Can nuclear theory help find an anti-viral drug for - COVID-19? Pietro Faccioli - Istituto Nazionale di Fisica Nucleare
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Can nuclear theory help find an anti-viral drug for COVID-19? Pietro Faccioli
A LONG JOURNEY
??????
REDUCTIONIST’S APPROACH TO
MOLECULAR BIOLOGY
Challenge:
Integrate ~106 coupled
Newton-type equations
looking for extremely
rare events
RARE EVENT PROBLEMS
MD
106s
MD Protein
, folding
ms s minutes
MD YIELDS CORRECT PROTEIN NATIVE STATES
Anton supercomputer MD
(DES Research)
Atomic-Level Characterization of the Structural Dynamics of Proteins
How Fast-Folding Proteins Fold
Atomic-Level Characterization of the Structural Dynamics of Proteins reso
David E. Shaw, et al.
David 330
Science E. Shaw , et al.
, 341 (2010); prot
Science
DOI: 330, 341 (2010);
10.1126/science.1187409 unst
DOI: 10.1126/science.1187409 Kresten Lindorff-Larsen,1*† Stefano Piana,1*† Ron O. Dror,1 David E. Shaw1,2† to f
sam
An outstanding challenge in the field of molecular biology has been to understand the process pert
by which proteins fold into their characteristic three-dimensional structures. Here, we report the hom
This copy is for your personal, non-commercial use only.
results of atomic-level molecular dynamics simulations, over periods ranging between 100 ms F
and 1 ms, that reveal a set of common principles underlying the folding of 12 structurally diverse we
This copy is for your personal, non-commercial use only.
proteins. In simulations conducted with a single physics-based energy function, the proteins, the
ZOOLOGY OF ENHANCED SAMPLING METHODS Markov State Models, Milestoning, Transition Path Sampling, Transition Interface Sampling, Forward Flux Sampling, Temperature Accelerated Molecular Dynamics, Metadynamics, Umbrella Sampling, Blue Moon Sampling, String Method,Stochastic Difference, … [and counting] They are all too computationally demanding for many biologically relevant problems.
A LONG JOURNEY
A USEFUL ANALOGY
Thermal activation ( = (KB T ) 1
)
kB T
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
Z xf Rt
d⌧ (M q̈+M q̇+rU (q))2
P (xf , t|xi ) = Dq e 4M 0
xi
Quantum tunneling
Z xf Rt 2
1
d⌧ ( M
2 q̇ +U (q))
KE (xf , t|xi ) = Dq e ~
~
0
xi
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
ADVANTAGES
tMFPT tTPT
✓ ◆
tM F P T
tT P T ⇠ ⌧0 log log
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
⌧0
VARIATIONAL APPROACHES TO
TRANSITION PATH SAMPLING
Dominant Reaction Pathways
PHYSICAL REVIEW LETTERS week ending PHYSICAL REVIEW LETTERS week ending
PRL 97, 108101 (2006) 8 SEPTEMBER 2006 PRL 99, 118102 (2007) 14 SEPTEMBER 2007
Dominant Pathways in Protein Folding Quantitative Protein Dynamics from Dominant Folding Pathways
1,2 3 4 5
P. Faccioli, M. Sega, F. Pederiva, and H. Orland M. Sega,1 P. Faccioli,2,3 F. Pederiva,4 G. Garberoglio,1 and H. Orland5
1
Dipartimento di Fisica Universitá degli Studi di Trento e I.N.F.N, Via Sommarive 14, Povo (Trento), I-38050 Italy 1
C.N.R./I.N.F.M. and Dipartimento di Fisica, Università degli Studi di Trento, Via Sommarive 14, Povo (Trento), I-38050 Italy
2
European Centre for Theoretical Studies in Nuclear Physics and Related Areas (E.C.T.*),
(2005) (2006)
2
Dipartimento di Fisica Università degli Studi di Trento e I.N.F.N, Via Sommarive 14, Povo (Trento), I-38050 Italy
Strada delle Tabarelle 284, Villazzano (Trento), I-38050 Italy 3
European Centre for Theoretical Studies in Nuclear Physics and Related Areas (E.C.T.), Strada delle Tabarelle 284,
3
C.N.R./I.N.F.M. and Dipartimento di Fisica, Universitá degli Studi di Trento, Via Sommarive 14, Povo (Trento), I-38050 Italy Villazzano (Trento), I-38050 Italy
4
Dipartimento di Fisica and C.N.R./I.N.F.M.-DEMOCRITOS National Simulation Center, Universitá degli Studi di Trento, 4
Dipartimento di Fisica and C.N.R./I.N.F.M.-DEMOCRITOS National Simulation Center, Università degli Studi di Trento,
Via Sommarive 14, Povo (Trento), I-38050 Italy Via Sommarive 14, Povo (Trento), I-38050 Italy
5
Service de Physique Théorique, Centre d’Etudes de Saclay, F-91191, Gif-sur-Yvette Cedex, France 5
Service de Physique Théorique, Centre d’Etudes de Saclay, F-91191 Gif-sur-Yvette Cedex, France
(Received 5 December 2005; published 6 September 2006)
(Received 30 January 2007; published 12 September 2007)
Dominant folding pathways of a WW domain
We present a method to investigate the kinetics of protein folding and the dynamics underlying the
formation of secondary and tertiary structures during the entire reaction. By writing the solution of the
We develop a theoretical approach to the protein-folding problem based on out-of-equilibrium
stochastic dynamics. Within this framework, the computational difficulties related to the existence of
