Dinamica Molecolare:
Applicazioni Biomediche e Farmaceutiche
Alejandro GiorgettiDip. di Biotecnologie
Università di Verona, Verona Italy
German Research School for Simulations Scienes(GRS) Julich, Germany
e-mail: [email protected]
Small molecules control a myriad of cellular functions by binding to their target macromolecules: ligands govern processes such as growth, programmed cell death, sensing, and metabolism. This key event triggers triggers complex cellular pathwayscomplex cellular pathways characterized by reactions, environmental changes, intermolecular interactions, and allosteric modificationsUltimately, understanding the molecular basis of ligand-target interactions requires the integration of biological complexes into cellular pathways: ““systems biologysystems biology””All of these processes involve molecular recognitionAll of these processes involve molecular recognitionNonmolecular modeling, which is advancing tremendously our understanding needs to be paralleledneeds to be paralleled by a quantitative molecularmolecular description of pathways
Molecular system-level understandingMolecular system-level understanding
Computational molecular biology methodsComputational molecular biology methods
The first strategy, the so-called protein bioinformaticsprotein bioinformatics, is aimed at the development of computational tools that enable to decipher the information encoded in the protein sequences, thus enabling the prediction of structure and function
The second strategy is based on the laws of physics. One of the most important methods here is molecular dynamicsmolecular dynamics (MD) , which predicts structural, dynamical, and energetic (bio)molecular properties based on Newton laws of motion.
L’utilizzo di tecniche computazionali nella moderna
ricerca biomedica e farmaceutica permette di svolgere
in silico una serie di analisi grazie alle quali i
ricercatori, nelle fasi di progettazione di un nuovo
farmaco, potrebbero risparmiare grandi risorse di
tempo e denaro in esperimenti chimici e biologici
A Digital Laboratory
“In the real world, this could eventually mean that most chemical experiments are conducted inside the silicon of chips instead of the glassware of laboratories. Turn off that Bunsen burner; it will not be wanted in ten years.”
- The Economist, reporting on the work of the 1998 Chemistry Nobel Prize Awardees
A Different Type of Simulation
● Many Physically-Based Simulations model easily observable real world phenomena.
● Molecular Dynamics Simulations model things too small for us to observe directly.
Why we do s i mul a t i on replace experiment
provoke experiment
explain experiment
aid in establishing intellectual property
In s o m e c a s e s , e x pe rim e nt is :
Blind Some properties cannot be observed on very short time-scales and very small space-scales
Wha t is Mo le c ula r Mo de ling ?
Molecular Modeling is concerned with the description of the atomic and molecular interactions that govern m ic ro s c o p ic and m a c ro s c o p ic behaviors of physical systems
Wha t is it g o o d fo r?The essence of molecular modeling resides in the connection between
the m a c ro s c o p ic world and the m ic ro s c o p ic world provided by the theory of statistical mechanics
Macroscopic observable (Solvation energy, affinity between two proteins, H-H distance, Conformation, ... )
Average of observable over selected microscopic states
Computational Tools
Types of phenomena
Timescale limitations✗Protein Folding - milliseconds/seconds (10-3-1s)✗Ligand Binding - micro/milliseconds (10-6-10-3 s)✗Enzyme catalysis - micro/milliseconds (10-6-10-3 s)✗Conformational transitions - pico/nanoseconds (10-12-10-9 s)✗Collective vibrations -1 picosecond (10-12 s)✗Bond vibrations - 1 femtosecond (10-15 s)
• Modeling the motion of a complex molecule by solving the wave functions of the various subatomic particles would be accurate…
• But it would also be very hard to program and take more computing power than anyone has!
Why Not Quantum Mechanics?
),,(),,(),,(2
22
zyxEzyxzyxUm
Ψ=Ψ+Ψ∇−
Classical Mechanics
● Instead of using Quantum mechanics, we can use classical Newtonian mechanics to model our system.
● This is a simplification of what is actually going on, and is therefore less accurate.
● To alleviate this problem, we use numbers derived from QM for the constants in our classical equations.
Molecular Modeling
For each atom in every molecule, we need:● Position (r)● Momentum (m + v)● Charge (q)● Bond information (which atoms, bond angles, etc.)
From Potential to Movement
To run the simulation, we need the force on each particle.
We use the gradient of the potential energy function.
Now we can find the acceleration.
iii amF =
VF ii − ∇=
2
2
dtrdm
drdV i
ii
=−
What is the Potential?
