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, 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

FLOW = CONDUCTANCE x FORCE

FORCE = RESISTANCE x FLOW

CONDUCTANCE = 1/RESISTANCE

A SUMMARY OF ALL LINEAR FLOW PROCESSES

PROCESS FLOW FORCE CONSTANT

DIFFUSION Jn /t

C=C1-C2 P

BULK FLOW Q p=p1-p2 LP

CURRENT

v/t

IV=V1-V2 G

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

INLET VALVE

OUTLETVALVE

PUMP

ORIFICE CONNECTING TANKS

RESERVOIR

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 90 - 120

mV Osmotically balanced (constant

volume)

EQUILIBRIUM RESULTS FROM

ISOLATING THE SYSTEM

INLET VALVE

OUTLETVALVE

PUMP

ORIFICE CONNECTING TANKS

RESERVOIR

CLOSED

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

PROCESS FLOW FORCE CONSTANT

DIFFUSION Jn /t

C=C1-C2 P

BULK FLOW Q p=p1-p2 LP

CURRENT

v/t

IV=V1-V2 G

MOST DYNAMIC PHYSIOLOGICAL PROCESSES ARE ANALOGS OF ELECTRICAL PROCESSES

x

LJ

C

COUPLED PROCESSES HAVE A NATURAL REPRESENTATION AS MULTI-PORT NETWORKS

x1

LJ1

C1x2C2

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]

EMEMBRANE

S

P

H+ [H+]

EXAMPLE: ATP SYNTHESIS IN MITOCHONDRIA-NETWORK I

IN THE REFERENCE STATE IT IS SIMPLY NETWORK II

x2L22

J1

x1

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,WATTLINGTON)

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 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

AM TJ

BM

BL

CL PL

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