Relational Systems Theory: An approach to complexity

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Relational Systems Theory An approach to
complexity

• Donald C. Mikulecky
• Professor Emeritus and Senior Fellow
• The Center for the Study of Biological Complexity

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MY SORCES

• AHARON KATZIR-KATCHALSKY (died in massacre in Lod
  Airport 1972)
• LEONARDO PEUSNER (alive and well in Argentina)
• ROBERT ROSEN (died December 29, 1998)

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ROUGH OUTLINE OF TALK

• ROSENS COMPLEXITY
• NETWORKS IN NATURE
• THERMODYNAMICS OF OPEN SYSTEMS
• THERMODYNAMIC NETWORKS
• RELATIONAL NETWORKS
• LIFE ITSELF

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COMPLEXITY

• REQUIRES A CIRCLE OF IDEAS AND METHODS THAT
  DEPART RADICALLY FROM THOSE TAKEN AS AXIOMATIC
  FOR THE PAST 300 YEARS
• OUR CURRENT SYSTEMS THEORY, INCLUDING ALL THAT IS
  TAKEN FROM PHYSICS OR PHYSICAL SCIENCE, DEALS
  EXCLUSIVELY WITH SIMPLE SYSTEMS OR MECHANISMS
• COMPLEX AND SIMPLE SYSTEMS ARE DISJOINT
  CATEGORIES

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CAN WE DEFINE COMPLEXITY?

• Complexity is the property of a real world
  system that is manifest in the inability of any
  one formalism being adequate to capture all its
  properties. It requires that we find distinctly
  different ways of interacting with systems.
  Distinctly different in the sense that when we
  make successful models, the formal systems needed
  to describe each distinct aspect are NOT
• derivable from each other

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COMPLEX SYSTEMS VS SIMPLE MECHANISMS

• SIMPLE
• LARGEST MODEL
• WHOLE IS SUM OF PARTS
• CAUSAL RELATIONS DISTINCT
• N0N-GENERIC
• ANALYTIC SYNTHETIC
• FRAGMENTABLE
• COMPUTABLE
• FORMAL SYSTEM

• COMPLEX
• NO LARGEST MODEL
• WHOLE MORE THAN SUM OF PARTS
• CAUSAL RELATIONS RICH AND INTERTWINED
• GENERIC
• ANALYTIC ? SYNTHETIC
• NON-FRAGMENTABLE
• NON-COMPUTABLE
• REAL WORLD

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COMPLEXITY VS COMPLICATION

• Von NEUMAN THOUGHT THAT A CRITICAL LEVEL OF
  SYSTEM SIZE WOULD TRIGGER THE ONSET OF
  COMPLEXITY (REALLY COMPLICATION)
• COMPLEXITY IS MORE A FUNCTION OF SYSTEM QUALITIES
  RATHER THAN SIZE
• COMPLEXITY RESULTS FROM BIFURCATIONS -NOT IN THE
  DYNAMICS, BUT IN THE DESCRIPTION!
• THUS COMPLEX SYSTEMS REQUIRE THAT THEY BE ENCODED
  INTO MORE THAN ONE FORMAL SYSTEM IN ORDER TO BE
  MORE COMPLETELY UNDERSTOOD

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THERMODYNAMICS OF OPEN SYSTEMS

• THE NATURE OF THERMODYNAMIC REASONING
• HOW CAN LIFE FIGHT ENTROPY?
• WHAT ARE THERMODYNAMIC NETWORKS?

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THE NATURE OF THERMODYNAMIC REASONING

• THERMODYNAMICS IS ABOUT THOSE PROPERTIES OF
  SYSTEMS WHICH ARE TRUE INDEPENDENT OF MECHANISM
• THEREFORE WE CAN NOT LEARN TO DISTINGUISH
  MECHANISMS BY THERMODYNAMIC REASONING

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SOME CONSEQUENCES

• REDUCTIONISM DID SERIOUS DAMAGE TO THERMODYNAMICS
• THERMODYNAMICS IS MORE IN HARMONY WITH
  TOPOLOGICAL MATHEMATICS THAN IT IS WITH
  ANALYTICAL MATHEMATICS
• THUS TOPOLOGY AND NOT MOLECULAR STATISTICS IS THE
  FUNDAMENTAL TOOL

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EXAMPLES

• CAROTHEODRYS PROOF OF THE SECOND LAW OF
  THERMODYNAMICS
• THE PROOF OF TELLEGENS THEOREM AND THE
  QUASI-POWER THEOREM
• THE PROOF OF ONSAGERS RECIPROCITY THEOREM

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HOW CAN LIFE FIGHT ENTROPY?