Fokker-Planck equation in terms of a path integral, we derive a Hamilton-Jacobi variational principle from
folding Škrbić , Roberto Covino , and Pietro Faccioli large time scale gaps are removed, and simulating the entire reaction in atomistic details using existing
a,b a,c a,b a,b,1
which we are able to compute the most probable pathway of folding. The methodSilvio a Beccara
is applied to the , Tatjana
of the Villin headpiece subdomain simulated using a Go model. An initial collapsing
a phase
Dipartimento by the degli Studi di Trento, Via Sommarive 14, I-38123 Povo (Trento),computers
drivenUniversità
di Fisica,
becomes feasible. We discuss how to determine the most probable folding pathway, identify
Italy; bINFN Istituto Nazionale di Fisica Nucleare
initial configuration is followed by a rearrangement phase, in which secondary structures
(National are for
Institute formed
Nuclearand
Physics), Gruppo Collegato di Trento, Via Sommarive 14, I-38123 Povo configurations
(Trento) Italy; representative of the
and cEuropean Centre for transition
Theoretical state, and compute the most probable transition time. We
Studies in Nuclear Physics
all computed paths display strong similarities. This completely general method does not require the prior and Related Areas, Strada delle Tabarelle 286, I-38123 Villazzano perform
(Trento), Italy an illustrative application of these ideas, studying the conformational evolution of alanine
knowledge of any reaction coordinate and is an efficient tool to perform simulations
Edited byof the entire
William A. Eaton,folding dipeptide, within an all-atom model
National Institutes of Health -NIDDK, Bethesda, MD, and approved December 19, 2011 (received for review July 27, 2011)
based on the empiric GROMOS96 force field.
process with available computers.
We investigate the folding mechanism of the WW domain Fip35 DOI: 10.1103/PhysRevLett.99.118102
Noé, et al. performed a Markov state model analysis of a large PACS numbers: 87.14.Ee, 83.10.Mj, 87.15.Cc
DOI: 10.1103/PhysRevLett.97.108101 PACS numbers:using a realistic
87.14.Ee, atomistic
83.10.Mj, force field by applying the Dominant
87.15.Cc number of short (≲200 ns) nonequilibrium MD trajectories (11)
Reaction Pathways approach. We find evidence for the existence performed on the WW domain of human Pin 1 protein. In their
of two folding pathways, which differ by the order of formation paper the authors reported a complex network of transition path-
(2012)
Understanding the kinetics of protein folding [1] and the structure was obtained from
of the twothe Brookhaven
hairpins. Protein
This result Data with the analysis of
is consistent A critical
ways, which differpartbyofthethe protein-folding
specific order in which problem is tolocal
the different under- In this Letter we further develop our formalism and we
dynamical mechanisms involved in the formation of their Bank. the experimental data on the folding kinetics of WW domains meta-stable
stand states were
its kinetics andvisited. On the other
the underlying hand, in processes.
physical all pathways To present the first DFP simulation performed in full atomistic
structures in an all-atom approach involves simulating a andon
Our study is based with
thetheanalogy
results obtained
betweenfrom large-scale molecular dynamics
Langevin the formation of hairpins takes place in a definite sequence (see
simulations of this system. Free-energy calculations performed in this aim,2).several
e.g., Fig. different
In particular, fromtheoretical
the statisticalmethods
model ithavewas in-been detail. We show how the DFP analysis gives access to
statistically significant ensemble of folding trajectories for diffusion and quantum propagation. Previous studies have important information about the dynamics of the folding
two coarse-grained models support the robustness of our results recently
ferred thatdeveloped,
in about 30% spanning from transitions,
of the folding analyticalthe approaches
second
a system of !104 degrees of freedom. Unfortunately, the exploited such a connection to study a variety of diffusive process, such as the characterization and determination of
and suggest that the qualitative structure of the dominant paths [1] to detailed
hairpin forms first, computer
as in the simulations
right box. [2,3]. A major prob-
existence of a huge gap between the microscopic time problems using path-integral methods
are mostly shaped by [4,5]. In this
the native work, Computing a folding
interactions. A indifferent conclusion has beenprocess
reached using
by Shaw, et al., by
Bias Functional Approach Self Consistent Path Sampling
lem simulating the folding standard mo- the transition state, and the most probable transition time.
