Systems-Based Approaches at the Frontiers of Chemical Engineering and Computational Biology: Advances and Challenges

Christodoulos A. Floudas Princeton University Department of Chemical Engineering Program of Applied and Computational Mathematics Department of Operations Research and Financial Engineering Center for Quantitative Biology Outline

• Theme: Scientific/Personal Journey • Research Philosophy at CASL (Computer Aided Systems Laboratory, Princeton University) • Research Areas: Advances & Challenges • Acknowledgements Greece Ioannina, Greece Ioannina,Greece (Courtesy of G. Floudas) Thessaloniki, Greece Aristotle University of Thessaloniki Department of Chemical Engineering Aristotle University of Thessaloniki Undergraduate Studies(1977-1982) Pittsburgh, PA Carnegie Mellon University Graduate Studies

How did it all start?

• Ph.D. Thesis: Sept. 82 – Dec. 85 •Advisor: Ignacio E. Grossmann

• Synthesis of Flexible Heat Exchanger Networks (82-85) • Uncertainty Analysis (82-85) Princeton, NJ Princeton University Computer Aided Systems Laboratory Interface Product & Process Systems Engineering • Chemical Engineering • Applied Mathematics Research • Operations Research Areas • Computer Science • Computational Chemistry Computational Biology & Genomics • Computational Biology

Unified Theory • address fundamental problems and applications via mathematical and Research modeling of microscopic, mesoscopic and macroscopic level Philosophy • rigorous optimization theory and algorithms • large scale computations in high performance clusters

Mathematical Modeling, Optimization Theory & Algorithms

Themes Discovery at the Macroscopic Level

Discovery at the Microscopic Level Research Areas (1986 – present)

Process Operations: Process and Product Scheduling, Planning and Design & Synthesis Uncertainty

Optimization Theory & Methods: - Mixed-Integer Nonlinear Optimization - Deterministic Global Optimization

Interaction of Design, Computational Biology & Synthesis & Control Genomics Process & Product Design and Synthesis (1986-)

Christodoulos A. Floudas Princeton University Process & Product Design and Synthesis

• Distillation Sequences (86-91) • Heat Exchanger Networks (86-91) • Reactor Networks and Reactor-Separator-Recycle (87-02) • Phase Equilibrium (94-02) • Azeotropic Separations (96-02)

• Shape Selective Separation/Catalysis (05-) Rational Design of Shape Selective Separation and Catalysis

C.E. Gounaris, C.A. Floudas, J. Wei Department of Chemical Engineering, Princeton University Fundamental Questions • Given a candidate set of zeolite portals and a pair of molecules (e.g., Molecule A and Molecule B), (a) can we identify the best zeolite portal which can separate molecule A from molecule B more effectively? (b) can we generate a rank-ordered list of zeolite portals for such separation? (c) can we identify such zeolite portals for any pair of molecules and the complete set of known zeolites? Molecular Footprints

• Start with a simple molecular model: • Atoms are spheres of some effective radius • Bond lengths and angles considered fixed

• Given this 3-d conformation, rotate suitably the molecule and project it onto the 2-d xy-plane • This projection is a set of circles • Circle centers are projections of atom nuclei • Circle radii are effective radii of atom spheres

• Different 3-d orientations result into different projections

• We define the molecular footprint to be such a projection that would likely be explored when penetration through a portal occurs Molecular Footprints - Examples

• Aromatics :

(a) benzene (b) toluene

(c) o-xylene (d) m-xylene (e) p-xylene

• Benzene is a planar molecule and results into a linear projection

• The other aromatics have “almost” linear footprints Strain-based Screening

• When a guest molecule approaches a host portal :

No passage - There is no orientation for which all projected atom nuclei fall inside the portal area

Constrained passage - There is some orientation for which all projected atom nuclei fall inside the portal area, but some circles have to be squeezed for a complete fit There is some orientation for which all Free passage - circles fall completely inside the portal area Strain-based Screening - Model

• Let us define : (squeezed radius) rs Amount of distortion on an atom : δ = (original radius) ro

⎛⎞ Total Strain for a guest molecule ⎛⎞11 11 SS=+=GH S ⎜⎟ − +⎜⎟ − ∑∑δ 12δδδ 6⎜⎟ 12 6 to penetrate through a host portal : ij⎝⎠ii⎝⎠ jj

