Wires Within Wires A Minimal Model for Computational Bioelectronic Peptide Design R. A. Mansbach 1 A. L. Ferguson 2 1 Physics Department 2 Materials Science Department University of Illinois at Urbana-Champaign Blue Waters Symposium, Sunriver, OR, June 4, 2018
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Wires Within WiresA Minimal Model for Computational Bioelectronic Peptide Design
R. A. Mansbach1 A. L. Ferguson2
1Physics Department
2Materials Science DepartmentUniversity of Illinois at Urbana-Champaign
Wall, Brian D., et al. “Supramolecular Polymorphism:Tunable Electronic Interactions within π-ConjugatedPeptide Nanostructures Dictated by Primary Amino AcidSequence.” Langmuir30.20 (2014): 5946-5956.
www.imore.com/sites/imore.com/files/styles/large/
public/topic_images/2015/
Galagan, Y.,& Andriessen, R. (2012).“Organic photovoltaics: technologies andmanufacturing.” INTECH Open AccessPublisher.
Wall, Brian D., et al. “Supramolecular Polymorphism:Tunable Electronic Interactions within π-ConjugatedPeptide Nanostructures Dictated by Primary Amino AcidSequence.” Langmuir30.20 (2014): 5946-5956.
www.imore.com/sites/imore.com/files/styles/large/
public/topic_images/2015/
Galagan, Y.,& Andriessen, R. (2012).“Organic photovoltaics: technologies andmanufacturing.” INTECH Open AccessPublisher.
Wall, Brian D., et al. “Supramolecular Polymorphism:Tunable Electronic Interactions within π-ConjugatedPeptide Nanostructures Dictated by Primary Amino AcidSequence.” Langmuir30.20 (2014): 5946-5956.
www.imore.com/sites/imore.com/files/styles/large/
public/topic_images/2015/
Galagan, Y.,& Andriessen, R. (2012).“Organic photovoltaics: technologies andmanufacturing.” INTECH Open AccessPublisher.
Side chain radius affects contact cluster growth more strongly
Contact Cluster Growth Fewer configurations
Increasing cross-section
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Wires WithinWires
Mansbach,Rachael
Motivation
Patchy Model
Results
Conclusionsand FutureWork
Identification of optimal parameter sets
Pareto frontier
Tradeoff between different objectives10 / 15
Wires WithinWires
Mansbach,Rachael
Motivation
Patchy Model
Results
Conclusionsand FutureWork
Five candidates flagged for future study
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Wires WithinWires
Mansbach,Rachael
Motivation
Patchy Model
Results
Conclusionsand FutureWork
Next steps: Active Learning
Brochu, Eric, Vlad M. Cora, and Nando De Freitas. “A tutorial on Bayesian optimization of expensive cost functions, with application to active user modeling and
Brochu, Eric, Vlad M. Cora, and Nando De Freitas. “A tutorial on Bayesian optimization of expensive cost functions, with application to active user modeling and
Brochu, Eric, Vlad M. Cora, and Nando De Freitas. “A tutorial on Bayesian optimization of expensive cost functions, with application to active user modeling and
Created a patchy model thatrecapitulates DXXX properties andreaches mesoscopic scale
Showed effects of changingparameter space
Identified potential ways to designfor optimal parameters
Part of a multiscale model forrational peptide design
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Wires WithinWires
Mansbach,Rachael
Motivation
Patchy Model
Results
Conclusionsand FutureWork
Acknowledgments
∗ *This research is part of the Blue Waterssustained-petascale computing project,which is supported by the National ScienceFoundation(awards OCI-0725070 and ACI-1238993)and the state of Illinois. Blue Waters is ajoint effort of the University of Illinois at
Urbana-Champaign and its National
Center for Supercomputing Applications.