scale of the rotational degrees of freedom !10"12 s and we develop the formalism to in
trajectory determine explicitly
atomistic detail the evo-about one hour on 48
only required analyzing a ms-long MD trajectory with multiple unfolding/
lecular dynamics (MD) is the huge gap between the time In addition, we show that in this formalism the native state
the macroscopic time scales of the full folding process lution of the position of each monomer of the protein,
Central Processing Units. The gain in computational efficiency refolding events, obtained using a special-purpose supercompu-
opens the door to awithout
systematic investigation scale ofIn‘‘elementary
that simulationmoves,’’ of theoforder
Fip35of was10 –100to ps, is characterized by a single effective parameter, and this
!10"6 –101 s makes it extremely computationally chal- during the entire folding transition, relying on a of the folding path- ter (12). the WW domain found
lenging to follow the evolution of a typical !100-residue
ways of a large number of globular proteins.
specific choice of the reaction coordinate. and thatunfold
fold and of thepredominantly
entire folding alongprocess,
a pathwaywhich ranges
in which hairpinfrom
1 a leads to an interesting relationship between kinetic and
Before entering the details of our ∣calculation,
is fully structured, before hairpin 2 begins to fold,
few microseconds for fast folders [4], up to several seconds as shown in the thermodynamical quantities.
protein for a time interval longer than a few tens of atomistic simulations protein folding it is con- left box of Fig. 2. In a recent paper (13), Krivov reanalyzed the
nanoseconds. venient to review the mathematical framework in a simple or even minutes for more complex proteins. This peculiar- Let us begin our discussion by briefly reviewing the key
same ms-long MD trajectory in order to identify an optimal set of
concepts of the DFP method, here presented for a simple
Several approaches have been proposed to overcome
such 114, 098103 (2015)
PRL computational difficulties and address the problem
case. For this purpose, let
U us consider
nveiling Langevin
the mechanism
P H Y S I C A L R E V I E W L E T T E R Snative structure remains one
by diffusion
of a point particle in one dimension, subject to an6 external
problems at the interface of
which
MARCH
proteins fold into their
week ending
of the 2015
contemporary
fundamental open
molecular biology,
ity of the
reaction
dynamics
folding process
coordinates.
WW domainapproach is thermally too
makeswas
His conclusion
demanding,
activated
thethat
brute-force
the foldingmolecular
andincipient
rather than a substantial
of this
downhillpart one-dimensional system, without loss of generality.
The DFP method can be applied to any system described
of identifying the relevant pathways of the folding re- potential U#x$: andthe
of thatefforts
the transition also occurs
in the field through a second
of protein-folding pathway, aims
simulation in
biochemistry, and biophysics. A critical point concerns the char- which hairpin 2 forms before hairpin 1. The statistical weights of by the over-damped Langevin equation
action [2]. Unfortunately, these methods are either af- D @U at bridging this gap.
Variational Scheme to Compute ProteintoReaction Pathways @x acterization
Using of the ensemble of reactive trajectories connecting
Atomistic the two pathways estimated from the number of folding events
fected by uncontrolled systematic errors associated %
the "denatured & !#t$; Force Fields (1) areIn a recent paper 20%[5] we presented a novel theoretical D @U
k T @xand native states, in configuration space. 80% ! 20% and ! 10%. @x
ad hoc approximations or can be applied only with to smallExplicit Solvent @t In thisB context, a fundamental question which has long been framework
While all thesefor investigating
theoretical studies theyield
folding
folding dynamics, named
times in rather @t
!"