• Every projection is associated with some total strain and there is an optimal projection that exhibits the minimum strain, denoted as S* • Define Strain Index : SI=+log(1 S * )

• SI is a measure of total distortion needed for penetration SI = 0 0 < SI < ∞ SI --> ∞ Strain-based Screening - Results • 38 molecules / 217 zeolite windows

Strain Index Strain-based Screening - Results • 38 molecules / 217 zeolite windows

Detail: Strain Index of aromatics on some 12-oxygen ring windows Interaction of Design & Control (1987-2000)

Christodoulos A. Floudas Princeton University Interaction of Design & Control

• Structural Properties: Generic Rank • Dynamic Operability of MIMO Systems: Time Delays & Transmission Zeroes • Multi-objective Framework for the Interaction of Design and Control • Optimal Control of Reactors • Dynamic Models in the Interaction of Design and Control Deterministic Global Optimization (1987-)

Christodoulos A. Floudas Princeton University Deterministic Global Optimization How/When did we start? Motivation: Multiple local minima in - distillation sequencing - heat exchanger networks - reactor network synthesis - pooling problems

Initial Studies: 1987-89 Historical Global Optimization Perspective 5496

2397 # Publications

1046

97 25 33

1960-1979 1980-1984 1985-1989 1990-1994 1995-1999 2000-2006 ChE Global Optimization Perspective: Early Contributions

Floudas, Agarwal, Ciric (1989)

Stephanopoulos & Westerberg (1975) Floudas & Visweswaran (1990)

Westerberg & Shah (1978) Wang & Luus (1978) ChE Publications

1975 1980 1985 1990 1995 2000 2005

Deterministic Global Optimization

• GOS: Global Optimum Search (88-89)

• GOP: Biconvex, Bilinear, Polynomial (90-96)

• aBB: Twice Continuously Differentiable Constrained Nonlinear Problems (94-98)

• SMIN-aBB, GMIN-aBB: Mixed-Integer Nonlinear (98-00)

• DAE: Differential-Algebraic Systems (98-02)

• Bilevel Nonlinear Problems (01-05)

• Convex Envelopes for Trilinear Monomials (03-04)

• Convex Underestimators for Trigonometric Functions (04-05)

• G-aBB: Generalized aBB (04-)

• P-aBB: Piecewise aBB (05-)

• Tight Convex Underestimators for General C2 Functions (06-) Deterministic Global Optimization: Chemical Engineering Applications

• Phase & Chemical Reaction Equilibrium

• Homogeneous, Heterogeneous & Reactive Azeotropes

• Pooling Problems

• Parameter Estimation & Data Reconciliation

• Trim Loss Minimization

• Generalized Pooling Problems

• Nesting of Arbitrary Shapes Generalized Pooling Problem Meyer, Floudas (2006) Sources Plants Destinations

Q1: What is the optimal topology? Binary Terms Q2: Which plants exist? Binary Variables Formulation of Generalized Pooling Problem

Objective: Minimize Overall Cost - Plant construction and operating costs - Pipeline construction and operating cost Binary Variables

a -y s,e: Existence of stream connecting source s to exit stream e. b - y t,e: Existence of stream connecting plant t to exit stream e. c - y t,t’: Existence of directed stream connecting plant t to plant t’. d - y s,t: Existence of stream connecting source s to plant t. e - y t: Existence of plant t. Problem Characteristics

- Mixed integer bilinear programming problem with bilinearities involving pairs of continuous variables, (b,f) and (c,f) and (d,f). - Nonconvex mass balance constraints on the species include bilinear terms. - Industrial case study: |C| = 3, |E| = 1, |S| = 7, |T| = 10. - Number of nonconvex equality constraints: |C| x (|T| + |E|). (33)

- Number of bilinear terms: |C| x |T| x (|E| + |S| + 2|T| - 2). (780) - Complex network structure with numerous feasible yet nonoptimal possibilities. - Number of binary variables: |T| x (|E| + |S| + |T|) + |S| x |E|. (187) - Fixing the y variables, the problem is a nonconvex bilinear NLP. Feasible Solutions

