Transcript Relational Systems Theory: An approach to complexity Donald C. Mikulecky Professor Emeritus and Senior Fellow The Center for the Study of Biological 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:
 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
 SIMPLE
 NO LARGEST MODEL
 LARGEST MODEL
 WHOLE MORE THAN SUM OF
 WHOLE IS SUM OF PARTS






PARTS
CAUSAL RELATIONS RICH AND
INTERTWINED
GENERIC
ANALYTIC  SYNTHETIC
NON-FRAGMENTABLE
NON-COMPUTABLE
REAL WORLD
 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
J
DIFFUSION
n /t
BULK FLOW Q
FORCE
CONSTANT
C=C1-C2
P
p=p1-p2
LP
V=V1-V2
G
v/t
CURRENT
I
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
OUTLET
VALVE
ORIFICE CONNECTING TANKS
PUMP
RESERVOIR
IT HAS A CIRCUIT ANALOG
J
x
L
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
CLOSED
OUTLET
VALVE
ORIFICE CONNECTING TANKS
PUMP
RESERVOIR
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
J
DIFFUSION
n /t
BULK FLOW Q
FORCE
CONSTANT
C=C1-C2
P
p=p1-p2
LP
V=V1-V2
G
v/t
CURRENT
I
MOST DYNAMIC PHYSIOLOGICAL PROCESSES
ARE ANALOGS OF ELECTRICAL PROCESSES
L
J
x
C
COUPLED PROCESSES HAVE A
NATURAL REPRESENTATION
AS MULTI-PORT
NETWORKS
J2
L
J1
x2
x1
C2
C1
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+]
H+
[H+]
E <-------------> [E]
S
P
E
MEMBRANE
EXAMPLE: ATP SYNTHESIS IN
MITOCHONDRIA-NETWORK I
IN THE REFERENCE STATE IT
IS SIMPLY NETWORK II
L22-L12
L11-L12
J2
J1
x1
L22
x2
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)
 KIDNEY
 GLOMERULUS (OKEN)
(FIDELMAN,WATTLING
TON)
 FOLATE METABOLISM
(GOLDMAN, WHITE)
 ATP SYNTHETASE
(CAPLAN,
PIETROBON, AZZONE)
 ADIPOCYTE
GLUCOSE
TRANSPORT AND
METABOLISM (MAY)
 FROG SKIN MODEL
(HUF)
 TOAD BLADDER
(MINZ)
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
LUMEN
AM
CL
PL
TJ
BL
CELL
BM
BLOOD
CB
PB
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, NONALGORITHMIC ASPECTS OF LIVING
SYSTEMS