Relational Systems Theory: An approach to complexity : Relational Systems Theory: An approach to complexity Donald C. Mikulecky
Professor Emeritus and Senior Fellow
The Center for the Study of Biological Complexity
MY SORCES: : 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)
ROUGH OUTLINE OF TALK : ROUGH OUTLINE OF TALK ROSEN’S COMPLEXITY
NETWORKS IN NATURE
THERMODYNAMICS OF OPEN SYSTEMS
THERMODYNAMIC NETWORKS
RELATIONAL NETWORKS
LIFE ITSELF
COMPLEXITY : 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
CAN WE DEFINE COMPLEXITY? : 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
COMPLEX SYSTEMS VS SIMPLE MECHANISMS : COMPLEX SYSTEMS VS SIMPLE MECHANISMS COMPLEX
NO LARGEST MODEL
WHOLE MORE THAN SUM OF PARTS
CAUSAL RELATIONS RICH AND INTERTWINED
GENERIC
ANALYTIC ? SYNTHETIC
NON-FRAGMENTABLE
NON-COMPUTABLE
REAL WORLD SIMPLE
LARGEST MODEL
WHOLE IS SUM OF PARTS
CAUSAL RELATIONS DISTINCT
N0N-GENERIC
ANALYTIC = SYNTHETIC
FRAGMENTABLE
COMPUTABLE
FORMAL SYSTEM
COMPLEXITY VS COMPLICATION : 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
THERMODYNAMICS OF OPEN SYSTEMS : THERMODYNAMICS OF OPEN SYSTEMS THE NATURE OF THERMODYNAMIC REASONING
HOW CAN LIFE FIGHT ENTROPY?
WHAT ARE THERMODYNAMIC NETWORKS?
THE NATURE OF THERMODYNAMIC REASONING : 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
SOME CONSEQUENCES : 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
EXAMPLES: : EXAMPLES: CAROTHEODRY’S PROOF OF THE SECOND LAW OF THERMODYNAMICS
THE PROOF OF TELLEGEN’S THEOREM AND THE QUASI-POWER THEOREM
THE PROOF OF “ONSAGER’S” RECIPROCITY THEOREM
HOW CAN LIFE FIGHT ENTROPY? : HOW CAN LIFE FIGHT ENTROPY? DISSIPATION AND THE SECOND LAW OF THERMODYNAMICS
PHENOMENOLOGICAL DESCRIPTION OF A SYTEM
COUPLED PROCESSES
STATIONARY STATES AWAY FROM EQUILIBRIUM
DISSIPATION AND THE SECOND LAW OF THERMODYNAMICS : 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?
PHENOMENOLOGICAL DESCRIPTION OF A SYTEM : 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
NETWORKS IN NATURE : 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”
A GENERALISATION FOR ALL LINEAR FLOW PROCESSES : A GENERALISATION FOR ALL LINEAR FLOW PROCESSES FLOW = CONDUCTANCE x FORCE
FORCE = RESISTANCE x FLOW
CONDUCTANCE = 1/RESISTANCE
A SUMMARY OF ALL LINEAR FLOW PROCESSES : A SUMMARY OF ALL LINEAR FLOW PROCESSES
COUPLED PROCESSES : COUPLED PROCESSES KEDEM AND KATCHALSKY, LATE 1950’S
J1 = L11 X1 + L12 X2
J2 = L21 X1 + L22 X2
STATIONARY STATES AWAY FROM EQUILIBRIUMAND THE SECOND LAW OF THERMODYNAMICS : STATIONARY STATES AWAY FROM EQUILIBRIUMAND THE SECOND LAW OF THERMODYNAMICS T Ds/dt = J1 X1 +J2 X2 > 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!
STATIONARY STATES AWAY FROM EQUILIBRIUM : 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
HOMEOSTASIS IS LIKE A STEADY STATE AWAY FROM EQUILIBRIUM : HOMEOSTASIS IS LIKE A STEADY STATE AWAY FROM EQUILIBRIUM
IT HAS A CIRCUIT ANALOG : IT HAS A CIRCUIT ANALOG x L J
COUPLED PROCESSES : COUPLED PROCESSES KEDEM AND KATCHALSKY, LATE 1950’S
J1 = L11 X1 + L12 X2
J2 = L21 X1 + L22 X2
THE RESTING CELL : THE RESTING CELL High potassium
Low Sodium
Na/K ATPase pump
Resting potential about 90 - 120 mV
Osmotically balanced (constant volume)
EQUILIBRIUM RESULTS FROM ISOLATING THE SYSTEM : EQUILIBRIUM RESULTS FROM ISOLATING THE SYSTEM
WHAT ARE THERMODYNAMIC NETWORKS? : 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
ELECTRICAL NETWORKS ARE THERMODYNAMIC : 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
A SUMMARY OF ALL LINEAR FLOW PROCESSES : A SUMMARY OF ALL LINEAR FLOW PROCESSES
MOST DYNAMIC PHYSIOLOGICAL PROCESSES ARE ANALOGS OF ELECTRICAL PROCESSES : MOST DYNAMIC PHYSIOLOGICAL PROCESSES ARE ANALOGS OF ELECTRICAL PROCESSES x L J C
COUPLED PROCESSES HAVE A NATURAL REPRESENTATION AS MULTI-PORT NETWORKS : COUPLED PROCESSES HAVE A NATURAL REPRESENTATION AS MULTI-PORT NETWORKS x1 L J1 C1 x2 J2
REACTION KINETICS AND THERMODYNAMIC NETWORKS : REACTION KINETICS AND THERMODYNAMIC NETWORKS START WITH KINETIC DESRIPTION OF DYNAMICS
ENCODE AS A NETWORK
TWO POSSIBLE KINDS OF ENCODINGS AND THE REFERENCE STATE
EXAMPLE: ATP SYNTHESIS IN MITOCHONDRIA : EXAMPLE: ATP SYNTHESIS IN MITOCHONDRIA EH+ <--------> [EH+] E <-------------> [E] E MEMBRANE S P H+ [H+]
EXAMPLE: ATP SYNTHESIS IN MITOCHONDRIA-NETWORK I : EXAMPLE: ATP SYNTHESIS IN MITOCHONDRIA-NETWORK I
IN THE REFERENCE STATE IT IS SIMPLY NETWORK II : IN THE REFERENCE STATE IT IS SIMPLY NETWORK II J1 L11-L12 L22-L12 J2
THIS NETWORK IS THE CANNONICAL REPRESENTATION OF THE TWO FLOW/FORCE ENERGY CONVERSION PROCESS : THIS NETWORK IS THE CANNONICAL REPRESENTATION OF THE TWO FLOW/FORCE ENERGY CONVERSION PROCESS ONSAGER’S 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
THE SAME KINETIC SYSTEM HAS AT LEAST TWO NETWORK REPRESENTATIONS, BOTH VALID : 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
SOME PUBLISHED NETWORK MODELS OF PHYSIOLOGICAL SYSTEMS : 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)
Cell Membranes Become Network Elements in Tissue Membranes : 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
An Epithelial Membrane in Cartoon Form: : An Epithelial Membrane in Cartoon Form:
A Network Model of Coupled Salt and Volume Flow Through an Epithelium : A Network Model of Coupled Salt and Volume Flow Through an Epithelium AM TJ BM BL CL PL CB PB CELL LUMEN BLOOD
TELLEGEN’S THEOREM : TELLEGEN’S THEOREM BASED SOLEY ON NETWORK TOPOLOGY AND KIRCHHOFF’S 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
RELATIONAL NETWORKS : 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 1:1 AND WHICH ARE IRREDUCABLE
LIFE ITSELF : 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