# Presentation: 174424

## Dynameomics: Protein Mechanics, Folding and Unfolding through Large Scale All-Atom Molecular Dynamics Simulations

- INCITE 6
- David A. C. Beck
- Valerie Daggett Research Group
- Department of Medicinal Chemistry
- University of Washington, Seattle
- November 15th, 2005

## Proteins 

**Proteins **

**Proteins are life’s machines, tools and structures**
**Many jobs, many shapes, many sizes**

## Proteins 

**Proteins **

**Proteins are life’s machines, tools and structures**
**Nature reuses designs for similar jobs**

**1hdd**

**1enh               1f43                      1ftt**

**1bw5                 1du6                 1cqt**

## Proteins 

**Proteins are hetero-polymers of specific sequence**
**There are 20 common polymeric units (amino acids)**
**Composed of a variety of basic chemical moieties**
**Chain lengths range from 40 amino acids on up**

- M   K    L    V    D   Y    A   G  E

## Proteins 

**Proteins are hetero-polymers that adopt a unique fold**

- ?

- M   K    L    V    D   Y    A   G  E

## Proteins 

**Protein folding as a reaction**

**Products**

**     ****Reactants**

**Transition state**

**Free**
**Energy**

**Bad**

**Good**

## Proteins 

**Protein folding ... **

**Native**

**     ****Denatured /**
**Partially Unfolded**

**Transition state**

**Free**
**Energy**

**Bad**

**Good**

## Proteins 

**Folded proteins**

**Native**

**     ****Denatured /**
**Partially Unfolded**

**Transition state**

**Free**
**Energy**

**Folded, active, functional, biologically relevant state (ensemble of conformers)**

**Bad**

**Good**

## Proteins 

**Folded proteins**

**Native**

**     ****Denatured /**
**Partially Unfolded**

**Transition state**

**Free**
**Energy**

**Static, 3D coordinates of some proteins’ atoms are available from x-ray crystallography & NMR**

**Bad**

**Good**

## Proteins 

**Folded proteins**

**Native**

**     ****Denatured /**
**Partially Unfolded**

**Transition state**

**Free**
**Energy**

**Static, 3D coordinates of some proteins’ atoms are available from PDB ****http://www.pdb.org**

**Bad**

**Good**

## Proteins 

**Folded proteins are complex and dynamic molecules**

**Native**

**     ****Denatured /**
**Partially Unfolded**

**Transition state**

**Free**
**Energy**

**Bad**

**Good**

**Notes:**
1872-1878 British photographer Eadweard Muybridge took the first successful photographs of motion, producing his multiple image sequences analyzing human and animal locomotion. California senator Leland Stanford commissioned Muybridge to determine whether the 4 legs of a galloping horse left the ground at the same time, so he set up 24 still cameras along a racetrack. As a horse ran by the cameras, the horse broke strings which were hooked up to each camera's shutter, thereby activating the shutter of each camera, capturing the image and exposing the film. Soon after, the photographs were projected in succession with a viewing device called a Zoogyroscope (aka Zoopraxiscope).

## Proteins 

**Folded proteins are complex and dynamic molecules**

**Native**

**     ****Denatured /**
**Partially Unfolded**

**Transition state**

**Free**
**Energy**

**Bad**

**Good**

**Notes:**
1872-1878 British photographer Eadweard Muybridge took the first successful photographs of motion, producing his multiple image sequences analyzing human and animal locomotion. California senator Leland Stanford commissioned Muybridge to determine whether the 4 legs of a galloping horse left the ground at the same time, so he set up 24 still cameras along a racetrack. As a horse ran by the cameras, the horse broke strings which were hooked up to each camera's shutter, thereby activating the shutter of each camera, capturing the image and exposing the film. Soon after, the photographs were projected in succession with a viewing device called a Zoogyroscope (aka Zoopraxiscope).

## Molecular Dynamics

**MD provides atomic resolution of native dynamics**

- PDB ID: 3chy, *E.* coli CheY 1.66 Å X-ray crystallography

## Molecular Dynamics

**MD provides atomic resolution of native dynamics**

- PDB ID: 3chy, *E.* coli CheY 1.66 Å X-ray crystallography

## Molecular Dynamics

**MD provides atomic resolution of native dynamics**

- 3chy, hydrogens added

## Molecular Dynamics

**Molecular Dynamics**

**MD provides atomic resolution of native dynamics**

- 3chy, waters added (i.e. solvated)