Objective function value: 1.086e6 Objective function value: 1.198e6

S1 S1

S2 S2 T3 T3 S3 S3 T7 T7 S4 E1 S4 E1 T9 T9 S5 S5 T10 T10 S6 S6

S7 S7

Objective function value: 1.132e6 Objective function value: 1.620e6

S1 S1

S2 S2

T2 T11 S3 S3

T3 T33 S4 E1 S4 E1 T7 T7 S5 S5 T9 T9 S6 S6

S7 S7 Industrial Case Study

Components: 3 Best known solution: 1.086 x 106 Sources: 7 Lower bound on solution: 1.070 x 106 Exit streams: 1 Absolute Gap: 0.016 x 106 Potential plants: 10 Relative Gap: 1.5 %

Formulation ℜ var. {0,1} var Constr. CPU (s) Obj (106) Nonconvex 207 187 424 2.5 1.086 Bilinear Terms 987 187 3544 58 0.550 RLT 3850 187 19321 3621 0.743 Subnetwork {t3, t7, t9, t10} Bin RLT N = 2 766 79 4866 519 0.977 Bin RLT N = 3 766 91 6234 816 1.005 Bin RLT N = 4 766 103 7602 3672 1.022 Bin RLT N = 5 766 115 8970 7617 1.031 Bin RLT N = 6 766 127 10338 85800 1.051 Bin RLT N = 7 766 139 11706 59486 1.070 Challenges/Opportunities Current Status: Great Success for Theory & Algorithm for Small to Medium-size Applications • Improved Convex Underestimation Methods • Now Theoretical Results on Convex Envelopes • Medium to Large-scale C2-NLPs – Pooling Problems • Medium to Large-scale MINLPs – Product & Process Design/Synthesis/Operations – Signal Transduction/Metabolic Pathways – Generalized Pooling Problems • New Theory and Algorithms for DAE Models • New Theory and Algorithms for Grey/Black box models • Multi-level Nonlinear Optimization Computational Biology & Genomics (1990-)

Christodoulos A. Floudas Princeton University Computational Biology & Genomics How/When did we start? Motivation: Multiple local minima in - Lennard-Jones Cluster packing - Structure prediction of small molecules - Structure prediction of oligo-peptides - Structure prediction in protein folding

Initial Studies: 1990-95 Computational Biology and Genomics

• Structure Prediction in Lennard-Jones Clusters & Acyclic Molecules (90-95)

• Structure Prediction in Protein Folding (95-)

• Dynamics in Protein Folding (96-00)

• Force Field Development (01-)

• De Novo Protein Design (01-)

• Protein-Peptide Interactions (95-03)

• Metabolic and Signal Transduction Networks (95-)

• Proteomics: Peptide & Protein Identification (05-) Structure Prediction in Protein Folding Amino acid sequence [PDB: 1q4sA ] MHRTSNGSHATGGNLPDVASHYPVAYEQTLDGTVGFVIDEMTPERATASVEVTDTLRQRWGLVHGGAYCALAEMLA TEATVAVVHEKGMMAVGQSNHTSFFRPVKEGHVRAEAVRIHAGSTTWFWDVSLRDDAGRLCAVSSMSIAVRPRRD Helical structure MHRTSNGSHATGGNLPDVASHYPVAYEQTLDGTVGFVIDEMTPERATASVEVTDTLRQRWGLVHGGAYCALAEMLA TEATVAVVHEKGMMAVGQSNHTSFFRPVKEGHVRAEAVRIHAGSTTWFWDVSLRDDAGRLCAVSSMSIAVRPRRD

Beta strand and sheet structure MHRTSNGSHATGGNLPDVASHYPVAYEQTLDGTVGFVIDEMTPERATASVEVTDTLRQRWGLVHGGAYCALAEMLA TEATVAVVHEKGMMAVGQSNHTSFFRPVKEGHVRAEAVRIHAGSTTWFWDVSLRDDAGRLCAVSSMSIAVRPRRD

3D Protein Structure Protein Folding: Advances

• Homology Modeling / Comparative Modeling – The probe and template sequences are evolutionary related – Honig et al.; Sali et al.; Fischer et al.; Rost et al; • Fold Recognition / Threading – For the query sequence, determine closest matching structure from a library of known folds by scoring function – Skolnick et al.; Jones et al.; Bryant et al.; Xu et al.; Elber et al.; – Baker et al.; Rychlewski & Ginalski; Honig et al. • First Principles with Database Information – Secondary and/or tertiary information from databases/statistical methods – Levitt et al.; Baker et al.; Skolnick, Kolinski et al.; Friesner et al. • First Principles without Database Information – Physiochemical models with most general application – Scheraga et al.; Rose et al.; Floudas et al. Enhanced ASTRO-FOLD Helix Prediction -Detailed atomistic modeling -Simulations of local interactions (Free Energy Calculations)