kB T @x
# !$t%; (1)
proteins with a typical folding time of the order of a few where !#t$ is a Gaussian noise with zero average and globular proteins in-
debated (1) is whether the folding of typical good agreement
hereafter Dominant with available
Foldingexperimental
Pathways (DFP), data on which
folding is
volves a few dominant pathways;
nanoseconds (fast folders). In this Letter, S. a we present
Beccara, 1,3 a 2
correlation
L. Fant, given by
and P. Faccioli 2,3,*h!#t$!#t 0 $i % 2D"#t " t0 $.i.e.,
In well
thisdefined and conserved
sequences of secondary and tertiary contact formation, or if it can
kinetics, they provide different pictures of the
based on a reformulation in terms of path integrals of the folding mechanism where U is the potential energy of the system, !$t% is a
novel approach to overcome 1 these difficulties: We adopt and raise a number of issues. Gaussian random force with zero average and correlation
European Centre for Theoretical Nuclearequation, D isRelated
Physics and the diffusion
Areas
take constant
through aofmultitude
place(ECT*-FBK), the particle in the different routes. A
of qualitatively dynamics described
Firstly, it is important by the Langevin
to assess the degree equation. The of
of heterogeneity DFP
the Langevin approach and devise a method
Strada to rigor-
delle Tabarelle solvent; k(Trento)
287, Villazzano B and T are, respectively,
38123, importantthe
Italy Boltzmann constant given by h!$t%!$t0 %i ! 2D"$t " t0 %. Note that in the origi-
(2015) (2017)
related question concerns the role of nonnative interac- analysis
the foldingallowsmechanism to compute rigorously
and to clarify whether (i.e., without
the most statisti-any
ously define2Dipartimento
and practically compute
di Fisica, the most
Università deglistatisti- and theVia
Studi di Trento, temperature.
Sommarivetions
14, in determining
Povo (Trento)the structure
38123, Italyof the folding pathways (2, 3). cally significant other
assumptions folding than
pathways thearevalidity
those in of whichthetheunderlying
hairpins nal Langevin equation there is a mass term, mx. ! However,
3
cally relevant protein folding
Trento pathway.
Institute As a first Physics
for Fundamental explor-and Applications (INFN-TIFPA), In principle, atomistic molecular
Via Sommarive 14, dynamics (MD) simulations form in sequence. Important as shown in [6], for proteins, this term can be neglected
provide a consistent framework to address these problems from a Langevin equation) the related
most questions
probableareconformational
also whether
atory application, we have studied the foldingPovo transi-
(Trento) 38123, Italy the folding mechanism is correlated with the structure of the beyond time scales of the order of 10 "13 s.
theoretical perspective. However, due to their high computational pathway connecting
initial denatured two from
conditions arbitrary
whichconformations. The ma-
the reaction is initiated
tion of the 36-monomer
(Received 23Villin headpiece
May 2014; revisedsubdomain
manuscript received 29 October 2014; published 4 March 2015)HUGE COMPUTATIONAL GAIN
Using top all- Using top
purpose special-purpose
supercomputers supercomputerVALIDATING SCPS AGAINST MD
106s
MD Protein
, folding
ms s minutesVENTURING INTO THE BIO-ZONE
106s
MD Variational
, Simulations
ms s minutes hoursA LONG JOURNEY
3.8
3.6
3.4
3.2
3
2.8
2.6
2.4
2.2
2
1.8
Experiment
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
Theory
-0.2
-0.4
-0.6
-0.8
-1
-1.2
-1.4
-3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5VALIDATION AGAINST EXPERIMENT
Experiment Challenge:
Most available techniques
provide only indirect
probes, we seek for
Theory
direct validation
2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5The Journal
ARTICLE ARTIC
ics of Chemical Physics scitation.org/journal/jc
TIME-DEPENDENT LINEAR SPECTROSCOPY
An analytic formula for the absorptionAn analytic formulκ
coefficient
be obtained by combining real and be obtained
imaginarybyparts,
combini
acc
Eqs. (34)–(36). It is instructive to Eqs. (34)–(36).
analyze It is instr
the structure of
nary part ImR(ω), which controlsnary part ImR(ω),
the position which
and the wi
resonances resonances
2ReΣn (ω)�(ω − En )2 + �Σn (ω)�2 �2
f f
ImR(ω) = − � ImR(ω) = −�
n −�(ω
n �(ω − En )2 − �Σf (ω)�2 � + 4�(ω − En
En )ReΣ
2
n
FIG.
sentation of the 1. (a)Eq.
Dyson Graphical representation
(44) for the exciton propa- of the Dyson Eq. (44) for the exciton propa-
gator. The
white triangle denotes theline
full with open white triangle
(non-perturbative) time- denotes the full (non-perturbative) time-
ordered
or, while the other exciton propagator,
continuous line appearing whilein the
the other continuous line appearing in the
he free exciton righthand-side
propagator. (b)represents
Example ofthe free
loop The splitting
exciton propagator.
diagram (b) Exampleandof loop diagram of theThe
shifting splitting
poles generatedand by
shiftin
the
Challenge: Σn (ω)b
f
approximation.neglected
The dashed in the
lineproposed approximation.
denotes the stochastic The dashed line denotes
coupling the
is determined stochastic coupling function
by the self-energy is determined
mped Langevinpropagator
oscillationsofofclassical damped Langevin
the configuration vector oscillations of the
Eq. (46). Forconfiguration
illustration vector
purposes,Eq. (46).
here weFor illustration
discuss its expr
δQ. (c) Estimating
term by the lowest-order
Ground state
self-energy thediagram.