## Molecular Dynamics

**MD provides atomic resolution of native dynamics**

- 3chy, waters and hydrogens hidden

## Molecular Dynamics

**MD provides atomic resolution of native dynamics**

- native state simulation of 3chy at 298 Kelvin, waters and hydrogens hidden

## Proteins 

**Folding & unfolding at atomic resolution**

**Native**

**     ****Denatured /**
**Partially Unfolded**

**Transition state**

**Free**
**Energy**

**Disordered, non-functional, heterogeneous ensemble of conformers**

**Bad**

**Good**

## Proteins 

**Proteins **

**Protein folding, why we care how it happens**

**Native**

**     ****Denatured /**
**Partially Unfolded**

**Transition state**

**Free**
**Energy**

**mutation**

**mutation**

**mutation**

**Many diseases are related to protein folding and / or misfolding in response to genetic mutation.**

**Notes:**
Diseases like BSE (Mad Cow), Alzheimer’s, cystic fibrosis, angiogenesis in cancers, etc.

## Proteins 

**Proteins **

**Protein folding, why we care how it happens**

**Native**

**     ****Denatured /**
**Partially Unfolded**

**Transition state**

**Free**
**Energy**

**mutation**

**mutation**

**mutation**

**We need to comprehend folding to build nano-scale biomachines (that could produce energy, etc...)**

## Proteins 

**Protein folding takes > 10 ****μ****s (often much longer)**

**Native**

**     ****Denatured /**
**Partially Unfolded**

**Transition state**

**Free**
**Energy**

**Bad**

**Good**

## Proteins 

**Protein folding is the reverse of protein unfolding**

**Native**

**     ****Denatured /**
**Partially Unfolded**

**Transition state**

**Free**
**Energy**

**Bad**

**Good**

## Proteins 

**Protein unfolding is relatively invariant to temperature**

**Native**

**     ****Denatured /**
**Partially Unfolded**

**Transition state**

**Free**
**Energy**

**Temperature**

**Bad**

**Good**

## Molecular Dynamics

**MD provides atomic resolution of folding / unfolding**

- unfolding simulation (reversed) of 3chy at 498 Kelvin, waters & hydrogens hidden

## Molecular Dynamics1

- Classically evolves an atomic system with time
**Potential function (a.k.a force field)**
- Describes the energies of interaction between atom centers
**Integration algorithm**
- Time dependent evolution of atomic coordinates in response to potential energy
**Statistical sampling ensemble**
- Fixed thermodynamic variables, i.e. NVE
- _N_umber of atoms, box _V_olume, total _E_nergy

- Beck, D.A.C. Daggett, V. Methods (2004) 31: 112-120

## Molecular Dynamics

**Potential function for MD****1,2**
***U = *****Bond + Angle + Dihedral + van der Waals + Electrostatic**

- Levitt M. Hirshberg M. Sharon R. Daggett V. Comp. Phys. Comm. (1995) 91: 215-231
- Levitt M. *et al.* J. Phys. Chem. B (1997) 101: 5051-5061

## Molecular Dynamics

**Molecular Dynamics**

**Potential function for MD****1,2**
***U = *****Bond + Angle + Dihedral**** + van der Waals + Electrostatic**

- Levitt M. Hirshberg M. Sharon R. Daggett V. Comp. Phys. Comm. (1995) 91: 215-231
- Levitt M. *et al.* J. Phys. Chem. B (1997) 101: 5051-5061

## Molecular Dynamics

**Molecular Dynamics**

**Potential function for MD****1,2**
***U = *****Bond + Angle + Dihedral**** + van der Waals + Electrostatic**

- Levitt M. Hirshberg M. Sharon R. Daggett V. Comp. Phys. Comm. (1995) 91: 215-231
- Levitt M. *et al.* J. Phys. Chem. B (1997) 101: 5051-5061

***b******0***

## Molecular Dynamics

**Molecular Dynamics**

**Potential function for MD****1,2**
***U = *****Bond + Angle + Dihedral**** + van der Waals + Electrostatic**

- Levitt M. Hirshberg M. Sharon R. Daggett V. Comp. Phys. Comm. (1995) 91: 215-231
- Levitt M. *et al.* J. Phys. Chem. B (1997) 101: 5051-5061

***θ******0***

## Molecular Dynamics

**Molecular Dynamics**

**Potential function for MD****1,2**
***U = *****Bond + Angle + Dihedral**** + van der Waals + Electrostatic**

- Levitt M. Hirshberg M. Sharon R. Daggett V. Comp. Phys. Comm. (1995) 91 215-231
- Levitt M. *et al.* J. Phys. Chem. B (1997) 101:25 5051-5061

***Φ******0***

## Molecular Dynamics

**Potential function for MD****1,2**
***U = *****Bond + Angle + Dihedral + ****van der Waals + Electrostatic**

- Levitt M. Hirshberg M. Sharon R. Daggett V. Comp. Phys. Comm. (1995) 91: 215-231
- Levitt M. *et al.* J. Phys. Chem. B (1997) 101: 5051-5061