β-sheet Prediction -Novel hydrophobic modeling -Predict list of optimal topologies (Combinatorial Optimization)

α proteins α / β proteins Interhelical Contacts Flexible Stems Loop Prediction -Maximize common residue pairs -Dihedral angle sampling -Rank-order list of topologies -Discard conformers by clustering (Novel Clustering Methodology) (MILP Optimization Model)

Derivation of Restraints -Dihedral angle restrictions -Cα−Cα distance constraints

Improved Distance Restraints -Iterative LP-based bound tightening approach

Tertiary Structure Prediction -Structural data from previous stages -Prediction via novel solution approach (Global Optimization and Torsional Angle Dynamics)

Force Field for High and Medium Resolution Decoys -Novel linear programming approach -Distinguishes high resolution structures (Large-scale linear programming) Structure Prediction- S824: Blind Test S824: 102 Residues (Professor Michael Hecht, Princeton University) No knowledge of secondary/tertiary structure Backbone variable restraints • α-helices: 5-21, 30-49, 56-75, 80-100 Distance restraints •Noβ sheet contacts •63lower and upper Cα-Cα for α-helices Klepeis, Floudas, Wei, Hecht, Proteins (2005) Tertiary Fold • Best Energy: -846.0 kcal/mol RMSD: 5.1 Å (Prediction:2003) S836 Lowest E vs. S836 (NMR-1): Blind Test S836: 102 Residues (Professor Michael Hecht, Princeton University) No knowledge of secondary/tertiary structure Lowest Energy: -1740 Kcal/mol RMSD: 2.84 A

1-4 1-2 2-3 3-4 Lowest RMSD: 2.39 A (Prediction:2006) S836 Lowest E vs. S836 (NMR 20 models)

1-4 1-2 2-3 3-4

Prediction: October 2006 Challenges and Opportunities • New/Improved Methods for Prediction of Helices • New/Improved Methods for Prediction of β-strands/β- sheet topologies • Loop Prediction (3-D) • Fixed stems (crystallography) • Flexible stems (first principles method) • Prediction of Disulfide Bridges • Force-field development for Fold Recognition • New/Improved Methods for Threading/Fold Recognition • Uncertainty in Force-fields • Packing of Helices in Globular Proteins • Prediction of Tertiary Interhelical Contacts in α and α/β proteins • Helical Membrane Proteins (e.g. GPCRs) • Improved prediction of Helical Sequences • Loop predictions • Packing of Helices in Lipid Bilayers • 3-D structure prediction De Novo Protein Design Define target template Design folded protein Backbone coordinates for N,Ca,C,O Which amino acid sequences will and possibly Ca-Cb vectors from PDB stabilize this target structure ?

Human β-Defensin-2 Full sequence design hbd-2 (PDB: 1fqq) Mayo et al.; Hellinga et al.; DeGrado et al; Saven et al.; Hecht et al. Challenges Combinatorial complexity -Backbone length : n In silico sequence selection -Amino acids per position : m Fold specificity mn possible sequences De Novo Protein Design Define target template Design folded protein Backbone coordinates for N,Ca,C,O Which amino acid sequences will and possibly Ca-Cb vectors from PDB stabilize this target structure ?

Human β-Defensin-2 Full sequence design hbd-2 (PDB: 1fqq) Mayo et al.; Hellinga et al.; DeGrado et al; Saven et al.; Hecht et al. Challenges Combinatorial complexity -Backbone length : n In silico sequence selection -Amino acids per position : m Fold validation/specificity mn possible sequences De Novo Protein Design Structure to Function Enhance Structural Stability

