Organization and Order USC Computer Science Colloquium 30 October - - PDF document

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Organization and Order

Organization and Order

30 October 2009

Alan Levin

ailevin@ix.netcom.com

USC Computer Science Colloquium

This briefing and related work available at http://ailevin.wordpress.com/ Agenda

• Introduction: Organization and how we model it
• Functional and structural modeling contexts
• Modeling: Rosen’s modeling relation and scientific models
• Bottom up and top down explanation
• Practical: Applying lessons from system engineering
• Structure and function on an even footing
• Application: Protein folding
• Progress predicting 3-D folding from sequence
• Conclusion

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Organization and Order 1

Organization Familiar, Not Well Explained

Organ Systems Ribosome Bacteria Flocking Birds

Introduction

• We see organization from molecular to ecosystem
• Defining biological characteristic
• Objective empirical data
• Used for classification categorization
• Explanations
• Self-organization, dissipative structures, bifurcation,

catastrophe, chaos, complexity theories

• Emergence: underlying models don’t predict it, or the

modelers didn’t expect it

• Order and organization often used synonymously
• Both seem to refer to pattern, regularity, symmetry
• Unfortunately this causes confusion

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Organization and Order 2

One Organism 1014 Cells 10-9 cal/deg 1022 Polymers 0.6 cal/deg 1025 Monomers 401 cal/deg

Organization Is Not Order

Introduction

∆S = klnW

• Almost all of the ∆S is in forming the polymers
• Any 1014 cells have entropy of a person
• All the entropy is in forming the polymers
• The ∆S for boiling a cup of water is 343 cal/K
• Organization is not the same as order
• We throw away what we want to study in studying the

molecular level

• Studying organization structurally leads to confusion
• Calculation
• 75kg person -->10 kg amino acids,120 g nucleotides
• k is 3.3 x 10-24 calories per degree Kelvin (cal/K)
• 1023 nucleotides and 1025 amino acids

41023 nucleic acids 201025proteins 400 cal/K from protein and 1 cal/K from nucleic acids

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Organization and Order 3

Organization Is Functional

“By thermodynamic criteria a biological system is not more ordered than a rock of the same weight.”

• L. Blumenfeld1

“When we talk about a ‘well-organized’ system–whether an organism, a business, a team, or a personal life–we are referring to how effectively it caries out certain activities, rather than to specific structural factors internal to the system.”

• J. Wicken6

Introduction

• Entropy analysis of organism very dissatisfying
• Nothing wrong with thermodynamics, but we are

asking the wrong sort of question

• A system at equilibrium may be orderly or disorderly

but it cannot be organized since it can’t do anything

• We need more than structural modeling for a scientific

explanation of organization

• What are functional models and how do they relate to

structural models?

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Organization and Order 4

How Do Function And Structure Relate?

• Modeling
• What kinds of explanations do the models provide?
• Rosen’s modeling relation
• Practical
• What kinds of modeling methods are available?
• System engineering process
• Application
• How can both models be applied to the same problem?
• Protein folding example

Introduction

• Models are about questions and answers
• Rosen was a controversial theoretical biologist
• Consider underlying assumptions of scientific models
• Also relates to measurements and prediction
• System engineering is critical to interpreting Rosen
• Practical experience separating function, structure

and reintegrating

• Many useful analogies in role of architecture
• This also provides underpinning for SE indicating

possible extensions of SE methods

• Protein folding
• “Simple” functional biological system
• Really just to test the concepts

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Organization and Order 5

Natural System Formal System Encoding Decoding Cause Infer

Modeling

Rosen’s Modeling Relation

The World

• r

Out There The Model

• r

In Here

• To the extent that we are closing the loop between formal

and natural systems we are doing science

• Encode perceptions (measurements) into symbols in a

math model

• Decode prediction from inferences in math model
• Relate inferential chain in the math to causal chain in

the world

• Encoding/decoding bridge “out there” and “in here,” and we

impute things to nature

• Laws, state spaces, abstract system spaces
• We pretend that nature is something with a

mathematical domain and range, but it’s not there

• ”Science, in fact, requires both; it requires an external,
• bjective world of phenomena, and the internal, subjective

world of the self, which perceives, organizes, acts, and understands.” R. Rosen5

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Organization and Order 6

Structural Models Explain Bottom Up

Differential Equations State Space Trajectories

Modeling

dx dt = (y x) dy dt = x( z) y dz dt = xy z

Benard Cells Fluid Element Pieces

• Structural Question: What is this system made of and how

does it work?