Need
the case of a single a theory
1PI term by the lowest-order self-energy diagram.
normal forof a single norm
mode the case
2 γ ⌦2 + i(ω − Edynamics
non-equilibrium n )�(ω
f − En ) δ− γ22
2 2
δ nm f our nm⌦f 2 +γ⌦
Σnm (ω)2 =
Equation
point (43) provides the starting point to apply non-
Σ (ω) =
ovides the starting to apply our non-
One exciton f
perturbative
mation scheme. approximation
To this end, we consider the To thisnmend,
scheme. of wequantum
consider
βM ⌦ �(ω −
the En )2 − ⌦2 � + γβM
electronic 2 (ω⌦ − En )
standard
on, obtained Dyson equation,
by resumming obtained
all 1-particle irre- by resumming all 1-particle irre-
ms for the ducible (1PI) diagrams
single-exciton propagator forGthe Thisexcitations
equation
[seesingle-exciton shows G
propagator in
how conformationally
[see This equation
the vibronic shows
correction ho
of the
Fig. 1(a)].
y representation and In frequency
omitting representation
all indices for function scalesallwith
and omitting indices for function
the temperature scalesviscosity.
and bath with the
sake of
Dyson equation simplicity, the Dyson equation reads
reads
evolving proteins
the shifting,
the shifting, splitting, and broadening of the splitting,
resonances an
when
when the difference between ω and thethe difference
excitonic betw
energieMOLECULAR QUANTUM FIELD THEORY*
Z Z
SM QF T [ , ¯,q]
Z= D D¯ Dq e
SM QF T [q, , ¯] = SOM [q] + SS [ , ¯] + Sint [q, , ¯]
Z t
2
SOM [q] = d⌧ (M q̈ + M q̇ + rU (q))
0 4M
XZ t
SSSel.[ [ ¯,, ¯] = d⌧ ¯n (⌧ ) i~@t h0nm m (⌧ )
0
XXZ
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
n,m t
[q, , ¯¯]] = ¯n
i
SSint
int [R, d⌧ fnm m rqi
0
i
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
nm i
P. Faccioli & E. Schneider (2013-2016)SOLVING MQFT: AN ARSENAL OF METHODS
Perturbation Theory
PRB 2012, PRB 2013, PRB 2016
Quantum MC
(for real time) PRB 2016
Renorm. Group &
Eff. Field Theory PRB 2013, JCP 2016EXAMPLES OF DIRECT COMPARISON WITH
EXPERIMENTS
7
Time resolved near UV CD*
Linear absorption spectrum
0.4
Experimental Calc. S S 1.2
(a) Calc. S S (b) Calc. SH HS
Experimental
Experimental
Calculated
Numerical
1
Normalized Absorption
0.2 0.8
() M 1cm 1
theory (a) (c) 0.6
0 0.4
0.2
0
0.2 (b) (d) 12000 12150 12300 12450 12600 12750
experiment Frequency (cm )
-1
FIG. 3. (a) Trimeric form of the FMO complex. Only the protein Microscopic Calculation of Absorption Spectra of Macromolecules: an Analytic Approach
scaffold is shown with its C3 symmetry. (b) Monomeric unit of Matteo Carli
the FMO with the 7 BChl-a (blue) wrapped in the protein scaffold. FIG. 4. Comparison between
Physics Department numerical
of Trento University, Via Sommarive 14, spectrum (red)
Povo (Trento), 38123, Italy andand the ex-
0.4 (c) Representation of the ENM corresponding to a single monomer. Scuola Internazionale Superiore di Studi Avanzati (SISSA), via Bonomea 265, Trieste 34136, Italy.
perimental spectrum (blue) from Ref. [58]. The non-perturbative ⇤
Michele Turelli and Pietro Faccioli
200 230 260 290
The red beads are centered at the CA position of each residue. The200 230 260 290
prediction has been
Physics obtained
Department via Viathe
of Trento University, algorithm
Sommarive in38123,
14, Povo (Trento), theItalySM. and
Trento Institute for Fundamental Physics and Applications (INFN-TIFPA), Via Sommarive 23, Povo (Trento), 38123, Italy
The total
spring-like Wavelength
bonds between (nm) beads falling within aWavelength radius of 10 Å (nm)
are simulation We timedevelopwas of 1 ps
a cross-disciplinary with
approach time-steps
to analytically compute optical of 0.05
response fs.