• DISSIPATION AND THE SECOND LAW OF THERMODYNAMICS
• PHENOMENOLOGICAL DESCRIPTION OF A SYTEM
• COUPLED PROCESSES
• STATIONARY STATES AWAY FROM EQUILIBRIUM

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DISSIPATION AND THE SECOND LAW OF THERMODYNAMICS

• ENTROPY MUST INCREASE IN A REAL PROCESS
• IN A CLOSED SYSTEM THIS MEANS IT WILL ALWAYS GO
  TO EQUILIBRIUM
• LIVING SYSTEMS ARE CLEARLY SELF - ORGANIZING
  SYSTEMS
• HOW DO THEY REMAIN CONSISTENT WITH THIS LAW?

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PHENOMENOLOGICAL DESCRIPTION OF A SYTEM

• WE CHOSE TO LOOK AT FLOWS THROUGH A STRUCTURE
  AND DIFFERENCES ACROSS THAT STRUCTURE (DRIVING
  FORCES)
• EXAMPLES ARE DIFFUSION, BULK FLOW, CURRENT FLOW

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NETWORKS IN NATURE

• NATURE EDITORIAL VOL 234, DECEMBER 17, 1971,
  pp380-381
• KATCHALSKY AND HIS COLLEAGUES SHOW, WITH
  EXAMPLES FROM MEMBRANE SYSTEMS, HOW THE
  TECHNIQUES DEVELOPED IN ENGINEERING SYSTEMS MIGHT
  BE APPLIED TO THE EXTREMELY HIGHLY CONNECTED AND
  INHOMOGENEOUS PATTERNS OF FORCES AND FLUXES WHICH
  ARE CHARACTERISTIC OF CELL BIOLOGY

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A GENERALISATION FOR ALL LINEAR FLOW PROCESSES
FLOW CONDUCTANCE x FORCE FORCE RESISTANCE x
FLOW CONDUCTANCE 1/RESISTANCE
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A SUMMARY OF ALL LINEAR FLOW PROCESSES
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COUPLED PROCESSES

• KEDEM AND KATCHALSKY, LATE 1950S
• J1 L11 X1 L12 X2
• J2 L21 X1 L22 X2

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STATIONARY STATES AWAY FROM EQUILIBRIUMAND THE
SECOND LAW OF THERMODYNAMICS

• T Ds/dt J1 X1 J2 X2 gt 0
• EITHER TERM CAN BE NEGATIVE IF THE OTHER IS
  POSITIVE AND OF GREATER MAGNITUDE
• THUS COUPLING BETWEEN SYSTEMS ALLOWS THE GROWTH
  AND DEVELOPMENT OF SYSTEMS AS LONG AS THEY ARE
  OPEN!

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STATIONARY STATES AWAY FROM EQUILIBRIUM

• LIKE A CIRCUIT
• REQUIRE A CONSTANT SOURCE OF ENERGY
• SEEM TO BE TIME INDEPENDENT
• HAS A FLOW GOING THROUGH IT
• SYSTEM WILL GO TO EQUILIBRIUM IF ISLOATED

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HOMEOSTASIS IS LIKE A STEADY STATE AWAY FROM
EQUILIBRIUM
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IT HAS A CIRCUIT ANALOG
J
x
L
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COUPLED PROCESSES

• KEDEM AND KATCHALSKY, LATE 1950S
• J1 L11 X1 L12 X2
• J2 L21 X1 L22 X2

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THE RESTING CELL

• High potassium
• Low Sodium
• Na/K ATPase pump
• Resting potential about 90 - 120 mV
• Osmotically balanced (constant volume)

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(No Transcript)
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EQUILIBRIUM RESULTS FROM ISOLATING THE SYSTEM
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WHAT ARE THERMODYNAMIC NETWORKS?

• ELECTRICAL NETWORKS ARE THERMODYNAMIC
• MOST DYNAMIC PHYSIOLOGICAL PROCESSES ARE ANALOGS
  OF ELECTRICAL PROCESSES
• COUPLED PROCESSES HAVE A NATURAL REPRESENTATION
  AS MULTI-PORT NETWORKS

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ELECTRICAL NETWORKS ARE THERMODYNAMIC

• RESISTANCE IS ENERGY DISSIPATION (TURNING GOOD
  ENERGY TO HEAT IRREVERSIBLY - LIKE FRICTION)
• CAPACITANCE IS ENERGY WHICH IS STORED WITHOUT
  DISSIPATION
• INDUCTANCE IS ANOTHER FORM OF STORAGE