• Answer: The pieces are incompressible fluid elements;

system DE explains system dynamics

• System inherits state space, DE from the pieces
• Different systems modeled by the same pieces
• Synthesis: choose pieces and build system model
• Agnostic to what the system does: no function
• Trajectories in state space are inference loop
• Lorenz attractor
• 2-D fluid flow with imposed temperature difference
• State variables are not physical coordinates
• Deterministic and chaotic depending on parameters
• http://mathworld.wolfram.com/LorenzAttractor.html

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Organization and Order 7

Functional Components Functional Architecture

Modeling

Functional Models Explain Top Down

A B C f g D q h

Mappings Chloroplast

f:A B

System

C

• m

p

• n

e n t

• What does this system do and how is it organized?
• Behavior and organization are explained by how

components cooperate (functional architecture)

• Components inherit function from system context
• Component is the atom of functional model
• Defined by mapping: constitutive, domain: influence

by system, range: influence on system

• Mappings can also be in domain/range e.g q
• Very different systems modeled by the same

architecture and have a similar organization

• Analysis: Study system behaviors to choose components
• Agnostic to what the system is made of: no stuff
• Inference loop is path through functional architecture
• This functional architecture has nothing to do with

chloroplasts

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Organization and Order 8

Lessons From System Engineering2

Practical

Requirements Analysis Functional Analysis Design Synthesis Design Loop Requirements Loop System

• Implementation

Operational

• Need
• Requirements loop is functional modeling
• Requirements analysis corresponds to encoding

functional observables and examining linkages

• Requirements describe system behaviors
• Functional analysis creates, refines functional

architecture

• Design loop is a metaphor for structural modeling
• Architecture covers many possible implementations
• Design synthesis does trade studies
• Requirements constrain specific implementation
• Separating function and implementation is one of the

great powers of system engineering

• Trade studies, prototypes divide and conquer
• therwise intractable problems

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Organization and Order 9

Function, Structure on an Even Footing

Practical

Nature

Top Down Describe Class of Systems Bottom Up Choose Specific System

?

• Structure constrains function
• Synthesize a structural model and analyze the

model’s dynamics looking for organized behavior

• Scientists call this emergence
• Function constrains structure
• Analyze a functional model and synthesize the

model’s components looking for structural dynamics

• System engineers call this a trade study
• Crucial to decode and encode between models
• Functional first if more interested in organization and you

think whole is more than sum of parts

• Structural first if more interested in composition and you

think whole is merely sum of parts

• Why do we study emergence in Lorenz attractor rather

than organization in convective flow?

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Organization and Order 10 Application

Why Protein Folding?

IVGGYTCGANTVPYQVSLN SGYHFCGGSLINSQWVVSA AHCYKSGIQVRLGEDNINV VEGNEQFISASKSIVHPSY NSNTLNNDIMLIKLKSAAS LNSRVASISLPTSCASAGT QCLISGWGNTKSSGTSYPD VLKCLKAPILSDSSCKSAY PGQITSNMFCAGYLEGGKD SCQGDSGGPVVCSGKLQGI VSWGSGCAQKNKPGVYTKV CNYVSWIKQTIASN

• Protein Sequence
• 3-D Folded Protein
• Folded proteins are ubiquitous functional components
• Biopolymer building blocks
• Metabolism, transport, regulation, …
• Wealth of physical, chemical, structural data
• 60K 3-D folded structures in Protein Data Bank4
• Many more protein sequences can be read off

genomes

• Bovine Trypsin: 223 Amino Acids, 11 peptide inhibitor, Ca

ion, 141 waters C gray, N blue, O red, S yellow

• Note tight 3-D structure
• Soluble proteins surprisingly dense
• Cartoon shows local helical, pleated sheet structures
• Local structures folded back on one another and

stabilized by disulfides and hiding “oily” side chains

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Organization and Order 11

Biennial Protein Folding Competition7

• Started with purely structural modeling
• Best models today use templates from Protein Data Bank
• With reasonable template, model is very good
• Structural heuristics optimize from template starting point
• Often the correct template is not found
• Purely structural models must be used
• Results are much poorer

Application

• Structural model pieces are amino acids
• Constitutive parameters: side chain
• Variable parameters: alpha carbon angles at least
• From sequence to folded 3-D structure
• Seemed straight forward 50 years ago, but…
• Many degrees of freedom, complex dynamics, solvent
• Small energy differences between folded states
• 223 amino acids gives 3223 = 10106 conformations
• From physical chemistry to bio-informatic heuristics
• With reasonable template, model is very good
• Structural studies now drive template heuristics

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Organization and Order 12

Evolution of Template Matching

Application

• Sequence matching
• Related evolutionary sequences
• Local structure matching
• Treat local structures as rigid units
• Threading
• Local structure motifs or folds

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Organization and Order 13

Why Does Threading Work So Well?