A single atom will be affected by the potential energy functions of every atom in the system:
● Bonded Neighbors● Non-Bonded Atoms (either other atoms in the
same molecule, or atoms from different molecules)
bondednonbonded EERV −+=)(
Non-Bonded Atoms
There are two potential functions we need to be concerned about between non-bonded atoms:
● van der Waals Potential● Electrostatic Potential
ticelectrostaWaalsdervanbondednon EEE += −−−
The van der Waals Potential
● Atoms with no net electrostatic charge will still tend to attract each other at short distances, as long as they don’t get too close.
● Once the atoms are close enough to have overlapping electron clouds, they will repel each other with astounding force
The van der Waals Potential
One of the most widely used functions for the van der Waals potential is the Lennard-Jones. It is a compromise between accuracy and computability.
∑
−=−
pairsnonbonded ik
ik
ik
ikJonesLennard r
CrAE 612
The van der Waals Potential
The Constants A and C depend on the atom types, and are derived from experimental data.
∑
−
pairsnonbonded ik
ik
ik
ik
rC
rA
612
The Electrostatic Potential
● Opposite Charges Attract● Like Charges Repel● The force of the attraction is inversely
proportional to the square of the distance
∑=pairsnonbonded ik
kiticelectrosta Dr
qqE
Coulomb’s Law
20
21
4 rqqF
π ε=
The Non-Bonded Potential
Combine the LJ and Electrostatic Potentials
ticelectrostaWaalsdervanbondednon EEE += −−−
Bonded Atoms
There are three types of interaction between bonded atoms:
• Stretching along the bond• Bending between bonds• Rotating around bonds
bondalongrotatebendanglestretchbondbonded EEEE −−−− ++=
Bond Length Potentials
Both the spring constant and the ideal bond length are dependent on the atoms involved.
∑ −=−pairs
bstretchbond bbKE2,1
20 )(
Bond Angle Potentials
The spring constant and the ideal angle are also dependent on the chemical type of the atoms.
∑ −=−angles
bendbond KE 20 )( θθθ
Torsional Potentials
Described by a dihedral angle and coefficient of symmetry (n=1,2,3), around the middle bond.
∑ −=−−pairs
bondalongrotate nKE4,1
))cos(1( φφ
Integration Algorithms
● Forces like the LJ potential have powers of 12, which would make Euler horribly unstable (even worse than usual)
● RK and Midpoint algorithms would seem to help● However, force calculations are extremely
expensive, and RK and Midpoint require multiple force calculations per timestep
Integration Algorithms
● Using RK is justifiable in other circumstances, because it allows you to take larger timesteps (two force calculations allowing you to more than double the timestep)
● This is normally not achievable in MD simulations, because the forces are very rapidly changing non-linear functions.
● We need an algorithm with the stability benefits of RK without the cost of extra force calculations!
From Potential to Movement
To run the simulation, we need the force on each particle.
We use the gradient of the potential energy function.
Now we can find the acceleration.
iii amF =
VF ii − ∇=
2
2
dtrdm
drdV i
ii
=−
• First, take a third-order Taylor step:
• Now take a step backward:
Verlet Algorithm
)()(!3
1)(21)()(
)(
432 tOttrttattvtr
ttr
∆+∆+∆+∆+
=∆+
)()(!3
1)(21)()(
)(
432 tOttrttattvtr
ttr
∆+∆−∆+∆−
=∆−
We divide the temporal interval [0,T] in small delta T intervals....so we can expand the position using the Taylor series in both directions around r.
Verlet Algorithm
● When adding the two formulas, the first and third derivatives cancel out:
● And we can express the next timestep in terms of the previous position and the current acceleration:
)()()(2)()( 42 tOttatrttrttr ∆+∆+=∆−+∆+
)()()()(2)( 42 tOttattrtrttr ∆+∆+∆−−=∆+
We divide
Verlet Algorithm
Pros:● Simple & Effective● Low Memory & CPU Requirements (don’t need to store
velocities or perform multiple force calculations)● Time Reversible● Very stable even with large numbers of interacting
particles
Cons:● Not as accurate as RK● We never calculate velocities!
(when would we need them?)
Obtaining Velocities
● We can estimate the velocities using a finite difference:
● This has a second order error, while our algorithm has a fourth order error
● There are variations of the Verlet algorithm, such as the leapfrog algorithm, which seek to improve velocity estimations.
)()]()([21)( 2tOttrttr
ttv ∆+∆−−∆+
∆=
Molecules in Solution
• In real situations, a molecule is rarely isolated. In biological systems, proteins, RNA, and DNA are immersed in a sea of water molecules
• To accurately portray the effect of the solvent molecules on a system, the solvent molecules must be free flowing
• How do we establish computational boundaries while keeping a realistic solvent simulation?
