WLAB GM - Nanocar

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# Research Update
## .red[Nanocar]
### WilmerLab Group Meeting
#### May 14, 2018

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<img src="/assets/img/presentations/nanocar-race-results.jpg" height=540>

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## Molecular Machines
.col2[Kinesin <img src="/assets/img/presentations/kinesin-walker.gif" height=210>]
--
.col2[Myosin 5 <img src="/assets/img/presentations/myosin5-animation.gif" height=210>]

???
Molecular machines are discrete number of molecular components that produce mechanical movements in response to specific stimuli (input).
The expression is often more generally applied to molecules that simply mimic functions that occur at the macroscopic level.
The term is also common in nanotechnology where a number of highly complex molecular machines have been proposed that are aimed at the goal of
constructing a molecular assembler.
In 1959, physicist Richard Feynman popularized the idea of nanomachines in his talk entitled "There's Plenty of Room at the Bottom".
--
 RNA Polymerase <img src="/assets/img/presentations/rna-polymerase-animation.gif" height=200>

???
Kinesins move along microtubule (MT) filaments, and are powered by the hydrolysis of adenosine triphosphate (ATP)
(thus kinesins are ATPases). The active movement of kinesins supports several cellular functions including mitosis,
meiosis and transport of cellular cargo, such as in axonal transport.

Myosin 5, is a motor found in non-muscle cells that is involved in moving proteins and vesicles (cargo)
around in cells along tracks of actin. Myosin 5 is a dimer, so it has two motor domains, and these take
alternate steps along actin, to carry its cargo to the right place in the cell.

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## Artificial Molecular Machines

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## Road Map

### Surface diffusion of large molecules
- Method development
- Experimental comparison

### Nanocar Design
- Directionality
- Speed
- Load capacity

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class: center, middle

### Surface diffusion of large molecules

.col3[DC<img src="/assets/img/presentations/DC.png" height=150>]
.col3[HtBDC<img src="/assets/img/presentations/HtBDC.png" height=150>]
.col3[Violet .red[Lander]<img src="/assets/img/presentations/VL.png" height=150>]

.col3[C60<img src="/assets/img/presentations/C60.png" height=150>]
.col3[.red[p-Carborane]<img src="/assets/img/presentations/PCARBORANE.png" height=150>]
.col3[PVBA<img src="/assets/img/presentations/PVBA.png" height=150>]

.col3[BtPHD<img src="/assets/img/presentations/BtPHD.png" height=150>]
.col3[DNHD<img src="/assets/img/presentations/DNHD.png" height=150>]
.col3[TPEE<img src="/assets/img/presentations/TPEE.png" height=150>]

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## HtBDC
<img src="/assets/img/presentations/HtBDC.png" height=350>

Activation Energy: 0. 57 eV ~ 13 kcal/mol

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## Molecular Dynamics

.col3[UFF<img src="/assets/img/presentations/traj-ff1.gif" height=300>]
--
.col3[UFF (5 eps)<img src="/assets/img/presentations/traj-ff3-5eps.gif" height=300>]
--
.col3[UFF + Coulomb<img src="/assets/img/presentations/traj-eqeq.gif" height=300>]
--

Predict very high diffusion compared to experimental data.

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## Experimental

.red[**HtBDC STM images | Δt = 13.9 s | T: 194 K**] <img src="/assets/img/presentations/htbdc-stm.png" height=150> 
Arrows indicate the direction in which molecules will have moved in the successive image.

.red[**PVBA | Δt = 220 s | T: 361 K**] <img src="/assets/img/presentations/pvba-stm.png" height=150> 
Images show that only a fraction of molecules moved. Each molecule is approximately 11 Å in length and 1.25 Å in width.
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## Transition State Theory (TST)
Systems characterized by a sequence of rare events can be described using TST.

- TST is primarily used to understand how chemical reactions take place.

- TST can also be used to calculate diffusion:
  - Diffusion can be approximated by a series of jumps between potential energy minima (lattice sites).
  - The rate constants for jumping between the sites can be converted to diffusivities.

???
Ex: Diffusion in zeolites occur outside the time scales accesible to molecular dynamics simulations,
which is typically limited to diffusion rates in the order of 10-12 cm2/s.

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### Arrhenius Equation (1889)

- Temperature dependence of a rate constant (mostly reaction rates)
- Activation energy
- Empirical relationship.

### Eyring Equation (1935)

???
A historically useful generalization supported by Arrhenius' equation is that, for many common
chemical reactions at room temperature, the reaction rate doubles for every 10 degree Celsius increase in temperature.
Moore's Law of chemical engineering.

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### Eyring Equation (1935)
- Statistical mechanics justification.

## Transmission coefficient

???
The transmission coefficient is used in physics and electrical engineering when wave propagation in a medium containing discontinuities is considered.
An electromagnetic (or any other) wave experiences partial transmittance and partial reflectance when the medium through which it travels suddenly changes.

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## dcTST (Dynamically Corrected Transition State Theory)

Enables calculation of self-diffusion coefficients for systems far beyond the time scales accessible to molecular dynamics.

