Topic 1 Flashcards
-Outline molecular dynamics method for sampling the configurational states of a system of particles -Write down an approximate expression for the total potential energy and use it to -Describe the terms in a typical molecular mechanics force field for biomolecules -Explain the length and time scale problems in molecular simulation.
…, … and … are key to biomolecular function
Structure, assembly and dynamics are key to biomolecular function
Define structure, assembly and dynamics of a biomolecule
Structure of a biomolecule is defined by the components that comprise it e.g the linking of amino acids in a protein.
Assembly is the coming together of many structured sub units in a certain way.
Dynamics describe how the biomolecule moves and is essential in understanding function as defines how a species interacts with another in time.
What do computer simulations do and what do they allows?
Allow the study of properties of a many body system by creating a mathematical model (e.g a molecular mechanics forcefield) to describe the system behaviour which can be run to sample configurational space of that system (main families are MS and MC)
Why bother using comupter simulations?
- Gain better understanding of the system at a molecular level which allows better design of experiments and help interpret data.
- Predict properties/behaviour from molecular structure.
- Simulate unrealistic experiments that explore extreme conditions or toy models (e.g turn off charges to investigate hydrophobic driven reactions)
What are some problems tackled by MS of proteins?
- Molecular recognition (e.g ligand binding to an active sight)
- Dynamic processes (e.g. ion transport)
What is an MD simulation and what does it allow us to do?
- Enable us to simulate the time evolution of a system of particles.
- Can extract thermodynamic and kinetic information through simulation of particles at a position at the beginning and end of many steps.
- Trajectories are generated through classical dynamics (ignore electronic effects) by solving newtons equations of motion.
How are newtonian principles employed in MD simulations?
- The force acting on an atom i due to all other particles in a system is linked to the potential experienced by atom I and its position
- Using newtons second law (F=ma) we can also find the particles acceleration
Why can MD trajectories not be solved analytically? What must be done instead
- Cannot be solved analytically for a many-body system as force acting on each particle depends on the position of all other particles at that moment in time.
- Instead F=ma is solved numerically using small time steps Δt (~fs) where the force is calculated at the end of each of these time steps then following on to the next one.
- Most commonly done with the Verlet algorithm
How can we link these microscopic results to macroscopic length scales?
- At the end of our simulation the atoms trajectory over time form an ensemble of microstates characterised by positions, r and momenta, p.
- Statistical mechanics can be used to link to experimentally observable properties through statistical average over a large number of time steps.
The approximation linking microscopic and macroscopic lengthscales can be made assuming our system is ergodic, what is ergodicity?
Every microstate corresponding to a given macrostate is accessible i.e can reach all other positions of a system from the starting position of a simulation.
Ergodicity is not always true in practice, why is this?
- A barrier that is too high can cause system to be kinetically trapped in a certain region of phase space, leaving the global minimum unexplored.
- If one is doing a grid-based lattice simulation getting stuck in local minima when starting on certain set of lattice coordinates can be a problem.
What is the verlet algorithm?
- r(t + Δt) = 2r(t) -r(t - Δt) + Δt2(F[t]/m).
- Assumed all variables can be approximated by a truncated Taylor expansion.
- From this can find a point on a function via its derivatives as interested in position with respect to time (current time + small time step; r(t + Δt)
- velocities for Kinetic energy can be estimated through
What are forcefields and why are they useful?
Molecular mechanics forcefields (interatomic potentials) acts as a cheap way of representing a large systems PES
Why not use quantum mechanics instead of forcefields?
Computational expense of highly precise calculations restricts system sizes to <100 atoms, proteins are at least 1000’s. For this reason, a ball and spring model is approximated.
Write down an approximate expression for the total potential energy
- VFF = VBond + Vangle + VTorsion + Vimproper + VVDW + VElectrostatic
- This is a general functional form for an interaction potential/force field (can be used for atomistic or coare grained models)
Describe the bond stretch terms in a typical molecular mechanics force field.
Follows a Harmonic potential with an ideal equilibrium value (corresponding to a specific parameter in a table) at a low enery between two high energy states (compress/stretched).
Describe the Angle bend terms in a typical molecular mechanics force field.
both follow a harmonic potential with an ideal equilibrium value (corresponding to a specific parameter in a table) at a low enery between two high energy states (bend/straight)
Describe the dihedral angle rotation terms in a typical molecular mechanics force field.
Uses a periodic funciton to model the torsion
Describe the improper rotation term in a typical molecular mechanics force field.
Follows a harmonic potential with an ideal equilibrium value (corresponding to a specific parameter in a table) at a low enery between two high energy states
Describe the vdW term in a typical molecular mechanics force field.
- Generally adopts a Lennard Jones potential,
- High energy region at close separation as atoms overlapping. Equilibrium distance at minimum -ve of maximum attraction. Energy tends to 0 as separation increases.
Describe the electrostatic term in a typical molecular mechanics force field.
- Follows classical coulomb potential
- Partial charge assigned to all atoms.
- High energy for like charges decays to 0 as separation increases.
- Plot mirrored in x-axis for unlike charges.
What defines the transferability of a force-field?
- The ability to re-use fore-field parameters across a range of different functional groups.
- More parameters may be accurate for a specific system but transfer poorly to another.
- Forcefields have been paramaterised to reproduce properties of proteins, lipids e.g CHARMM, AMBER. Same functional form but differing parameters (different torsion angle for amino acids)
What is the time scale problem? What is a chemcial example that suffers from this?
- Larger than that of length scale, avoiding getting stuck in local minima can use up most simulation time without sampling desired configurational space.
- Can occur if waiting for a rare event to occur, but instead getting stuck behind a kinetic barrier.
- No way to know if this has occurred as the PES is not available prior to the simulation.