Periodic Boundary Conditions
• Simulate a segment of molecules in a larger solution by having repeatable regions
• Potential calculations are run only on each atom’s closest counterpart in the 27 cubes
• When an atom moves off the edge, it reappears on the other side (like in asteroids)
Cutoff Methods
● Ideally, every atom should interact with every other atom
● This creates a force calculation algorithm of quadratic order
● We may be able to ignore atoms at large distances from each other without suffering too much loss of accuracy
Cutoff Methods
● Truncation – cuts off calculation at a predefined distance
● Shift – alters the entire function as to be zero at the cutoff distance
● Switch – begins tapering to zero as the function approaches the cutoff distance
Thermodynamic ensembles
Bo l z mann ( c ano ni c al ) d i s t r i but i o n
The partition function
The ensemble average
Ergodic hypothesis
Sampling of various ensembles
- FABP : proteine coinvolte in malattie come: la dislipidemia, l'obesità, la resistenza all'insulina e il diabete di tipo-2, che sono causa di gravi sindromi cardiovascolari e mortalità.
- GCSF : una proteina utilizzata per trattare la neutropenia, malattia caratterizzata da concentrazioni molto basse di neutrofili in sangue.
Argomenti
I lipidi sono i componenti vitali di molti processi biologici e sono cruciali nella patogenesi di certe malattie: dislipidemia, l'obesità, la resistenza all'insulina e il diabete di tipo-2
Ruolo giocato dai chaperoni (proteine di trasporto) lipidici, le proteine che legano gli acidi grassi (FABPs) - nei processi biologici da essi mediati e nell'omeostasi metabolica sistemica attraverso la regolazione dei diversi segnali lipidici, e di evidenziare il loro significato terapeutico.
- partecipano in modo attivo al trasporto dei lipidi verso compartimenti specifici nella cellula.
- La FABP epatica (L-FABP) e ileale (Il-FABP o Il-BABP) possono svolgere un ruolo importante e poco studiato nel controllo lipidico.
FABPs
- nuova ipotesi sul meccanismo d'azione di queste proteine che agiscono come interruttori molecolari attivati in modo allosterico da molecole lipidiche e/o da membrane per la regolazione del trafficolipidico.
Pedò et al. JMB. 2009
- Studio dell'interazione della proteina apo con la membrana.
Villareal et al. 2008
Long et al. 2009
- Dinamiche dell'entrata ed
uscita dei ligandi
(Accelerated MD simulations)
- Questa ipotesi cambia completamente le prospettive degli interventi terapeutici, indirizzandoli verso sistemi capaci di intervenire nella modulazione dell'interazione proteina-membrana
Potenziale elettrostatico: proteina Holo (con ligando)
Potenziale elettrostatico: proteina Apo (senza ligando)
Interazione con la membrana cellulare →
Rilascio del ligando
Dinamica Molecolare della FABP in Acqua per 100 ns.Lontano dai tempi fisiologici, ma insieme ad esperimenti di NMR potrebbe fornire dati importanti riguardo ai meccanismi molecolari
Neutropenia: G-CSF
● La neutropenia è la diminuzione del numero dei granulociti neutrofili, o neutrofili, uno dei 5 tipi di globuli bianchi che circolano nel sangue periferico
● La neutropenia può essere congenita o acquisita. Fra le forme acquisite, che insorgono cioè dopo la nascita, le cause più frequenti sono probabilmente i farmaci e le infezioni virali.
● Tra i farmaci è da ricordare la chemioterapia antitumorale che, quasi sempre, provoca una diminuzione prevedibile del numero dei granulociti neutrofili più o meno grave: se il numero è inferiore a 1000 per microlitro di sangue esiste il rischio di infezioni anche gravi.
- Il fattore stimolante le colonie di granulociti – G-CSF (fattore di crescita emopoietico: aiuta la differenziazione)
Sono note 2 leggere varianti:
• una che consiste di 174 amminoacidi e
• l’altra che consiste di 177 amminoacidi.
• è una glicoproteina
• presenta un solo sito di glicosilazione legato all’ossigeno ed • un peso molecolare apparente di circa 21 KDa.
• La molecola è stabilizzata dalla presenza di due legami disolfuro. Essa mostra una struttura tridimensionale compatta, che presenta 4 a-eliche.