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A SUMMARY OF ALL LINEAR FLOW PROCESSES
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MOST DYNAMIC PHYSIOLOGICAL PROCESSES ARE ANALOGS
OF ELECTRICAL PROCESSES
L
J
C
x
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COUPLED PROCESSES HAVE A NATURAL REPRESENTATION
AS MULTI-PORT NETWORKS
J2
L
J1
x2
C1
x1
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REACTION KINETICS AND THERMODYNAMIC NETWORKS

• START WITH KINETIC DESRIPTION OF DYNAMICS
• ENCODE AS A NETWORK
• TWO POSSIBLE KINDS OF ENCODINGS AND THE REFERENCE
  STATE

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EXAMPLE ATP SYNTHESIS IN MITOCHONDRIA
EH lt--------gt EH
H
H
E lt-------------gt E
S
P
E
MEMBRANE
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EXAMPLE ATP SYNTHESIS IN MITOCHONDRIA-NETWORK I
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IN THE REFERENCE STATE IT IS SIMPLY NETWORK II
L22-L12
L11-L12
J2
J1
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THIS NETWORK IS THE CANNONICAL REPRESENTATION OF
THE TWO FLOW/FORCE ENERGY CONVERSION PROCESS

• ONSAGERS THERMODYNAMICS WAS EXPRESSED IN AN
  AFFINE COORDINATE SYSTEM
• THAT MEANS THERE CAN BE NO METRIC FOR COMPARING
  SYSTEMS ENERGETICALLY
• BY EMBEDDING THE ONSAGER COORDINATES IN A HIGHER
  DIMENSIONAL SYSTEM, THERE IS AN ORTHOGANAL
  COORDINATE SYSTEM
• IN THE ORTHOGANAL SYSTEM THERE IS A METRIC FOR
  COMPARING ALL SYSTEMS
• THE VALUES OF THE RESISTORS IN THE NETWORK ARE
  THJE THREE ORTHOGONAL COORDINATES

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THE SAME KINETIC SYSTEM HAS AT LEAST TWO NETWORK
REPRESENTATIONS, BOTH VALID

• ONE CAPTURES THE UNCONSTRAINED BEHAVIOR OF THE
  SYSTEM AND IS GENERALLY NON-LINEAR
• THE OTHER IS ONLY VALID WHEN THE SYSTEM IS
  CONSTRAINED (IN A REFERENCE STATE) AND IS THE
  USUAL THERMODYNAMIC DESRIPTION OF A COUPLED SYSTEM

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SOME PUBLISHED NETWORK MODELS OF PHYSIOLOGICAL
SYSTEMS

• SR (BRIGGS,FEHER)
• GLOMERULUS (OKEN)
• ADIPOCYTE GLUCOSE TRANSPORT AND METABOLISM (MAY)
• FROG SKIN MODEL (HUF)
• TOAD BLADDER (MINZ)

• KIDNEY (FIDELMAN,WATTLINGTON)
• FOLATE METABOLISM (GOLDMAN, WHITE)
• ATP SYNTHETASE (CAPLAN, PIETROBON, AZZONE)

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Cell Membranes Become Network Elements in Tissue
Membranes

• Epithelia are tissue membranes made up of cells
• Network Thermodynamics provides a way of modeling
  these composite membranes
• Often more than one flow goes through the tissue

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An Epithelial Membrane in Cartoon Form
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A Network Model of Coupled Salt and Volume Flow
Through an Epithelium
CL
PL
LUMEN
AM
TJ
BL
CELL
BM
BLOOD
PB
CB
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TELLEGENS THEOREM

• BASED SOLEY ON NETWORK TOPOLOGY AND KIRCHHOFFS
  LAWS
• IS A POWER CONSERVATION THEOREM
• STATES THAT VECTORS OF FLOWS AND FORCES ARE
  ORTHOGONAL.
• TRUE FOR FLOWS AT ONE TIME AND FORCES AT ANOTHER
  AND VICE VERSA
• TRUE FOR FLOWS IN ONE SYSTEM AND FORCES IN
  ANOTHER WITH SAME TOPOLOGY AND VICE VERSA

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RELATIONAL NETWORKS

• THROW AWAY THE PHYSICS, KEEP THE ORGANIZATION
• DYNAMICS BECOMES A MAPPING BETWEEN SETS
• TIME IS IMPLICIT
• USE FUNCTIONAL COMPONENTS-WHICH DO NOT MAP INTO
  ATOMS AND MOLECULES 11 AND WHICH ARE IRREDUCABLE

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LIFE ITSELF

• CAN NOT BE CAPTURED BY ANY OF THESE FORMALISMS
• CAN NOT BE CAPTURED BY ANY COMBINATION OF THESE
  FORMALISMS
• THE RELATIONAL APPROACH CAPTURES SOME OF THE
  NON-COMPUTABLE, NON-ALGORITHMIC ASPECTS OF LIVING
  SYSTEMS