Molecular Control Engineering

From Enzyme Design to Quantum Control

Molecular Control Engineering

From Enzyme Design to Quantum Control

Raj Chakrabarti

School of Chemical EngineeringPurdue University

Raj Chakrabarti

School of Chemical EngineeringPurdue University

What is Molecular Control Engineering?

Control engineering: Manipulation of system dynamics through nonequilibrium modeling and optimization. Inputs and outputs are macroscopic variables.

Molecular control engineering: Control of chemical phenomena through microscopicinputs and chemical physics modeling. Adapts to changes in the laws of Nature at these length and time scales.

Aims

Reaching ultimate limits on product selectivity Reaching ultimate limits on sustainability Emulation of and improvement upon Nature’s strategies

Approaches to Molecular Optimization and Control

Static Optimization Dynamic Control

Molecular Structure/Function Optimization: Enzyme Design

Control of Biochemical Reaction Networks

[protein pic][protein pic]

msms

femtoseconds,angstroms

femtoseconds,angstroms

milliseconds, micrometersmilliseconds, micrometers

picoseconds,nanometerspicoseconds,nanometers

Coherent Control of Chemical Reaction Dynamics

How enzymes work

How to design them?

What makes them optimal for catalysis, and how to improve?

Problem: hyperastronomical sequence space

Catalytic Nucleophile Ser62

General acid/baseY159 Electrostatic stabilizer

Lys65

Catalytic nucleophileGlu-299

General acid/baseGlu-200

DD-peptidase -gal

Catalytic Mechanisms of EnzymesCatalytic Mechanisms of Enzymes

A model fitness measure for enzyme sequence optimizationA model fitness measure for enzyme sequence optimization

Catalytic constraint: interatomic distances rij < hbond dist

Catalytic constraint: interatomic distances rij < hbond dist Enzyme-substrate

binding affinity

Enzyme-substratebinding affinity

• Minimize J over sequence space

• Represent dynamical constraint with requirement that total energy of complex minimized for any sequence

• Omits selection pressure for product release

• Minimize J over sequence space

• Represent dynamical constraint with requirement that total energy of complex minimized for any sequence

• Omits selection pressure for product release

slack variableslack variable

1

1 1

2hbond,

N

i

N

jijijijijbind seqrrseqGseqJ

The physics in the model: sequence optimization requires accurate energy functions and solvation models

10o resolution rotamer library (297 proteins)

Ghosh, A., Rapp, C.S. & Friesner, R.A. (1998) J. Phys Chem. B 102, 10983-10990.

Xiang, Z. and Honig, B. (2001) J. Mol. Biol. 311: 421-430.

Friesner, R.A, Banks, J.L., Murphy, R.B., Halgren, T.A. et al. (2004) J. Med. Chem. 47, 1739-1749.Jacobson, M.P., Kaminski, G.A. Rapp, C.S. & Friesner, R.A. (2002) J. Phys. Chem. B 106, 11673-11680.

S-GB continuum solvation

OPLS-AA molecular mechanics force field + Glidescore semiempirical binding affinity scoring function

Streptavidin Native –10.04 kcal/mol

Computational sequence optimization correctly predicts most residues in ligand-binding sites and enzyme active sites

9 / 10 residues predicted correctly in top 0.5 kcal/mol of sequences

Chakrabarti, R., Klibanov, A.M. and Friesner, R.A. Computational prediction of native protein ligand-binding and enzyme active site sequences. PNAS, 2005.

CO2- is covalent attachment site

for biomolecules

Glucose-binding protein Native –8.81 kcal/mol

0

0.1

0.2

0.3

0.4

0.5

0.6

D A F R S Q E Y H I L K N G T W V M

Fre

qu

ency

0

0.1

0.2

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0.5

0.6

D A F R S Q E Y H I L K N G T WV M

Fre

quency

Computed

Observed (sequence alignment)

Computed amino acid distributions contain detailed evolutionary information

• Computed residue frequencies often mirror natural frequencies

OH

OH

Anomeric promiscuityEpimeric promiscuity

Chakrabarti, R., Klibanov, A.M. and Friesner, R.A. PNAS, 2005.