## Molecular Dynamics

**Non-bonded components of potential function**
***U******nb****** = *****van der Waals + Electrostatic**
***To a large degree, protein structure is dependent on non-bonded atomic interactions***

## Molecular Dynamics

**Molecular Dynamics**

**Non-bonded components of potential function**
***U******nb****** = *****van der Waals + Electrostatic**

## Molecular Dynamics

**Molecular Dynamics**

**Non-bonded components of potential function**
***U******nb****** = *****van der Waals + Electrostatic**

## Molecular Dynamics

**Molecular Dynamics**

**Non-bonded components of potential function**
***U******nb****** = *****van der Waals + Electrostatic**

- +            -

## Molecular Dynamics

**Molecular Dynamics**

**Non-bonded components of potential function**
***U******nb****** = *****van der Waals + Electrostatic**

- +            +

## Molecular Dynamics

**Non-bonded components of potential function**
***U******nb****** = *****van der Waals + Electrostatic**

**NOTE:**
**Sum over all pairs of N atoms, or**
**                                       ****pairs**

**N is often between 5x10****5**** to 5x10****6**
**For 5x10****5**** that is 1.25x10****11**** pairs**
**THAT IS A LOT OF POSSIBLE PAIRS!**

## Molecular Dynamics

**Time dependent integration of classical equations of motion **

**Notes:**
So that’s the potential function U. But today I am going to be talking about molecular dynamics simulations.

I like to say that: 
Molecular dynamics is the time dependent integration of the classical equations of motion for molecular systems. 

But what does that really mean?

## Molecular Dynamics

**Time dependent integration **

**Notes:**
Lets consider a single particle, this little black spot here. With him and the equations on the left, I’m going to quickly describe MD in the microcanonical ensemble.

Here, the knowns are in red. Clearly, we know the position of this guy: x; we also know its current velocity v, and its mass, m. We also know the magnitude of the time-step, or delta t. We know it, because we specify it.
In a previous slide I showed you our potential function, U. Here, F, the force acting on the atom, is calculated U with respect to x (the atomic position)

## Molecular Dynamics

**Time dependent integration **

**Notes:**
And from Newton’s 2nd law, we can calculate the atomic acceleration, a imparted by that force.

## Molecular Dynamics

**Time dependent integration **

**Notes:**
Now, using a finite difference method we can calculate a new velocity for the next time step. Notice the delta t: I spoke about eariler. If this time step is too large, the continuity of the MD trajectory will be compromised; too small and you waste computational resources. Michel Levitt and others have shown that a 2 femtosecond time-step makes the best use of computational resources while preserving the integrity of the simulation.

OK, so we know the new velocity which means we know the kinetic energy of the system and summing that with the potential we know the total energy of the system.

## Molecular Dynamics

**Time dependent integration **

**Notes:**
Similar to the new velocity calculation, we can now calculate the new position, x2.

## Molecular Dynamics

**Time dependent integration **

**Notes:**
And we have effectively calculated a 2 femtosecond section of our simulation.  We plug the new position, x2, back into the potential function:

## Molecular Dynamics

**Time dependent integration **

**Notes:**
and the process begins again by recalculating the force and so on.

## Molecular Dynamics

**Time dependent integration **

**Evaluate forces and perform integration for every atom**
**Each picosecond of simulation time requires 500 iterations of cycle**
**E.g. w/ 50,000 atoms, each ps (10****-12**** s) involves 25,000,000 evaluations**

**Notes:**
But in a real system we have 10s of thousands of atoms, not one. So we have to evaluate the forces and perform the integration on every atom. With the 2fs time step I described, this requires 500 iterations of the cycle for each picosecond of simulation time.  

As an example, a system with 50,000 atoms, each ps of simulation time involves 25 million evaluations: so obviously this is a very computationally intensive process.

## Molecular Dynamics

**Scalable, parallel MD & analysis software:**

***in lucem *****Molecular Mechanics****1**

***il*****mm**

- Beck, Alonso, Daggett, (2004) University of Washington, Seattle

**Notes:**
But in a real system we have 10s of thousands of atoms, not one. So we have to evaluate the forces and perform the integration on every atom. With the 2fs time step I described, this requires 500 iterations of the cycle for each picosecond of simulation time.  

As an example, a system with 50,000 atoms, each ps of simulation time involves 25 million evaluations: so obviously this is a very computationally intensive process.