Enhance Functionality Combinatorial complexity • Backbone length : n • Amino acids per position : m mn possible sequences Multiplicity of sequences • How to determine most stable ? • How to determine most functional ? De Novo Protein Design Framework: Advances Klepeis, Floudas,Lambris & Morikis,JACS(2003); Klepeis et al., IECR(2004) Loose, Klepeis, Floudas, PROTEINS (2004); Fung, Rao, Floudas et al., JOCO (2005) Fung, Taylor, Floudas et al., OMS (2006) Sequence selection • Identify target template for desired fold; specify coordinates of backbone • Identify possible residue mutations •Introduce distance dependent pairwise potential based on Ca • Generate rank-ordered energetic list from mixed-integer linear (MILP) Fold Validation via Astro-Fold • Model selected sequences using flexible, detailed energetics •Employ global optimization for free system •Employ global optimization for system constrained to template •Calculate relative probability for structures similar to desired fold Compstatin Potent inhibitor of third component of complement with Dr. John Lambris Structural features (Univ. of Pennsylvania) and Dr. Dimitri Morikis • Cyclic, 13 residues (Univ. of California, Riverside) • Disulfide Bridge Cys2-Cys12 • Central beta-turn Gln5-Asp6-Trp7-Gly8 • Hydrophobic core • Acetylated form displays higher inhibitory activity

Functional features • Binds to and inactivates third component of complement • Structure of bound complex not yet available In Silico De Novo Design

Ac-compstatin Analog Ac-V4Y/H9A x7 x16 Analog Ac-W4Y/H9A x45 Klepeis, Floudas, Morikis, Tsokos, Argyropoulos, Spruce, Lambris (2003) J. American Chemical Society. Klepeis, Floudas, Morikis, Lambris (2004) Ind. & Eng. Chem. Res. Fung, Rao, Floudas (2005); Fung, Taylor, Floudas (2006) Challenges and Opportunities • Improved Methods for In Silico Sequence Selection with flexible templates from 2013 to 2050 to 20100 • Improved Force-field development for De Novo Protein Design • Simultaneous Sequence and Structure Selection • Design of Peptidic Inhibitors for Complement 3 • Design of novel human β-defensin • Discovery of novel GPCRs • De Novo Design of Medium-size Proteins • Map Sequences to Known Folds Proteomics: Peptide and Protein Identification via Tandem Mass Spectroscopy

Protein sample Protein identifications

l E ABC a x n p o e i Protein t r i a level m t u e p n Validation t m a o l

C Peptide grouping

Enzymatic ? digestion LKYVI STCMYAR DILNG

Peptide GAWKLK ILFADG level

Peptide Mixture Peptide Identifications Mixture separation MS-MS sequencing Validation Database search

MS-MS spectra level

MS-MS spectra Peptide & Protein Identification via Tandem MS

• Database-based methods • Correlate the experimental spectra with spectra of peptides/proteins which exist in the databases • De Novo Methods • Predict peptides without sequence databases • Exhaustive listing; sub-sequencing; graphical • Graph theory and shortest path algorithms • Graph theory and dynamic programming • Bayesian scoring of random peptides Novel Concept: use of mixed-integer linear optimization (MILP)MILP to solve the peptide sequencing problem

Key idea Utilization of binary variables to model logical decisions: 1 = yes; 0 = no

Selection of peaks (pi) Paths between peaks (wij) DeDe NovoNovo Framework:Framework: PILOTPILOT

Peptide identification via Integer Linear Optimization and Tandem mass spectrometry Challenges and Opportunities

• Develop a De Novo computational approach based on a novel Mixed-Integer Linear Optimization (MILP) framework for the peptide identification using only information of the ion peaks in the spectrum • Develop a hybrid method in combination with database methods • Develop a novel approach which will account for experiment uncertainty • Develop computational methods for protein identification • Develop approaches for predicting protein-protein interactions in a complex mixture of proteins using tandem MS/MS and protein cross-linking technology Process Operations: Scheduling & Planning (1996-)

Christodoulos A. Floudas Princeton University Process Operations: Scheduling & Planning How/When did we start? Suggestion of Prof. R.W.H. Sargent, Imperial College, Fall 1992.