Number of residues correctly predicted

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0 1 2 3 4 5 6 7

Fra

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seq

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0 1 2 3 4 5 6 7 8 9 10

Catalytic constraints shift sequence distributions and are associated with “evolutionary temperatures”

DD-peptidase -gal

+ 1 kcal/mol

+2 kcal/mol

Constrained

Max entropy distributionsMax entropy distributions

multiple moments, evolutionary T’smultiple moments, evolutionary T’s

~ single moment, evolutionary T~ single moment, evolutionary T

,0

1ln bind bind optS Z seq G seq G

T

dseqGseqGT

Z optbindbind

,

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, hbond1 10

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bind bind opt iji j ij

S Z seq G seq G r seq rT T

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bind bind opt iji j ij

Z G seq G r seq r dseqT T

High-resolution sequence optimization is robust across diverse functional families

Peptide

Nucleotide

Sugar

0

0.2

0.4

0.6

0.8

1

1.2

Phe120 Asn161 Trp233 Arg285 Thr299 Ser326 Ser62 Lys65 Tyr159

Rm

sd t

o n

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e (A

)

Computational active site optimization is structurally accurate to near-crystallographic resolution

Nature Chemical Biology Volume 4 Number 5 May 2008:

“In a study by Chakrabarti et al. it was suggested that different enzyme active sites in natural proteins vary in their designability – that is, the number of sequences that are compatible with a specified structure and function.”

Chakrabarti R. Klibanov AM, Friesner RA. Sequence optimization and designability of enzyme active sites. Proc Natl Acad Sci USA 102:12035-12040, 2005

Current Opinion in Biotechnology Volume 18 2007:

•“ …Chakrabarti et al. found that they could recover the majority of wild type enzyme sequences by optimizing enzyme-substrate binding affinity while imposing geometric constraints on catalytic side-chain conformations.”

• “…Work by Chakrabarti et al. May also be useful for guiding the search for protein scaffolds suitable for introduction of de novo activity.”

“Of Outstanding Interest”: Chakrabarti R, Klibanov AM, Friesner RA. Computational prediction of native protein-ligand binding and enzyme active site sequences. Proc Natl Acad Sci USA 102: 10153-10158, 2005.

Reviews on Computational Sequence Optimization and Designability of EnzymesReviews on Computational Sequence Optimization and Designability of Enzymes

Sirtuin enzymes and regulation of age-related physiology

Sinclair DA. (2005) Mech. Ageing Dev. 126:987–1002Brooks CL, Gu W. (2008) Cancer Cell 13:377–78Brooks CL, Gu W. (2009) Nat. Rev. Cancer 9:123–28Luo J, Nikolaev AY, Imai S, Chen D, Su F, et al. (2001) Cell 107:137–48Vaziri H, Dessain SK, Eaton EN, Imai SI, Frye RA, et al. (2001) Cell 107:149–59

2008: GSK acquiresSirtris Pharmaceuticals for US $700 M

2010: Pfizer contests efficacy of drug leads from Sirtris experimental screening

2010: GSK terminates drugdevelopment of several sirtuin activators

Sirtuin enzymatic activities

Michan S and Sinclair D (2007) Biochem J 404, 1-13.

Sirtuins control metabolic pathways and aging through amino acid deacetylation

Feedback regulated by their reaction byproducts

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

D A F R S N E Y H I L K N G T W V

0

0.1

0.2

0.3

0.4

0.5

0.6

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D A F R S N E Y H I L K N G T W V C

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D A F R S N E Y H I L K N G T W V C

Computational sequence optimization and experimental mutagenesis of Sirtuins

New enzymes - Improved catalytic turnover Altered substrate selectivity

New enzymes - Improved catalytic turnover Altered substrate selectivity

3 permissible mutations identified by modeling at a target position

3 permissible mutations identified by modeling at a target position

43 mutation combinations = 64 sequence variations

43 mutation combinations = 64 sequence variations

Example of screening focused library of sequence variants

Example of screening focused library of sequence variants

3 positions subject to mutagenesis3 positions subject to mutagenesis

Synthetic gene assembly and variant library construction via DNA synthesis Synthetic gene assembly and variant library construction via DNA synthesis

Biological selection of variant library Biological selection of variant library

From Enzyme Design to Dynamic Bionetwork Control

• Maximizing kcat/Km of a given enzyme does not always maximize the fitness of a network of enzymes and substrates

• More generally, modulate enzyme activities in real time to achieve maximal fitness or selectivity of chemical products

• Lessons for control of metabolic networks via drug dosage (e.g. sirtuin inhibitors)

The Polymerase Chain Reaction: An example of bionetwork control

Nobel Prize in Chemistry 1994; one of the most cited papers in Science (12757 citations in Science alone)

Produce millions of DNA molecules starting from one

Used every day in every Biochemistry and Molecular Biology lab ( Diagnosis, Genome Sequencing, Gene Expression, etc.)