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### FCC (110) Surface
.col2[x-direction <img src="/assets/img/presentations/tst-fcc-110-x.png" alt="us-fcc-110-x" height=300>]
.col2[y-direction <img src="/assets/img/presentations/tst-fcc-110-y.png" alt="us-fcc-110-y" height=300>]

???
https://pubs.acs.org/doi/full/10.1021/jp0542470

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## Calculating hopping rate

- *kA→B*: hopping rate from state A → B
- *K*: transmission coefficient (0 - 1)
- *M*: mass of the molecule
- *T*: temperature
- *F(q)*: free energy at coordinate *q*
- *: transition state

???
k formula:
k_{A \rightarrow B} = \kappa {\sqrt{ \dfrac{1}{2 \pi M \beta}}} \dfrac{ e^{- \beta F(q^*)} } { \int e^{- \beta F(q)}dq }

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## Calculating self-diffusion coefficient

- *Ds*: self-diffusion coefficient
- *kA→B*: hopping rate from state A → B
- *n*: dimensionality
- *λ*: hopping length

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## Umbrella Sampling
.col2[*x-direction* <img src="/assets/img/presentations/us-fcc-110-x.png" alt="us-fcc-110-x" height=280>]
.col2[*y-direction* <img src="/assets/img/presentations/us-fcc-110-y.png" alt="us-fcc-110-y" height=280>]

???
Umbrella sampling is a technique used to improve sampling of a system where ergodicity is hindered by the form of the system's energy landscape.
Basically, you sample your system on the direction that you are interested to study.
--

The molecule is attached to a point in space using a spring. 
For each point an MD simulation is performed.

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## Procedure
- Initially the smallest repeating lattice is divided into grid points.

- For each grid point a constrained MD simulation is performed.
- Weighted Histogram Analysis Method (WHAM) is used to calculate free energy profiles.
- Hopping rate can then be calculated using dcTST equation.
- The self-diffusion coefficient can be calculate using the hopping rate.

???
WHAM Manual: http://membrane.urmc.rochester.edu/sites/default/files/wham/doc.pdf

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## Minimization

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## Constrained NVT

.col2[*x-direction* <img src="/assets/img/presentations/us-fcc-110-grid-x.png" height=150>]
.col2[*y-direction* <img src="/assets/img/presentations/us-fcc-110-grid-y.png" height=150>]

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### Activation Energy

- The barriers obtained using WHAM analysis are around 0.15 kcal/mol.
- The experimental activation energy for HtBDC is 0.57 eV which is approximately 13 kcal/mol.
- This means we are 2 orders of magnitude lower.
- Let's bump up the interaction energy.

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## Increase pairwise energy

<img src="/assets/img/presentations/htbdc-high-energy-buckle.gif" alt="htbdc-buckle" height=242>
 
--
.col2[<img src="/assets/img/presentations/lizard-sand.gif" alt="lizard-sand" height=250>]

--
.col2[<img src="/assets/img/presentations/octopus-sand.gif" alt="octopus-sand" height=250>]

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## Rigid simulation (y)

.col2[<img src="/assets/img/presentations/cnvt2-wham-y-f.png" height=250>]
.col2[<img src="/assets/img/presentations/cnvt2-wham-y-p.png" height=250>]

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## Rigid simulation (x)

.col2[<img src="/assets/img/presentations/cnvt2-wham-x-f.png" height=250>]
.col2[<img src="/assets/img/presentations/cnvt2-wham-x-p.png" height=250>]

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## Pairwise Energy

.col2[<img src="/assets/img/presentations/cnvt2-epair-x.png" height=250>]

.col2[<img src="/assets/img/presentations/cnvt2-epair-y.png" height=250>]

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# <div class="font-effect-anaglyph">Thank you!<div>

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# Mean Squared Displacement

Mean squared displacement is calculated using the formula below:

where N is the number of timesteps, r(t) is the position of particle at time t and dt is time delta.

In order to understand the type of diffusion one can calculate MSD for different timedelta values
and plot MSD vs dt.

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### MSD vs dt

The shape of the MSd vs dt curve gives information about the type of the motion of the particle.
For true random walk (brownian motion) a linear line is expected.
If there are other forces affecting the motion of the particle then different behaviours can be expected.

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## LAMMPS

#### US - Minimization
Calculate min energy and distance for each point

#### US - NVT & Spring (eps: 5)
Attached spring (k:5 kcal/mol) to each point and performed NVT simulations for 5 ns (dt: 1 fs).
Performed WHAM analysis which resulted in barriers ~0.15 kca/mol.
The activation energy of the molecule is 0.57 eV which corresponds to ~13 kcal/mol.
This suggests that surface-molecule interaction energy should be ~100 times larger.

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#### US - NVT & Spring (eps: 500)
This resulted in molecule to explode (bonded atoms becoming too far apart).
This is presumably because the molecule is initially placed ~5 A above the surface and with the NVT
simulation the molecule is attracted to the surface with so much speed that the atoms just gain too much velocity.
This veolcity is however different for each atom therefore they might fly apart from each other losing bonds.
This can be alleviated by minimizing the system first.

Moreover by changing the epsilon coefficient the equilibrium z-distance might be changed.
Instead of using the same z position for the spring, for these simulations I decided to use the last z position from the minimization.

#### US - Minimization - NVT & Spring (eps: 500)

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# <div class="font-effect-anaglyph">Thank you!<div>

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