functions of open macro-
molecular systems, by exploiting the mathematical formalism of quantum field theory (QFT). Indeed, the en-
shown in grey. (d) Atomic structure of the BChla (grey) with the 8 tries of the density matrix for the electronic excitations interacting with their open dissipative environment
are mapped into vacuum-to-vacuum Green’s functions in a fictitious relativistic closed quantum system. We
beads chosen for its coarse-grained model in the ENM (red). The show that by re-summing appropriate self-energy diagrams in this dual QFT it is possible to obtain analytic
expressions for the response functions in Mukamel’s theory. This yields physical insight into the structure and
Article
beads are centered at the positions of the MG, C2A, C2B, C2C,
Cite This: J. Am. Chem. Soc. 2018, 140, 3674−3682
Withinand the MQFT,
microscopic model parameters.the conformational
For illustration, we apply this scheme to compute dynamics
the linear absorption is de-
dynamics of vibronic resonances, since their frequency and width is related to fundamental physical constants
pubs.acs.org/JACS
spectrum of the Fenna-Matthews-Olson (FMO) light harvesting complex, comparing analytic calculations, nu-
C2D atoms for the chlorin ring and at the C2, C10, C18 positions scribed by the Langevin equation. For sake of simplic-
merical Monte Carlo simulations and experimental data.
Atomic Detail of Protein Folding Revealed by an Ab Initio
for the three beads
Reappraisal of Circular Dichroism of the phytol tail. The atomic labelling is the ity, we assign the same viscosity
I. INTRODUCTION systems parameter to theall
[13, 17–26]. In this context, beads,
Feynman-Vernon
sameSimone
Alan Ianeselli, found
†
Orioli,inGiovanni
the crystal
‡,∥
structure
Spagnolli, Pietro file (PDB:3EOJ).
†
Faccioli,* Lorenzo Cupellini, ,‡,∥ §
1
g = 150 ps . In principle, viscosity
path integral formalism offers several advantages [10, 27–
coefficients
34]. For example, for toeach
in makes it straightforward of
deal with the
Sandro Jurinovich,§ and Benedetta Mennucci*,§ The relaxation dynamics of optically induced electronic
excitations in macromolecular systems has been extensively dynamics of atomic nuclei at the classical level, while retain-
the constituents may be evaluated from microscopic molec-
†
Centre for Integrative Biology, Trento University, Via Sommarive 9, 38128 Povo, Trento, Italy ing a full quantum description of the excitons [10, 29–34].
* with B. Mennucci’s Lab (U.as Pisa)
‡ studied during the last several years, in view of its important
Physics Department, Trento University, Via Sommarive 14, 38128 Povo, Trento, Italy Within these mixed quantum-classical schemes it is possible
biological and technological implications. For example, the
ular dynamics simulations, e.g. as picoseconds,
by computing appropriate
§
Dipartimento di Chimica e Chimica Industriale, University of Pisa, via G. Moruzzi 13, 56124, Pisa, Italy to simulate the real-time dynamics for time intervals long
∥
propagation of excitons in light harvesting complexes pro-
INFN-TIFPA, Via Sommarive 14, 38128 Povo, Trento, Italy using a Quantum Monte Carlo algorithm.A LONG JOURNEY
3.8
3.6
3.4
3.2
3
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1.8
Experiment
1.6
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0.8
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-3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5EXPLORING BIOLOGICAL PROCESSES
Article
All-Atom Simulations Reveal How Single-Point
Mutations Promote Serpin Misfolding
Fang Wang,1 Simone Orioli,2,3 Alan Ianeselli,2,3 Giovanni Spagnolli,2,3 Silvio a Beccara,2,3 Anne Gershenson,4,*
Pietro Faccioli,2,3,* and Patrick L. Wintrode1,*
1
Department of Pharmaceutical Sciences, University of Maryland School of Pharmacy, Baltimore, Maryland; 2Dipartimento di Fisica, Università
degli Studi di Trento, Povo (Trento), Italy; 3Trento Institute for Fundamental Physics and Applications, Povo (Trento), Italy; and 4Department of
Biochemistry and Molecular Biology, University of Massachusetts Amherst, Amherst, Massachusetts
ABSTRACT Protein misfolding is implicated in many diseases, including serpinopathies. For the canonical inhibitory serpin a1-anti-
trypsin, mutations can result in protein deficiencies leading to lung disease, and misfolded mutants can accumulate in hepatocytes,
leading to liver disease. Using all-atom simulations based on the recently developed bias functional algorithm, we elucidate how wild-
type a1-antitrypsin folds and how the disease-associated S (Glu264Val) and Z (Glu342Lys) mutations lead to misfolding. The dele-
terious Z mutation disrupts folding at an early stage, whereas the relatively benign S mutant shows late-stage minor misfolding. A
number of suppressor mutations ameliorate the effects of the Z mutation, and simulations on these mutants help to elucidate the
relative roles of steric clashes and electrostatic interactions in Z misfolding. These results demonstrate a striking correlation between
atomistic events and disease severity and shine light on the mechanisms driving chains away from their correct folding routes.