March 2005: Roche Molecular Diagnostics PCR patents expire

2008-2012: Celera and New England Biolabs License Chemical PCR Patents; Roche negotiates for Chemical PCR Patents

04/21/23 School of Chemical Engineering, Purdue University 19

DNA Melting

PrimerAnnealing

Single Strand – Primer Duplex

Extension

DNA MeltingAgain21

, 21 SSDmm kk

DNASS tt kk 12

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DNAEDE

DENDENDE

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SPEESP

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PCR and Disease Diagnostics

Trinucleotide Repeat Diseases

Huntington’s Disease Muscular Dystrophy Fragile X (Autism’s leading cause)

R. Chakrabarti and C.E. Schutt, Nucleic Acids Res., 2001R. Chakrabarti and C.E. Schutt, Gene 2002R. Chakrabarti, in PCR Technology: Current Innovations, 2003

Race for Diagnostic Methods: Standard PCR generally fails due to nonspecific amplification. First FDA-compliant Fragile X test based on Chemical PCR

Chemical PCR: uses solvent engineering of PCR reaction media, to alter kinetic parameters of the reaction network and enable sequencing of untractable genomic DNA

Race for Diagnostic Methods: Standard PCR generally fails due to nonspecific amplification. First FDA-compliant Fragile X test based on Chemical PCR

Chemical PCR: uses solvent engineering of PCR reaction media, to alter kinetic parameters of the reaction network and enable sequencing of untractable genomic DNA

R. Chakrabarti and C.E. Schutt, Chemical PCR: Compositions for enhancing polynucleotide amplification reactions. US Patent 7.772.383, issued 8-10-10. R. Chakrabarti and C.E. Schutt, Compositions and methods for improving polynucleotide amplification reactions using amides, sulfones and sulfoxides: II. US Patent 7.276,357, issued 10-2-07.

R.Chakrabarti and C.E. Schutt, US Patent 6,949,368, issued 9-27-05.

R. Chakrabarti and C.E. Schutt, Chemical PCR: Compositions for enhancing polynucleotide amplification reactions. US Patent 7.772.383, issued 8-10-10. R. Chakrabarti and C.E. Schutt, Compositions and methods for improving polynucleotide amplification reactions using amides, sulfones and sulfoxides: II. US Patent 7.276,357, issued 10-2-07.

R.Chakrabarti and C.E. Schutt, US Patent 6,949,368, issued 9-27-05.

Parallel Parking and Bionetwork Control

Tight spots: Move perpendicular to curb through sequences composed of Left, Forward + Left, Reverse + Right, Forward + Right, Reverse

Stepping on gas not enough: can’t move directly in direction of interest

Must change directions repeatedly

Left, Forward + Right, Reverse enough in most situations

Stepping on gas not enough: can’t move directly in direction of interest

Must change directions repeatedly

Left, Forward + Right, Reverse enough in most situations

Wild Type DNA

Mutated DNA

The DNA Amplification Control Problem and Cancer DiagnosticsThe DNA Amplification Control Problem and Cancer Diagnostics

Can’t maximize concentration of target DNA sequence by maximizing any individual kinetic parameter

Analogy between a) exiting a tight parking spot

b) maximizing the concentration of one DNA sequence in the presence of single nucleotide polymorphisms

Can’t maximize concentration of target DNA sequence by maximizing any individual kinetic parameter

Analogy between a) exiting a tight parking spot

b) maximizing the concentration of one DNA sequence in the presence of single nucleotide polymorphisms

TrDNADESS

DNAfDNAtT

CCCCx

Txfdt

dxst

CtCMin

.....,.....,

,

121 .

2max

)(

For N nucleotide template – 2N + 4 state equations

Typically N ~ 103

Optimal Control of DNA Amplification

R. Chakrabarti et al. Optimal Control of Evolutionary Dynamics, Phys. Rev. Lett., 2008K. Marimuthu and R. Chakrabarti, Optimally Controlled DNA amplification, in preparation

FMO photosynthetic protein complex transports solar energy with ~100% efficiency

Phase coherent oscillations in excitonic transport: exploit wave interference

Biology exploits changes in the laws of nature in control strategy: can we?

