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

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

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

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)

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

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, 12467 (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!

Cyrus Levinthal  (1922 –1990)

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)!

Two views on the protein folding/unfolding Oleg PTITSYN (1929-1999) Stepwise hypothesis: Piotr PRIVALOV, 1932 Experiment: “all-or-none” (no intermediates) intermediates U N U N BUT: folding/unfolding is reversible: [Segawa, Sugihara, 1984]

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

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”

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

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

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

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

? … 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

? … 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

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

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

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

“all-or-none” 310 320

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

#  BARRIER

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

__

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

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

L2/3 ~L 34.5 3-L/ps 100 500 100

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

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

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

Lecture 21

TWO VIEWS ON THE PROTEIN FOLDING PUZZLE ALEXEI V. FINKELSTEIN Institute of Protein Research, Russian Academy of Sciences, Pushchino, Moscow Region 142290, 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.

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)

«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

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)].

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)

«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

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