INTRODUCTION
RESEARCH ARTICLE
Understanding how mutations alter protein misfolding pro- mediate state (4). Similarly, Z secretion from cells is slow,
Full atomistic model of prion structure and
pensities and the physicochemical mechanisms underlying
this shift is key to clarifying the molecular basis of many dis-
and although some Z species are targeted for degradation
(5–7), misfolded Z accumulates in the endoplasmic reticu-
conversion
Teaming up with
eases. One set of relatively common protein-misfolding dis- lum, where it can polymerize (8). Despite numerous exper-
eases known as serpinopathies arises when mutations in imental studies (9–13), little is known about the structure of
inhibitory serpins lead to misfolding, thus reducing the
Giovanni Spagnolli ID , Marta1 misfolded species
Rigoli ID 1,2 for any
, Simone A1AT
Orioli 2,3 disease-associated mutant,4
, Alejandro M. Sevillano ID ,
secreted levels of these important protease inhibitors
Pietro Faccioli 2,3 (1). hindering
, Holger Wille 5 efforts to
ID , Emiliano either1 rescue
Biasini , Jesús theR.folding
Requenaof these
ID
6 species
Mutations in the canonical secretory serpin a1-antitrypsin or to target them for degradation.
1 Department of Cellular,
theComputational and Integrative Biology (CIBIO)–University of Trento, Povo TN,
E. Biasini’s lab (DICIBIO)
(A1AT) result in the most common serpinopathies: Molecular dynamics (MD) simulations offer an attractive
ITALY, 2 Department of Physics, Povo, Trento TN, ITALY, 3 INFN-TIFPA, Povo (Trento), ITALY,
A1AT deficiencies. In these deficiencies, low circulating approach to studying protein folding and misfolding, as
4 Department of Pathology–University of California—San Diego, San Diego, California, United States of
A1AT levels dysregulate leukocyte serine proteases, result- they can in principle reveal folding pathways and intermedi-
America, 5 Department of Biochemistry and Centre for Prions and Protein Folding Diseases–University of
ing in lung disease, which can be Alberta, slowedEdmonton
but not (AB),
halted ates6 in
CANADA, atomistic
CIMUS detail.
Biomedical To date,
Research the application
Institute & Department ofofall-atom
Medical
a1111111111
by A1AT augmentation therapy (2).Sciences, Extremely University of SantiagoMD
pathogenic de Compostela-IDIS, Santiago, SPAIN
simulations to investigate protein folding and misfolding
a1111111111
A1AT mutations such as Z (Glu342Lys) can lead to both has been limited to small, single-domain proteins with rela-
a1111111111 * giovanni.spagnolli@unitn.it (GS); emiliano.biasini@unitn.it (EB); jesus.requena@usc.es (JRR)
lung disease, because of loss of function, and liver disease, tively short folding times. In particular, recent developments,
a1111111111
a1111111111 All-Atom Simulation of the HET-s Prion Replication
because of A1AT accumulation in the endoplasmic reticulum
of hepatocytes, which generate most of the circulating A1AT.
