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: 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 ROSEN’S COMPLEXITY NETWORKS IN NATURE THERMODYNAMICS OF OPEN SYSTEMS THERMODYNAMIC NETWORKS RELATIONAL NETWORKS LIFE ITSELF

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

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 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: 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? 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 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 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 NATURE EDITORIAL: VOL 234, DECEMBER 17, 1971, pp “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 FLOW = CONDUCTANCE x FORCE FORCE = RESISTANCE x FLOW CONDUCTANCE = 1/RESISTANCE

A SUMMARY OF ALL LINEAR FLOW PROCESSES

COUPLED PROCESSES KEDEM AND KATCHALSKY, LATE 1950’S J1 = L11 X1 + L12 X2 J2 = L21 X1 + L22 X2

STATIONARY STATES AWAY FROM EQUILIBRIUM AND 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 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

IT HAS A CIRCUIT ANALOG x L J

COUPLED PROCESSES KEDEM AND KATCHALSKY, LATE 1950’S J1 = L11 X1 + L12 X2 J2 = L21 X1 + L22 X2

THE RESTING CELL High potassium Low Sodium Na/K ATPase pump Resting potential about mV Osmotically balanced (constant volume)

EQUILIBRIUM RESULTS FROM ISOLATING THE SYSTEM

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 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

MOST DYNAMIC PHYSIOLOGICAL PROCESSES ARE ANALOGS OF ELECTRICAL PROCESSES x L J C

COUPLED PROCESSES HAVE A NATURAL REPRESENTATION AS MULTI- PORT NETWORKS x1x1 L J1 C1 x2x2 C2 J2

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 EH+ [EH+] E [E] E MEMBRANE S P H+ [H+]

EXAMPLE: ATP SYNTHESIS IN MITOCHONDRIA-NETWORK I

IN THE REFERENCE STATE IT IS SIMPLY NETWORK II x2x2 L22 J1 x1x1 L11-L12 L22-L12 J2

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 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 SR (BRIGGS,FEHER) GLOMERULUS (OKEN) ADIPOCYTE GLUCOSE TRANSPORT AND METABOLISM (MAY) FROG SKIN MODEL (HUF) TOAD BLADDER (MINZ) KIDNEY (FIDELMAN,WATTLIN GTON) FOLATE METABOLISM (GOLDMAN, WHITE) ATP SYNTHETASE (CAPLAN, PIETROBON, AZZONE)

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 Network Thermodynamics Often more than one flow goes through the tissue

An Epithelial Membrane in Cartoon Form:

A Network Model of Coupled Salt and Volume Flow Through an Epithelium AMTJ BM BL CLPL CB PB CELL LUMEN BLOOD

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 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 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