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Wires WithinWires
Mansbach,Rachael
Choice ofparameterspace forsweep
Examples ofsingle-parametercomputations
Additional data
Ideal Gas Modelof Aggregation
Backup Slides
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Mansbach,Rachael
Choice ofparameterspace forsweep
Examples ofsingle-parametercomputations
Additional data
Ideal Gas Modelof Aggregation
Initial Parameter Sweep: Aromatic Cores
Non cofacial aromatic εBB
Set to 1 kBT
Cofacial aromatic εA
Cv
~ 18 kT
Sweep over 2.5-7.5kBT depth2 / 13
Wires WithinWires
Mansbach,Rachael
Choice ofparameterspace forsweep
Examples ofsingle-parametercomputations
Additional data
Ideal Gas Modelof Aggregation
Initial Parameter Sweep: Side Chains
Side chain εSC
~ 2 kT
Sweep over 0.2-10 kBT
Side chain σSC
Sweep over 1.0 -1.75 nm
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Choice ofparameterspace forsweep
Examples ofsingle-parametercomputations
Additional data
Ideal Gas Modelof Aggregation
Example of growth rate calculations
εA = 2.5 kBT
σSC = 1.5 nm
Main Text Backups
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Choice ofparameterspace forsweep
Examples ofsingle-parametercomputations
Additional data
Ideal Gas Modelof Aggregation
Dependence of fractal dimension on parameter space
Fractal dimension of region II-A
Approximate length scale of fibril width and monomer packingModerately (anti)correlated with optical cluster growth rate
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Choice ofparameterspace forsweep
Examples ofsingle-parametercomputations
Additional data
Ideal Gas Modelof Aggregation
Optical versus contact cluster growth rate
Optical Cluster Growth Rate
Optical vs Contact Cluster Growth Rate
Main Text Backups
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Choice ofparameterspace forsweep
Examples ofsingle-parametercomputations
Additional data
Ideal Gas Modelof Aggregation
Pareto Optimization
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Choice ofparameterspace forsweep
Examples ofsingle-parametercomputations
Additional data
Ideal Gas Modelof Aggregation
Mathematical Formulation
Separate contributions
S({nk}) =∑k
nkkB ln
(Ve5/2
Λ3knk
)+∑k
nksk + Ssolv, (1)
U({nk}) =∑k
nkuk + Uinter + Usolv, (2)
Probability of a microstate
P({nk}) =e−β(Usolv−TSsolv)
Q
[∏k
(Ve5/2
Λ3knk
)nk]e−β
∑k nkgk , (3)
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Choice ofparameterspace forsweep
Examples ofsingle-parametercomputations
Additional data
Ideal Gas Modelof Aggregation
Probability with respect to a reference state
Reference State
N isolated monomers: ({n1 = N, ni = 0}, i > 1)
Probability
P({nk})
P(n1 = N)=
[∏k
(Ve5/2
Λ3knk
)nk]e−β
∑k nk gk
(Ve5/2
Λ31N
)Ne−βNg1
(4)
= e−β(∑
k nk gk−Ng1) NN ∏k k
32nk
e52 (N−
∑k nk ) ∏
k nnkk
(Λ1
L
)3(N−∑
k nk )
, (5)
ln
[P({nk})
P(n1 = N)
]=− β
∑k
nkgk − Ng1
+ 3
N −∑k
nk
ln
(Λ1
L
)
+ N ln N −5
2
N −∑k
nk
+∑k
3
2nk ln k −
∑k
nk ln nk .
(6)
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Examples ofsingle-parametercomputations
Additional data
Ideal Gas Modelof Aggregation
Thermodynamic limit
Fixed number concentration
ρ ≡ NV
Mass fraction
fk ≡ knkN∑
k fk = 1, fk ∈ [0, 1]∀k
Probability
ln
[P({fk})P(f1 = 1)
]=− Nβ
(∑k
fkgk
k− g1
)+ 3N
(1−
∑k
fk
k
)ln(ρ1/3Λ1
)
+ N∑k
fk
kln
(k5/2
fk
)−
5
2N
(1−
∑k
fk
k
).
(7)
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Examples ofsingle-parametercomputations
Additional data
Ideal Gas Modelof Aggregation
Constrained optimization
Free energy of formation
gk = ∆gk + kg1, (8)
∑k
fkgk
k− g1 =
∑k
fk∆gk
k. (9)
Most probable mass fraction in the thermodynamic limit
{fk}∗ = max{fk}
−β∑k
fk∆gk
k+∑k
fk
k ln
(k5/2e5/2
fkρΛ31
) + ln(ρΛ3
1
)−
5
2
(10)
= max{fk}
[−β∑k
fk∆gk
k+∑k
fk
kln
(k5/2e5/2
fkρΛ31
)], (11)
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Choice ofparameterspace forsweep
Examples ofsingle-parametercomputations
Additional data
Ideal Gas Modelof Aggregation
Approximation of most probable mass fraction for DFAG
Model Parameters
∆g1 ≡ 0 (12)
∆g2 = −14.5 kBT (13)
∆gk = ∆g2 + (k − 2)(−25 kBT )(14)
ρ = 2.6497× 1027 m−3 (15)
T = 298K (16)
mmon = 1151.2 g-mol−1 (17)
Λ1 = 2.9807× 10−12 m−1 (18)
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Choice ofparameterspace forsweep
Examples ofsingle-parametercomputations
Additional data
Ideal Gas Modelof Aggregation
Dependence of growth and alignment on free energies
Threshold of large-scale aggregation may coincide with good core alignment