Motivation: Are Continuous-Time Formulations Effective for Short-Term Scheduling? Initial Studies: 1996-98 Process and Product Operations: Scheduling, Planning & Uncertainty • Short-Term Scheduling: Unit-Specific Event-Based Continuous-Time Approach (98-) • Design, Synthesis & Scheduling (01-) • Medium-Term Scheduling (02-) • Reactive Scheduling (05-) • Scheduling with Resources (04-) • Scheduling under Uncertainty (04-) • Planning & Scheduling (05-) Process Operations: Scheduling • Given: – Production in terms of task sequences – Pieces of equipment and their ranges of capacities – Intermediate storage capacity – Production requirement – Time horizon under consideration • Determine: – Optimal sequence of tasks taking place in each unit – Amount of material processed at each time in each unit – Processing time of each task in each unit • so as to optimize a performance criterion, – Maximization of production, minimization of makespan, etc. Process Operations: Scheduling - Advances Floudas & Lin, (2004a): C&ChE; Floudas & Lin (2005): Annals of OR • From Discrete-Time to Continuous-Time Scheduling Approaches Global Event Based Models Unit-Specific Event Based Models – Significant reduction of binary variables (combinatorial complexity) – Better solutions & improved integrality gap – Address industrial case studies effectively • Short-term scheduling (days) • Medium-term scheduling (weeks) – Rolling horizon approaches – Decomposition methods • Periodic scheduling Short-Term, Medium-Term and Reactive Scheduling of an Industrial Polymer Compounding Plant Plant Data Description • Over 80 different products considered in time horizon (250 overall) • Over 85 orders in nominal schedule and over 65 orders added in reactive schedule • Basic operations: reaction, filtering, storage, filling •Units: reactors, filters, prill tower, swing and product tanks, filling stations – (85 units) • Scheduling horizon: ~ 2 weeks • Storage limitations on reactors and tanks • Campaign mode production for prill tower and associated units • Additional considerations: – Clean-up times for each unit switching between tasks – Demands with intermediate due dates – Different types of final products Process Alternatives: Polymer Compounding Plant

F Type 1 I1 Type 3 I2 Type 4b P Type 6 P

F Type 1 I1 Type 6 P

F Type 1 I1 Type 4a P Type 6 P

F Type 1 I1 Type 4b P Type 6 P

F Type 2 I1 Type 4a P Type 6 P

F Type 1 I1 Type 4a I2 Type 5 P Type 6 P

F Type 2 I1 Type 4a I2 Type 4a P Type 6 P State-Task Network (STN) Representation Mathematical Framework • Decompose the large and complex problem for a long time period into smaller short-term scheduling sub-problems in successive time horizons. • Decomposition determines each time horizon as well as the products to include based on: – Number of products with demands – Complexity of corresponding process recipes – Resulting computational complexity • Connection between consecutive time horizons: – Available starting time of units – Available intermediate materials Industrial Polymer Compounding Plant: Case Study 2

Dr. J. Kallrath, BASF Dr. A. Schreieck, BASF Stacy Janak • Campaign Mode Production determined first • Nominal and Reactive Scheduling performed • Time horizons considered: 18 days • Constraint to limit lateness of orders to be <= 24 hours Case 2: Nominal: Process Units (18 days) Case 2: Nominal: Storage Units (18 days) Case 2: Results Summary (18 days)

Extra Productio % Profit % Time n (tons) Increase Value Increase (hr.) Nominal 2323.191 202774.07 Demand 20.49 20.33 1848.11 Nominal Prod. 2799.119 244006.16 Reactive 2264.578 171556.64 Demand 35.41 41.14 1504.47 Reactive Prod. 3066.419 242128.48

• In both cases, production is increased significantly compared to the required demand. The value of the profit also increased compared to the value of the required demand. • In the reactive schedule, the overall demand has decreased compared to the nominal schedule, but the production and profit have increased. • The extra time is the total time available for additional production in all the reactors where blocks of time must be 11 hours or greater. Challenges/Opportunities

• Modeling to reduce/close the integrality gap • New/Improved Methods for Medium-term scheduling • Multi-site production scheduling • Reactive Scheduling • Scheduling under Uncertainty • Design/Synthesis and Scheduling under Uncertainty • Planning and Scheduling • Planning under Uncertainty • Validation/Application to Manufacturing Operations Acknowledgements Aristotle University of Thessaloniki Undergraduate Studies

Prof. V. Papageorgiou Prof. C. Georgakis Prof. S. Nychas Prof. M. Assael Prof. I. Vasalos Organic Chemistry Process Control Fluid Mechanics DiplomaThesis Petroleum Technologies

Prof. Bekiaroglou Prof. A. Karabelas Physical Chemistry Process Design Graduate Studies

How did it all start?