such as the Anton special-purpose supercomputer (14) and
the massively distributed folding@home project (15), have
With the exception of liver transplants, Abstract
there are no effective made it possible to generate in silico several reversible
treatments1,2for A1AT-associated liver disease 2,3 #
(3). folding/unfolding
1,2
events for4a number of small globular 2,3#
pro-
Luca Terruzzi *, Giovanni Spagnolli
Prions
In vitro, the pathogenic A1AT Z mutant folds very * ,
areAlberto
unusual Boldrini
protein teins, (A LONG JOURNEY
3.8
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Experiment
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-3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5! ROLE OF PROTEIN INACTIVATION
MOST OF BIOLOGICAL FUNCTIONS IN CELLS ARE CARRIED
OUT BY PROTEINS
MOST OF MEDICINAL CHEMISTRY IS BASED ON
INHIBITING BIOLOGICAL FUNCTIONS OF PROTEINSPHARMACOLOGICAL PROTEIN INACTIVATION BY
! FOLDING INTERMEDIATE TARGETING
patent file # 102018000007535 (with E. Biasini)
Protein Protein
DNA mRNA Ribosome
folding function
RNA
silencing
Eliminating
Suppressing Suppressing Imparing
protein from
genome transcription folding functionPHARMACOLOGICAL PROTEIN INACTIVATION BY
! FOLDING INTERMEDIATE TARGETING
Unfolded I1 I2 Native state
state
drug I3
Unfolded proteins DegradationA F I R S T VA L I D AT I O N
Inactivation of SM875 [µM]
Cellular Vhc 0.01 0.03 0.1 0.3 1 3 10 30 50
150
PrPC Expression (% Vhc)
Prion protein 37
100
PrPC ***
50
***
25 0
10
30
1
1
3
c
0.
Vh
SM875 [µM]
20
(ii) SM875 [µM]
Vhc 1 3 10 30
50 NEGR-1
(iii)PPI-FIT PIPELINE
in-vitro evaluation
Computing the folding In-silico virtual
of the effect of the Refinement
pathways screening on folding
selected compounds SAR,
characterizing intermediate targets
on protein expression pharmaco-kinetics,
intermediate states
…..
FINAL GOAL
Preclinical
and clinical trials
Slide courtesy of Sibylla Biotech SRL18
Joining Forces against COVID-19
Maria Letizia Emiliano Biasini Pietro Faccioli Graziano Lolli
Barreca
30.000 cores in 8 data
centers
Lidia Pieri Giovanni Tania Luca Terruzzi Andrea Astolfi
Alberto Boldrini
Spagnolli Massignan16
SARS-CoV-2 Replication
Spike
ACE2
Goals:
Repurposing of approved drugs!
Looking for suppressors of ACE2
expression levels
Figure taken from:
https://theconversation.com/where-are-we-at-with-developing-a-vaccine-for-coronavirus-13478414
PPI-FIT ON ACE2
Out of 9000 candidates, we found 35 molecules binding in-silico the
intermediate. Validation experiments on cellular bio-assays are ongoing.BREAKING NEWS!! (17/05/2020)
So far, Sibylla Biotech has tested 14 virtual hits
ONE DISPLAYS A PROMINENT EFFECT WITH CLEAR
DOSE-RESPONSE RELATIONSHIP AND VERY LOW
TOXICITY
200
Ace2 expression (%Vhc)
150
100
0.01
0.03
50
Vhc
100
300
0.1
0.3
10
30
1
3
0
01
03
1
3
0
1
3
10
30
0
0
0.
0.
10
30
0.
0.
[µM]PPI-FIT Pipeline
in-silico hit compounds in-vitro evaluation
ACE-2 folding in-vitro evaluation
identification. Virtual of the effect of
pathway of the effect of the
screening on FDA compounds lowering
reconstruction and selected compounds
approved or the expression of ACE2
intermediate state on ACE2 expression
investigational drugs on SARS-COV-2
characterization (degradation wanted)
virus replication
FINAL GOAL
Preclinical
and clinical trialsMAIN TAKE-HOME MESSAGES
Fundamental research matters!
The usefulness of theoretical physics
extends beyond its natural cultural perimeter
Major research infrastructures for
fundamental research can be
re-purposed
Technological transfer can boost research
and help advance Science18
People
Maria Letizia Emiliano Biasini Pietro Faccioli Graziano Lolli
Barreca PhD PhD PhD PhD
Lidia Pieri Giovanni Tania Andrea Astolfi
Alberto Boldrini Luca Terruzzi
PhD Spagnolli Massignan PhD PhD
Founder - CEO Founder Staff Staff Consultant
Chief Scientist (Computational) Staff (Wet Lab) (Computational) Medicinal ChemistAcknowledgments Italy: Trento: E. Biasini, A. Ianeselli (2014-2017), G. Spagnolli S. A Beccara (2009-2017), S. Orioli (2014-2018), E. Schneider (2012-2015), M. Carli (2017), M. Turelli (2018), F. Mascherpa (2014), G. Garberoglio, F. Pederiva, M. Sega, R. Covino (2012-2015), Pisa: B. Mennucci, L. Cupellini, S. Jurinovich Perugia: L. Barreca SISSA: C. Micheletti, A. Laio Europe: U. Compostela: J. Raquena U. Zurich: B. Schuler CEA-Saclay: H. Orland USA: U. Maryland: P. Wintrode U. Mass.: A. Gershenson
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