Mathematical Modeling at Amgen: A Systematic Approach

1
Mathematical Modeling at Amgen A Systematic
Approach

• David Balaban, Mike Toupikov, Mark Durst, and
  others from
• Systems Informatics (SI)
• February 12, 2014

2
Roadmap

• Modeling principles
• Models along the Commercialization Path
• Discovery
• Testing
• Manufacturing
• Models of the Commercialization Path
• Economic Process Models
• Capacity Management
• Modeling Patterns
• Conclusion

3
Formal Systems Can Describe Parts of Natural
Systems Under Limited Conditions
4
Newtons Laws Predict Projectile Motion
5
Difference Equations Approximate Differential
Equations
6
Computer Programs Are the Formal Systems That
Make Predictions Practical
7
Creation of Complex Models Requires
Multi-disciplinary Cooperation
Applied Mathematician
Computer Scientist
Scientist
8
The Differential Equations Can Be Refined to
Create a More Accurate Prediction
9
The Discrete Approximation Can Also Be Improved
10
A New Possibly Better Simulation Can Be Created
11
Three Very Different Natural Systems Will be
Described
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They Are Each Described by a Different Equation
13
All the Equations Are of the Same Form the
Natural Systems are Analogous
14
Modeling Provides Benefits Along the
Commercialization Path
15
Discovery

• Screening
• Protein
• Cellular
• Mechanism of action
• Reaction system

16
Robust Regression Automatically Manages Noisy
Dose Response Data

• M-estimation
• Current regression technique after manual
  editing

17
Dose Response Curves Have a Unique Non-heuristic
Representation in Scale Space
18
Scale Space Representations Classify Does
Response Curves
19
Chemical Networks at Equilibrium Can Model
Complex Ligand Binding
20
Mathematical and Computational Representations
Generate Predictions
21
More Complex Networks May Require More Complex
Mathematical Representations
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Testing

• In vitro
• In vivo
• Cellular assays
• Animal tests
• In clinical trials
• Measurement
• Design

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A Sequence of Models Drives Large Molecule Drug
Discovery First In Vitro With Mouse Proteins and
Cells
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A Sequence of Models Drives Large Molecule Drug
Discovery Then In Vivo With Mice
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The Same Sequence is Then Applied In Vitro To
Monkey and Human Proteins and Cells
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Then In Vivo To Monkeys and Humans
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All the Previous Models Can Be Grouped to
Distinguish Human Experimentation
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Human Trials Must Always Be Done. In Vitro and
Animal Studies Insufficient
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Clinical Studies Describe Population Effects
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PK Model Predicts Drug Concentration in Plasma
SC injection site
ka
kcp
Central V2
Peripheral V3
kpc
Elimination k
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PKPD Model Describes Responses of Physiological
Systems
32
Population PKPD Explains Differences in Response
Among Individuals
33
Trial Simulations Test Clinical Trial Designs
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Manufacturing

• Equipment
• Production
• Formulation / storage
• Process economics

35
Simulation Helps Establish Device Equivalence
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Complex Bioreactor Simulations Starts With
Simpler Parts
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Complex Bioreactor Simulations Starts With
Simpler Parts
CO2 reacts with water to form HCO3-
CO2 and O2 are sparged for pH and pO2 control
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Creating the Full Simulation Presents Many
Technical Challenges

• Fluid Flow / Mixing
• Bubble gas exchange
• Cell growth and chemistry
• Temperature control
• . . .

39
Model Successfully Predicted the CO2 Response in
Production Bioreactors under Current Agitation
Conditions
40
Protein Denaturation Can Be Described By a System
of Differential Equations
41
Accelerated Stress Testing Determines Parameters
Needed to Predict Shelf Life
42
The Commercialization Path Itself Can Be Modeled
43
Process and Unit Operation Simulators are Core to
Economic Process Models
44
Key Predictions Are Produced by the Inventory
Management Simulator
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These Key Predictions Require Cost Functions
Based on More Complex Models
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Capacity Models Can be Built for Research and
Preclinical Development
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Modeling Patterns

• Individual / population
• Forward / reverse
• Desired behaviors preserved functorially

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Individual Patterns

• Formal systems can mirror natural systems
• Can be created for many natural systems
• Correspondence holds for limited range of
  conditions
• No universal models
• Analogous natural systems can share behaviors
• Enabled by common formal model
• e.g. adsorption and binding
• Scaled up systems are analogous.
• The common formal model is dimensionless
• Dimensionless groups crystallize important
  behavior
• e.g. tumor morphology
• Forward/Reverse models drive quantitative science
• e.g. curve fitting, experimental design

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Group Patterns

• Individual/Group models describe populations
• Cellular assays individual vs groups of cells
• Clinical trials individual vs groups of
  patients
• Statistical focus
• Related collections of models describe scientific
  strategies.
• Capture hierarchical complexity
• e.g. PKDM, drug discovery

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Different Aspects of the Model Require Different
Mathematical Approaches
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Many Scientific Problems Combine Forward and
Reverse Formal Systems
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Rigorous Requirements Traceability Can Guarantee
that Good Behavior is Preserved
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Domain Experts Working with Mathematical Modelers
Improve Quality and Efficiency at Amgen

• Reveal commonalities between problems and provide
  new solution strategies.
• Facilitate scientific insight.
• Identify new technology options.
• Improve product and process quality.
• Reduce labor intensive activities.
• Predict and avoid capacity crunches.

54
Acknowledgements
Staff Member Degree Area of Expertise
Sunil Dalal PhD, Biomedical Eng Biophysics, state space modeling
Mark Durst (Group Leader) PhD, Mathematics Modern Statistics, mathematical modeling
Zhiwu Fang PhD, Mechanical Eng Computational fluid dynamics, porous media flow
Igor Fomenko PhD, Applied Math Stochastic differential equations, multi-scale problems
Gilles Gnacadja PhD, Math Algebra, optimization
Alexander Gorlin PhD, Math (AI) Discrete modeling, combinatorial algorithms
Darrell Lewis-Sandy BS, Chemical Eng Process engineering, fluid mechanics
Graham Mathews PhD Math Discrete event simulation, functional programming
Alexander Shoshitaishvili PhD, Math Catastrophe theory, anticipatory systems
Mikhail Toupikov PhDs, Elec Eng, Applied Math Wavelets, large scale simulation
Jian Zhang PhD, Computational Physics Physics, parallel algorithms
David Balaban PhD, Mathematics Functional programming, automatic programming, category theory
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END
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Tumor Growth Can be Modeled as Incompressible
Fluid Flow
John Lowengrub Dept Math, UCI
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Dimensionless Groups Determine Tumor Morphology
Apoptosis vs. mitosis
Necrosis
Mitosis vs. relaxation
Necrosis vs. Mitosis