• Ph.D. Thesis: Sept. 82 – Dec. 85 •Advisor: Ignacio E. Grossmann

• Synthesis of Flexible Heat Exchanger Networks (82-85) • Uncertainty Analysis (82-85) Carnegie Mellon University Graduate Studies

Prof. I.E. Grossmann

Prof. L.T. Biegler Prof. K.O. Kortanek Prof. A.W. Westerberg

Prof. M. Jhon Prof. D. Prieve Prof. G. Powers Prof. P. Sides Prof. J.L. Anderson Princeton University Chemical Engineering Senior Theses

Jeff Wilke 5/89 A. Rojnuckarin 5/94 J. Bossert 5/96 Russell Allgor 5/88 C. Papouras 5/89 Navin Nayak 5/96

T. Hene 5/97 Duncan Rein 5/97 M.Ow 5/98 M. Matz 5/98 C. Gaffney 5/99 B.Mickus 5/2003

Michael Pieja 5/01 Christopher R. Loose 5/02 David R. Volk 5/02 Jared Jensen 5/03 Sasha Rao 5/04

Ralph Kleiner 5/05 Marty Taylor 5/05 Huan Zheng 5/05 Paul Reiter 5/05 Rachel Hoff 5/05 Cole DeForest May 2006 Chemical Engineering Senior Theses with Scholarly Publications

Jeff Wilke 5/89 A. Rojnuckarin 5/94 J. Bossert 5/96 Russell Allgor 5/88 C. Papouras 5/89 Navin Nayak 5/96

Duncan Rein 5/97 T. Hene 5/97 M.Ow 5/98 M. Matz 5/98 C. Gaffney 5/99 B.Mickus 8/2000-5/2003

Christopher R. Loose 5/02 David R. Volk 5/02 Michael Pieja 5/01 Jared Jensen 5/03 Sasha Rao 5/04

Huan Zheng 9/02-5/05 Rachel Hoff 5/05 Ralph Kleiner 9/02-5/05 Marty Taylor 5/05 Paul Reiter 5/05 Cole DeForest May 2006 Princeton University – CASL Graduate Students

G.E. PaulesA.R. Ciric A. Aggarwal A.C. Kokossis P. Psarris M.L. Luyben V. Visweswaran

C.M. McDonald C.D. Maranas V. Hatzimanikatis C.S. Adjiman C.A. Schweiger S.T. Harding W.R. Esposito J.L. Klepeis

H.D. Schafroth X. Lin Z.H. Gumus C.A. Meyer S.L. Janak S.R. McAllister

H.K. Fung C.E. Gounaris R. Rajgaria P.A. DiMaggio M.P. Tan P. Verderame Princeton University - CASL Post-doctoral Associates

A. Georgiou (88-90) V. Vassilliadis (93-94) I.P. Androulakis (93-96) M.G. Ierapetritou (96-98)

S. Caratzoulas (01-02) J.L. Klepeis (02-03) K.M. Westerberg (97-02)

I.G. Akrotirianakis (01-04) M.A. Shaik (05-present) M. Monnigmann (04-05) Research Collaborators

Prof. J.R. Broach Prof. M. Hecht Prof. H.Th. Jongen Prof. J.D. Lambris Prof. D. Morikis Prof. A. Neumaier Prof. P.M. Pardalos Princeton University Princeton University RTWH Aachen Univ. Pennsylvania UC at Riverside Univ. Vienna Univ. Florida

Prof. E.N. Pistikopoulos Prof. H. Rabitz Prof. R. Siliciano Prof. O. Stein Prof. J. Wei Prof. H.A. Weinstein Imperial College Princeton University Johns Hopkins Univ. RTWH Aachen Princeton University Cornell Medical School Princeton CHE Colleagues

Prof. P.G. Debenedetti Prof. R. Jackson Prof. I.A. Aksay Prof. J.B. Benziger Prof. I.G. Kevrekidis Prof. A.Z. Panagiotopoulos Prof. R.K.Prud’homme

Prof. R.A. Register Prof. D.A. Saville Prof. W.R. Schowalter Prof. S.Y. Shvartsman Prof. S. Sundaresan Prof. T.K. Vanderlick Prof. J. Wei

Prof. J.D. Carbeck Prof. W.B. Russel Prof. S.M. Troian Prof. D.W. Wood Funding

• National Science • Mobil Foundation •Eastman •Amoco • National Institutes of • E.I. Du Pont Nemours Health • Shell Laboratorium • Air Force Office of • ExxonMobil Scientific Research • General Motors • Environmental • Delphi Protection Agency • Arkema (Atofina) • AspenTech • BASF