Funziona come fattore di crescita e di differenziazione per i neutrofili ed i loro precursori. Inoltre sembra attivare i neutrofili maturi.- I neutrofili sono leucociti capaci di ingerire e uccidere i batteri -. G-CSF sembra agire in sinergia con altri fattori di crescita per stimolare crescita e differenziazione di varie altre cellule emopoietiche progenitrici. In più questa citochina promuove la proliferazione e la migrazione di cellule endoteliali.
Le attività di laboratorio consistono nella coniugazione delle proteine terapeutiche con un polimero idrofilico biocompatibile
ad alto peso molecolare (Polietilenglicole; PEG) per ottenere
derivati con più lunga permanenza in circolo
Il processo di PEGhilazione utilizzato avviene per via enzimatica
tramite la transglutamminasi di origine batterica (MTGase) espressa in Streptomyces Mobaraensis
G-CSF
Enzima: MTGase
Studio dell'interazione enzima - proteina
Studio dinamica Coarse – Grained
Configurazioni: Aperta e Chiusa
Identificazione degli aminoacidi coinvolti nell'interazione (modificati dall'enzima)
Dinamica molecolare della proteina G-CSF e analisi della flessibilità:
- Identificazione del sito di legame per il PEG: Glutamine, Flessibili, Accessibili
Flessibilità !!
Maullu et al. 2009. FEBS journal
' In our view, it is relevant that computational predictions,
based on publicly available methods, are nowadays
sufficiently reliable to allow the identification of targets of
enzymatic modifications and the redesign of proteins with the
desired properties, as substantiated by the results of our
mutant design experiments, where we could redirect the
enzyme specificity to different sites ' ....
Maullu et al. 2009. FEBS journal
Ringraziamenti
● Prof. H. Molinari● Dr. M. Assfalg● Dr. M. D'Onofrio● Serena Zanzoni
(NMR group Università di Verona)
● Prof. V. Torre● Prof. E. Cherubini● Prof. P. Carloni● Dr. M. Griguol● Dr. A. Maul● Ha-Hung-Chuong Nguyen
(SISSA and Julich, Germany)
● Prof. A. Tramontano● Dr. D. Raimondo
'La Sapienza', Roma● Dr. M. Valentini (CRS4 Sardegna)● BioKer Sardegna
● Michela Dallera● Gabriele Tosadori
Applied Bioinformatics group
Università di Verona
HCN channels
Activated by membrane hyperpolarizationModulated by interaction with cyclic nucleotidesTetramericSimilar topology to voltage-gated K+ channelsCation selective: K+ > Na+ .Problem: No Crystal structure available (pore)
S1 S2 S3 S4 S5 S6+ +
++
N-Terminal
CNBD
P-helix-Loop
C-Linker
+ + + + + + + + + + + +
- - - - - - - - - - - - - -
-50 mV
Cytoplasm
Extracellular
Heart and brain pacemaking regulation
Sea urchin sperm (spHCN) Mammalian heart and brain: HCN1-4
Lys433Modello Strutturale del canale HCN.
- Inserito in membrana per ottimizzazione- solvatato- Ioni K+ nella regione del 'filtro'
Vista dall'alto
Vista semplificata Zoom 'filtro ed ioni'
Interazioni nella regione del 'filtro
Ci sono differenze significative tra il canale al K+ (a sinistra)
ed il HCN (permeabile sia al K+ che al Na+
Simulazione MD →
Ipotesi: 'filtro' più flessibile
→ Canale meno selettivo.
Giorgetti et al. 2005. Biophys. journal
Close
Open
Target: spHCN
G461
T464N465
Q468
HCN channels: Gating Model
I nostri modelli, insieme ai lavori esperimentali del Lab. di Vincent Torre hanno permesso la modellizzazione del canale aperto e chiuso
I modelli sono stati usati da altri per l'individuazione del sito di legame di due molecole blockers.
Giorgetti et al. 2005. Biophys. journal
Cheng et al. 2007
http://www.wallpaperseek.com/brain-smoker-wallpapers_w5020.html
HCN di cervello bloccato dalla Nicotina
Il lab. Del Prof. Cherubini (SISSA) ha appena scoperto che la nicotina, interagendo con i canali HCN espressi nel cervello potrebbe avere delle conseguenze a livello di regolazione del 'pacemaker' del sistema nervoso.I modelli ci permettono di ipotizzare il sito di legame della nicotina.
Griguoli et al. 2010. Journal of Neuroscience
' In conclusion, nicotine, by directly blocking Ih in O-
LM interneurons disrupts the temporal coding
necessary for network synchronization and for
generation of the theta rhythm crucial for the
processing and storage of information in the brain.
This may be relevant for smokers '....
Griguoli et al. 2010. Journal of Neuroscience