From bionetwork control to coherent control of chemical processes

Potential Energy Surface with two competing reaction channels

Saddle points separate products from reactants

Dynamically reshape the wavepacket traveling on the PES to maximize the probability of a transition into the desired product channel

Coherent Control versus Catalysis

probability densityprobability density

timetime interatomic distanceinteratomic distance

C. Brif, R. Chakrabarti and H. Rabitz, New J. Physics, 2010.

C. Brif, R. Chakrabarti and H. Rabitz, Control of Quantum Phenomena. Advances in Chemical Physics, 2011.

C. Brif, R. Chakrabarti and H. Rabitz, New J. Physics, 2010.

C. Brif, R. Chakrabarti and H. Rabitz, Control of Quantum Phenomena. Advances in Chemical Physics, 2011.

Femtosecond Quantum Control Laser Setup

2011: An NSF funded quantum control experiment collaboration between Purdue’s Andy Weiner (a founder of fs pulse shaping) and Chakrabarti Group

Coherent Control of State Transitions in Atomic Rubidium

R. Chakrabarti, R. Wu and H. Rabitz, Quantum Multiobservable Control. Phys. Rev. A, 2008.

R. Chakrabarti, R. Wu and H. Rabitz, Quantum Pareto Optimal Control. Phys. Rev. A, 2008.

R. Chakrabarti, R. Wu and H. Rabitz, Quantum Multiobservable Control. Phys. Rev. A, 2008.

R. Chakrabarti, R. Wu and H. Rabitz, Quantum Pareto Optimal Control. Phys. Rev. A, 2008.

Few-Parameter Control of Quantum DynamicsFew-Parameter Control of Quantum Dynamics

Conventional strategies based on excitation with resonant frequencies fails to achieve maximal population transfer to desired channels

Selectivity is poor; more directions of motion are needed to avoid undesired states

Conventional strategies based on excitation with resonant frequencies fails to achieve maximal population transfer to desired channels

Selectivity is poor; more directions of motion are needed to avoid undesired states

Optimal Control of Quantum DynamicsOptimal Control of Quantum Dynamics

Shaped laser pulse generates all directions necessary for steering system toward target state

Exploits wave-particle duality to achieve maximal selectivity, like coherent control of photosynthesis

Shaped laser pulse generates all directions necessary for steering system toward target state

Exploits wave-particle duality to achieve maximal selectivity, like coherent control of photosynthesis

A Foundation for Quantum System Control

K. Moore, R. Chakrabarti, G. Riviello and H. Rabitz, Search Complexity and Resource Scaling for Quantum Control of Unitary Transformations. Phys. Rev. A, 2010

R. Wu, R. Chakrabarti and H. Rabitz, Critical Topology for Optimization on the Symplectic Group. J Opt. Theory, 2009

R. Chakrabarti and H. Rabitz, Quantum Control Landscapes, Int. Rev. Phys. Chem., 2007

R. Chakrabarti, Notions of Local Controllability and Optimal Feedforward Control for Quantum Systems. J. Physics A: Mathematical and Theoretical, 2011.

R. Chakrabarti and A. Ghosh. Optimal State Estimation of Controllable Quantum Dynamical Systems. Phys. Rev. A, 2012.

.

Summary

• Can reach ultimate limits in sustainable and selective chemical engineering through advanced dynamical control strategies at the nanoscale

• Requires balance of systems strategies and chemical physics

• New approaches to the integration of computational and experimental design are being developed

Reviews of our work

Protein Design and Bionetwork Control

“Progress in Computational Protein Design”, Curr. Opin. Biotech., 2007

“Do-it-yourself-enzymes”, Nature Chem. Biol., 2008

R. Chakrabarti in PCR Technology: Current Innovations, CRC Press, 2003.

Media Coverage of Evolutionary Control Theory: The Scientist, 2008. Princeton U Press Releases

Quantum control

R. Chakrabarti and H. Rabitz, “Quantum Control Landscapes”, Int. Rev. Phys. Chem., 2007

C. Brif, R. Chakrabarti and H. Rabitz, “Control of Quantum Phenomena” New Journal of Physics, 2010; Advances in Chemical Physics, 2011

R. Chakrabarti and H. Rabitz, Quantum Control and Quantum Estimation Theory, Invited Book, Taylor and Francis, 2013.