• Threading greatly constrains structural modeling
• Protein conformation space is extremely large
• The fold space in Protein Data Bank is surprisingly small8
• Why is the fold space so small?
• Sequence variation must leave function close to wild type
• Naturally occurring folds constrained by evolutionary history
• Threading literally works from function to structure
• Theading: “Can this sequence perform template functions?”
• Protein Data Bank fold space is evolved biological function

Application

• For 223 amino acids estimate 3223 = 10106 conformations
• Only three alpha carbon angles per position
• Particles in universe 1080 ?
• Part of why problem is hard bottom up
• Fold space in PDB seems to be several thousand families
• Evolution is inherently constrained functionally
• Always working from an existing functional context
• Helpful or harmful depends on organism, environment
• Exploring possibility near existing functional success

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Organization and Order 14

Conclusion

• System engineering provides powerful insights to science
• Functional analysis and system architecture methods
• Interplay of function and structure to extend science
• Well suited to tasks of proteomics, synthetic biology, bio/eco

technical challenges

• Function constrains intractable structural problems
• Recent progress in protein modeling demonstrates this
• Critical in synthetic biology, other complex problems
• Organization is functional, order is structural
• We demystify emergence simply by explaining it functionally
• Function and structure are complementary, neither is more

physical nor more empirical

• Organization must be measured by functional metrics
• SE in some sense grew out of OR in response to Nuclear

age and Space age technical problems

• Can a new methodology grow out of SE in response

to synthetic biology and other complex eco/bio problems?

• Proteomics asks how the proteins in a pathway, organelle,
• rganism cooperate
• This is a functional question
• State space grows like number of pieces factorial
• Order and organization metrics
• Entropy, information important in science, engineering
• Stat Mech links entropy and structural information
• Similar functional metric for functional information
• Organization and order subtlety interdependent
• Order limits maximal organization and organization

limits minimal order

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Organization and Order 15

References

1. Blumenfeld L. (1981) Problems of Biological Physics. Berlin, New York: Springer-Verlag. 2. Defense Acquisition University (2005) Systems Engineering Fundamentals January 2001. Fort Belvoir, VA 3. Levin, A. (2009) A Top-Down Approach to a Complex Natural System: Protein Folding. Axiomathes. DOI: 10.1007/s10516-009-9093-0. 4. RCSB Protein Data Bank. Cited October 6, 2009 http://www.rcsb.org/pdb/statistics/contentGrowthChart.do?content=total&se qid=100 5. Rosen, R. (1991) Life Itself : a comprehensive inquiry into the nature, origin, and fabrication of life. New York: Columbia University Press. 6. Wicken, J. (1987) Evolution, Thermodynamics, and Information: extending the Darwinian program. New York: Oxford University Press. 7. Zhang, Y. (2008) Progress and Challenges in Protein Structure Prediction. Current Opinion in Structural Biology, 18(3), 342-348. 8. Zhang, Y, Skolnick J (2005)The protein structure prediction problem could be solved using the current PDB library. PNAS USA 102(4):1029-1034

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Photo Credits

• Benard Cells

http://www.catea.gatech.edu/grade/mecheng/mod8/mod8.h tml

• Chloroplast

http://research.nmsu.edu/molbio/bioinfo/tutorials/clip_art/in dex.html http://www.nrc- cnrc.gc.ca/eng/education/biology/gallery/chloroplast.html

• Bovine Trypsin Figures

http://www.proteopedia.org/wiki/index.php/1ox1

• Monomers

http://www.coolschool.ca/lor/BI12/unit2/U02L02/AminoAcid .jpg

• Lorenz Attractor

http://en.wikipedia.org/wiki/Lorenz_attractor

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Organization and Order 16

Carlson’s Law

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Organization and Order 17

Bovine Trypsin 10x1

http://www.proteopedia.org/wiki/index.php/1ox1

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