Organization and Order USC Computer Science Colloquium 30 October 2009 Alan Levin ailevin@ix.netcom.com 0 Organization and Order 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 1
Introduction Organization Familiar, Not Well Explained Ribosome Bacteria Organ Systems Flocking Birds 1 Organization and Order 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 2
Introduction Organization Is Not Order 10 -9 cal/deg 0.6 cal/deg One Organism 10 14 Cells 401 cal/deg 10 22 Polymers 10 25 Monomers ∆ S = klnW 2 Organization and Order Almost all of the ∆ S is in forming the polymers Any 10 14 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) 10 23 nucleotides and 10 25 amino acids 4 1023 nucleic acids 20 1025 proteins 400 cal/K from protein and 1 cal/K from nucleic acids 3
Introduction Organization Is Functional “By thermodynamic criteria a biological system is not more ordered than a rock of the same weight.” L. Blumenfeld 1 “ 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. Wicken 6 3 Organization and Order 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? 4
Introduction 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 4 Organization and Order 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 5
Modeling Rosen’s Modeling Relation The World or Out There Decoding Cause Natural Formal Infer System System Encoding The Model or In Here 5 Organization and Order 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, objective world of phenomena, and the internal, subjective world of the self, which perceives, organizes, acts, and understands.” R. Rosen 5 6
Modeling Structural Models Explain Bottom Up dx dt = � ( y � x ) dy dt = x ( � � z ) � y dz dt = xy � � z Fluid Element Pieces Differential Equations Benard Cells State Space Trajectories 6 Organization and Order 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 7
Modeling Functional Models Explain Top Down C o m p f:A B o n e n t System Functional Components Mappings q A f C D h B g Chloroplast Functional Architecture 7 Organization and Order 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 8
Practical Lessons From System Engineering 2 Operational Requirements •Need Analysis Requirements Loop Functional Analysis Design Loop Design System Synthesis •Implementation 8 Organization and Order 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 9
Practical Function, Structure on an Even Footing Top Down Describe Class of Systems Nature ? Bottom Up Choose Specific System 9 Organization and Order 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? 10
Application Why Protein Folding? •Protein Sequence •3-D Folded Protein IVGGYTCGANTVPYQVSLN SGYHFCGGSLINSQWVVSA AHCYKSGIQVRLGEDNINV VEGNEQFISASKSIVHPSY NSNTLNNDIMLIKLKSAAS LNSRVASISLPTSCASAGT QCLISGWGNTKSSGTSYPD VLKCLKAPILSDSSCKSAY PGQITSNMFCAGYLEGGKD SCQGDSGGPVVCSGKLQGI VSWGSGCAQKNKPGVYTKV CNYVSWIKQTIASN 10 Organization and Order 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 Bank 4 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 11
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