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

Blue Waters Symposium, Sunriver, OR, June 4, 2018

Wires WithinWires

Mansbach,Rachael

Motivation

Patchy Model

Results

Conclusionsand FutureWork

π-conjugated self-assembling optoelectronic peptides

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.

topic-apple-watch-all.png?itok=OUtlCphV2 / 15

Wires WithinWires

Mansbach,Rachael

Motivation

Patchy Model

Results

Conclusionsand FutureWork

π-conjugated self-assembling optoelectronic peptides

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.

topic-apple-watch-all.png?itok=OUtlCphV2 / 15

Wires WithinWires

Mansbach,Rachael

Motivation

Patchy Model

Results

Conclusionsand FutureWork

π-conjugated self-assembling optoelectronic peptides

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.

topic-apple-watch-all.png?itok=OUtlCphV2 / 15

Wires WithinWires

Mansbach,Rachael

Motivation

Patchy Model

Results

Conclusionsand FutureWork

DXXX series demonstrates hierarchical assembly

Optical Clusters

Contact Clusters

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Wires WithinWires

Mansbach,Rachael

Motivation

Patchy Model

Results

Conclusionsand FutureWork

DXXX series demonstrates hierarchical assembly

Optical Clusters Contact Clusters

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Wires WithinWires

Mansbach,Rachael

Motivation

Patchy Model

Results

Conclusionsand FutureWork

Reaching longer time and length scales

Minimal coarse-grained model

Large computational infrastructure

Do parameter sweep over welldepths and radii to gainunderstanding of effect of differentinteraction parameters on assemblyat mesoscale

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Wires WithinWires

Mansbach,Rachael

Motivation

Patchy Model

Results

Conclusionsand FutureWork

Reaching longer time and length scales

Minimal coarse-grained model

Large computational infrastructure

Do parameter sweep over welldepths and radii to gainunderstanding of effect of differentinteraction parameters on assemblyat mesoscale

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Wires WithinWires

Mansbach,Rachael

Motivation

Patchy Model

Results

Conclusionsand FutureWork

Understanding chemical interactions at low resolution

Minimal coarse-grained model

Large computational infrastructure

Do parameter sweep over welldepths and radii to gainunderstanding of effect of differentinteraction parameters on assemblyat mesoscale

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Wires WithinWires

Mansbach,Rachael

Motivation

Patchy Model

Results

Conclusionsand FutureWork

Aggregate shape and fractal dimension match previous work

Ardona, Herdeline Ann M., and John D. Tovar. “Energy transfer within responsiveπ-conjugated coassembled peptide-based nanostructures in aqueous

environments.” Chemical Science 6.2 (2015): 1474-1484.6 / 15

Wires WithinWires

Mansbach,Rachael

Motivation

Patchy Model

Results

Conclusionsand FutureWork

Interaction parameters control aggregate morphology

Increasing side chain stickiness increases disorder

Side chain size controls transition between flat ribbon and twisted fibril

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Wires WithinWires

Mansbach,Rachael

Motivation

Patchy Model

Results

Conclusionsand FutureWork

Optical cluster growth is primarily controlled by side chaininteractivity

Optical Cluster Growth

Increasing sidechain well depthincreasesfavorability of sidechain–side chaininteractions

Biggest increase asside chaininteractivitydecreases belowcore–coreinteractivity

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Wires WithinWires

Mansbach,Rachael

Motivation

Patchy Model

Results

Conclusionsand FutureWork

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

hierarchical reinforcement learning.” arXiv preprint arXiv:1012.2599 (2010).12 / 15

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

hierarchical reinforcement learning.” arXiv preprint arXiv:1012.2599 (2010).12 / 15

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

hierarchical reinforcement learning.” arXiv preprint arXiv:1012.2599 (2010).12 / 15

Wires WithinWires

Mansbach,Rachael

Motivation

Patchy Model

Results

Conclusionsand FutureWork

Why Blue Waters?

Scale of problem

300 simulations of 10,648monomersEach simulation requires multipleGPU acceleration and produces10-20 gigabytes of data to beanalyzed

Big data research infrastructure

Access to broader big datacommunity

https://www.slideshare.net/sergejsgroskovs/

pragmatism-philosophy-of-science-lecture-slides

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Wires WithinWires

Mansbach,Rachael

Motivation

Patchy Model

Results

Conclusionsand FutureWork

Why Blue Waters?

Scale of problem

300 simulations of 10,648monomersEach simulation requires multipleGPU acceleration and produces10-20 gigabytes of data to beanalyzed

Big data research infrastructure

Access to broader big datacommunity

https://www.slideshare.net/sergejsgroskovs/

pragmatism-philosophy-of-science-lecture-slides

13 / 15

Wires WithinWires

Mansbach,Rachael

Motivation

Patchy Model

Results

Conclusionsand FutureWork

Broader Impact

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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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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Choice ofparameterspace forsweep

Examples ofsingle-parametercomputations

Additional data

Ideal Gas Modelof Aggregation

Backup Slides

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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

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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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Additional data

Ideal Gas Modelof Aggregation

Example of growth rate calculations

εA = 2.5 kBT

σSC = 1.5 nm

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Additional data

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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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Optical versus contact cluster growth rate

Optical Cluster Growth Rate

Optical vs Contact Cluster Growth Rate

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Ideal Gas Modelof Aggregation

Pareto Optimization

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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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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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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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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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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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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

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