino
acid
residues
N secondary
structure
elements
Complete conformation
space volume ~ LN
NOT Levinthal’s 3L or 10L or (102)L
(N  L/15 or N  (34.5)L1/3)
But energy funnels, of course,
accelerate folding even more, which is especially important for long protein chains

38. Two views of the protein folding puzzle
BIOMAT 2017, the 7-th international Symposium
Moscow, Russia, October 30 - November 3, 2017
Two views of the protein folding puzzle
Alexei V. Finkelstein,
A.Y. Badretdin, O.V. Galzitskaya, D.N. Ivankov, N.S. Bogatyreva, S.O. Garbuzynskiy
Institute of Protein Research, RAS, RF;
NCBI-NIH, USA;
BGP-CRG, IST, UPF, Spain
Gratitude to:
- Anonymous referees of our papers
- Programs MCB, RFBR, HHMI – for support of the 1st part of this work;
- Russian Science Foundation – for support of the 2nd part of this work

40. Lecture 21

42. TWO VIEWS ON THE PROTEIN FOLDING PUZZLE
ALEXEI V. FINKELSTEIN
Institute of Protein Research, Russian Academy of Sciences, Pushchino, Moscow Region , Russian Federation
The ability of protein chains to spontaneously form their spatial structures is a long-standing puzzle in molecular biology.
This review describes physical theories of rates of overcoming the free-energy barrier separating the natively folded (N) and unfolded (U) states of protein chains in both directions: “U-to-N” and “N-to-U”. In the theory of protein folding rates a special role is played by the point of thermodynamic (and kinetic) equilibrium between the native and unfolded state of the chain; here, the theory obtains the simplest form. Paradoxically, a theoretical estimate of the folding time is easier to get from consideration of protein unfolding (the “N-to-U” transition) rather than folding, because it is easier to outline a good unfolding pathway of any structure than a good folding pathway that leads to the stable fold, which is yet unknown to the folding protein chain. And since the rates of direct and reverse reactions are equal at the equilibrium point (as follows from the physical “detailed balance” principle), the folding time can be derived from the easier estimated unfolding time: theoretical analysis of the “N-to-U” transition outlines the range of protein folding rates in a good agreement with experiment, although experimentally measured folding times for single-domain globular proteins range from microseconds to hours: the difference (10–11 orders of magnitude) is the same as that between the life span of a mosquito and the age of the Universe.
Supplemental theoretical analysis of folding (the “U-to-N” transition), performed at the level of formation and assembly of protein secondary structures, outlines the upper limit of protein folding times (i.e., of the time of search for the most stable fold). Both theories come to essentially the same results; this is not a surprise, because they describe overcoming one and the same free-energy barrier, although the way to the top of this barrier from the side of the unfolded state is very different from the way from the side of the native state; and both theories agree with experiment. In addition, they predict the maximal size of protein domains that fold under solely thermodynamic (rather than kinetic) control and explain the observed maximal size of the “foldable” protein domains.

43. Self-organization (non-assisted folding):
The chain of a globular protein
is capable [Anfinsen, 1961; Merrifield, 1969]
of refolding, i.e., after unfolding, it can
spontaneously
restore its native 3D structure in vitro
Folding time:
in vitro: microseconds to hours
in vivo: within minutes
(Biosynthesis AND folding of even large
globular proteins takes minutes in vivo)
Self-organization (refolding) in vitro is most typical for:
globular, water-soluble,
non-modified,
single-domain protein (or separated domains)

45. «Golden triangle» for folding rates of globular proteins
Folding of 107 single-domain proteins under the aqueous conditions (no denaturant)
& their folding under the “mid-transition” conditions
-G  10RT
in water
= 0
100 a.a. residues:
Upper limit of protein that folds under complete thermodynamic control
Structures of larger proteins are restricted by kinetic control

46. Kinetic control: structures of larger proteins are restricted.
In particular [Taylor et al., Structure 17, 1244 (2009)],
larger proteins have smaller Baker’s “contact order” (CO),
i.e., they have less contacts between remote chain regions,
because the folding time rapidly grows with AbsCO = CO  L
[Ivankov, Garbuzynskiy, Alm, Plaxco, Baker, Finkelstein. Protein Sci., 12:2057 (2003)].

47. RATE > 107s-1/(LL/15) or RATE > 107s-1 /(LL2/3/4)
folding (experiment):
from [Rollins, Dill, 2014]
RATE > 107s-1/(LL/15) or
≳3/2L1/3
RATE > 107s-1 /(LL2/3/4)
Limitation of
possible protein
chain folds (weak
entangling)
<80100 a.a.:
Sampling of all conformations at the level of secondary structures
DOES NOT limit protein folding: the sampling rate exceeds the “bio-limit”
(all or almost all secondary structures
are at the protein surface)
>100 a.a.:
LIMITS possible protein structures
[cf. Garbuzynskiy et al., PNAS, 2013] 
(simplified topologies: small CO,
the Plaxco-Simons-Baker’s
“contact order”)
“Simple” protein
chain folds (weak
entangling)

48. «Golden triangle» for folding rates of globular proteins
Folding of 107 single-domain proteins under the aqueous conditions (no denaturant)
& their folding under the “mid-transition” conditions
-G  10RT
in water
= 0
600 a.a. residues: Larger globular domain cannot fold within a “bio-reasonable” time

49. in CATH:
no such compact domains;
there are a few strongly oblong or oblate
600 residues is indeed the upper limit of size of known globular protein domains