## Molecular Dynamics

***il*****mm***** *****is***** *****written in C (ANSI / POSIX)**
**64 bit math**
**POSIX threads / MPI**
**Software design philosophy:**
**Kernel**
**Compiles user’s molecular mechanics programs**
**Schedules execution across processor and machines**
**Modules, e.g.**
**Molecular Dynamics**
**Analysis**

**Notes:**
So now I am going to tell you some specifics about how I implemented the methods I just described to you.

## Molecular Dynamics

***il*****mm***** *****is***** *****written in C (ANSI / POSIX)**
**64 bit math**
**POSIX threads / MPI**
**Software design philosophy:**
**Kernel**
**Compiles user’s molecular mechanics programs**
**Schedules execution across processor and machines**
**Modules, e.g.**
**Molecular Dynamics**
**Analysis**

**Notes:**
So now I am going to tell you some specifics about how I implemented the methods I just described to you.

## Dynameomics 

**Simulate representative protein from all folds**

## Dynameomics 

**Dynameomics **

**Simulate representative protein from all folds**
**Nature reuses designs for similar jobs**

**1hdd**

**1enh               1f43                      1ftt**

**1bw5                 1du6                 1cqt**

## Dynameomics 

**Dynameomics **

**Simulate representative protein from all folds**

- 1. Day R., Beck D. A. C., Armen R., Daggett V. Protein Science (2003) 10: 2150-2160.

- fold

- population

- coverage

- 150 folds represent ~ 75%
- of known protein structures

- fold

**1**

**Notes:**
OK, so ilmm works.  

Now I am going to tell you about some of the applications of ilmm in the Daggett lab.

First: dynameomics.  This is an on-going project that Ryan Day and myself have endevoured.  The goal is to simulation 30 proteins that were identified as representing about 50% of protein domains in the PDB.  Here are the 30 structures; about 8 have been examined with a 11 ns natice state simulation and two 11ns thermal denaturation studies.

## Dynameomics 

**Simulate representative protein from all folds**
**Native (folded) dynamics**
**20 nanosecond simulation at 298 Kelvin**
**Folding / unfolding pathway**
**3 x 2 ns simulations at 498 K**
**2 x 20 ns simulations at 498 K**
**Each target requires 6 simulations**
**	****	****	****=**
**	****	****    ****MANY CPU HOURS**

## Dynameomics 

**NERSC DOE INCITE award**
**2,000,000 + hours**
**906 simulations of 151 protein folds on Seaborg**
**One to two simulations per node (8 – 16 CPUs / simulation)**
**Opportunity to tune *****il*****mm for maximum performance**

## Dynameomics

**Load balancing**
**Even distribution of non-bonded pairs to processors**

**~20%**
**faster**

## Dynameomics

**Parallel efficiency **
**Threaded computations on 16 CPU IBM Nighthawk**

*p*, number of processors
*t*(*p*), run-time using *p* processors

- parallel efficiency,

**Notes:**
The single CPU ilmm performance compared to ENCAD is not astounding;  For a small system on a single CPU, ECNAD can out perform ilmm by 5 to 15 %. This is due to two factors: the dominant one being that ilmm uses 64 bit math operations which are more expensive than 32 bit operations on the Intel style hardware we have in the lab. Second, ilmm, even for a single processor job, still has some of the overhead of parallelization.

But what is very encouraging is the parallel effeciency of the alogirthms.  Here I am showing you normalized run times for the same simulation performed with 1, 2 and four processors on a quad pentium three xeon. The time for a one processor job is normalized to 1. In perfect paralleization, the 2 cpu value should be exactly 50% and the 4 cpu value should be exactly 25 %.  As you can see, ilmm is pretty close to these numbers.

## Dynameomics 

**Dynameomics **

**Simulate representative from top 151 folds**
- 151 folds represent about 75% of known proteins
- ~ 11 μs of combined sim. time from 906 sims!
- ~ 2 terabytes of data (w/ 40 to 60% compression!)
- ~ 75 / 151 have been analyzed
- Validated against experiment where possible

## Dynameomics 

**Now what?**
**Simulate the top 1130 folds (>90%)**
**More CPU time**
**Share simulation data from top 151 folds w/ world:**
**	****	****         **_[www.dynameomics.org](http://www.dynameomics.org/)_
**Coordinates, analyses, available via WWW**
**MicrosoftSQL database w/ On-Line Analytical Processing (OLAP)**
**End-user queries of coordinate data, analyses, etc.**
**Data mining**
**More CPU time, clever statistical algorithms, etc.**

## Acknowledgements

- DOE / NERSC’s INCITE  (David Skinner, *et al*)
- NIH
- Microsoft, Inc.
- Structures rendered using Chimera, Molscript, Raster3D & PyMOL