Organization and Order - WordPress.com · Biopolymer building blocks Metabolism, transport, regulation, … Wealth of physical, chemical, structural data 60K 3-D folded structures

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Organization and Order0

Organization and Order

30 October 2009

Alan [email protected]

USC Computer Science Colloquium

This briefing and related work available athttp://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 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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One Organism

1014 Cells

10-9 cal/deg

1022 Polymers

0.6 cal/deg

1025 Monomers

401 cal/deg

Organization Is Not OrderIntroduction

∆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 acids201025proteins400 cal/K from protein and 1 cal/K from nucleic acids

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Organization Is Functional

“By thermodynamic criteria a biological system is notmore ordered than a rock of the same weight.”

L. Blumenfeld1

“When we talk about a ‘well-organized’ system–whetheran organism, a business, a team, or a personal life–weare referring to how effectively it caries out certainactivities, rather than to specific structural factorsinternal 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 scientificexplanation of organization

What are functional models and how do they relate tostructural models?

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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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NaturalSystem

FormalSystem

Encoding

DecodingC

ause Infer

Modeling

Rosen’s Modeling Relation

The Worldor

Out There

The Modelor

In Here

To the extent that we are closing the loop between formaland natural systems we are doing science

Encode perceptions (measurements) into symbols in amath 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,

objective world of phenomena, and the internal, subjectiveworld of the self, which perceives, organizes, acts, andunderstands.” R. Rosen5

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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 howdoes 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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Functional Components

Functional Architecture

Modeling

Functional Models Explain Top Down

A

BC

f

gD

q

h

Mappings

Chloroplast

f:A B

System

Component

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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Lessons From System Engineering2

Practical

RequirementsAnalysis

FunctionalAnalysis

DesignSynthesis

DesignLoop

RequirementsLoop

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

otherwise intractable problems

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Function, Structure on an Even FootingPractical

Nature

Top DownDescribe Class of

Systems

Bottom UpChoose 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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Application

Why Protein Folding?

IVGGYTCGANTVPYQVSLNSGYHFCGGSLINSQWVVSAAHCYKSGIQVRLGEDNINVVEGNEQFISASKSIVHPSYNSNTLNNDIMLIKLKSAASLNSRVASISLPTSCASAGTQCLISGWGNTKSSGTSYPDVLKCLKAPILSDSSCKSAYPGQITSNMFCAGYLEGGKDSCQGDSGGPVVCSGKLQGIVSWGSGCAQKNKPGVYTKVCNYVSWIKQTIASN

•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 offgenomes

Bovine Trypsin: 223 Amino Acids, 11 peptide inhibitor, Caion, 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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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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Evolution of Template MatchingApplication

Sequence matching Related evolutionary sequences

Local structure matching Treat local structures as rigid units

Threading Local structure motifs or folds

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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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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 Nuclearage and Space age technical problems

Can a new methodology grow out of SE in responseto synthetic biology and other complex eco/bioproblems?

Proteomics asks how the proteins in a pathway, organelle,organism 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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References

1. Blumenfeld L. (1981) Problems of Biological Physics. Berlin, New York:Springer-Verlag.

2. Defense Acquisition University (2005) Systems Engineering FundamentalsJanuary 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, 2009http://www.rcsb.org/pdb/statistics/contentGrowthChart.do?content=total&seqid=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: extendingthe 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 couldbe 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.html

Chloroplasthttp://research.nmsu.edu/molbio/bioinfo/tutorials/clip_art/index.htmlhttp://www.nrc-cnrc.gc.ca/eng/education/biology/gallery/chloroplast.html

Bovine Trypsin Figureshttp://www.proteopedia.org/wiki/index.php/1ox1

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

Lorenz Attractorhttp://en.wikipedia.org/wiki/Lorenz_attractor

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Carlson’s LawBack Up

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Bovine Trypsin 10x1

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

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