Physiological Variability John Doyle Ben Recht Experiments Theorycomputation

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Physiological Variability John Doyle Ben Recht Experiments Theory/computation Control and dynamical systems Caltech

Physiological Variability John Doyle Ben Recht Experiments Theory/computation Control and dynamical systems Caltech

My interests Multiscale Physics Network Centric, Pervasive, Embedded, Ubiquitous Core theory challenges Systems Biology

My interests Multiscale Physics Network Centric, Pervasive, Embedded, Ubiquitous Core theory challenges Systems Biology

Collaborators and contributors (partial list) Biology: Csete, Yi, El-Samad, Khammash, Tanaka, Arkin, Savageau, Simon,

Collaborators and contributors (partial list) Biology: Csete, Yi, El-Samad, Khammash, Tanaka, Arkin, Savageau, Simon, Af. CS, Kurata, Smolke, Gross, Kitano, Hucka, Sauro, Finney, Bolouri, Gillespie, Petzold, F Doyle, Stelling, Caporale, … Theory: Parrilo, Carlson, Murray, Vinnicombe, Paganini, Mitra Papachristodoulou, Prajna, Goncalves, Fazel, Liu, Lall, D’Andrea, Jadbabaie, Dahleh, Martins, Recht, many more current and former students, … Web/Internet: Li, Alderson, Chen, Low, Willinger, Kelly, Zhu, Yu, Wang, Chandy, … Turbulence: Bamieh, Bobba, Mc. Keown, Gharib, Marsden, … Physics: Sandberg, Mabuchi, Doherty, Barahona, Reynolds, Disturbance ecology: Moritz, Carlson, … Finance: Martinez, Primbs, Yamada, Giannelli, … Current Caltech Former Caltech Longterm Visitor Other

Thanks to • • • Boeing NSF ARO/ICB AFOSR NIH/NIGMS DARPA Lee Center for

Thanks to • • • Boeing NSF ARO/ICB AFOSR NIH/NIGMS DARPA Lee Center for Advanced Networking (Caltech) Hiroaki Kitano (ERATO) Braun family

Overview • • Heart rate variability From recent talks at meetings of – Intensive

Overview • • Heart rate variability From recent talks at meetings of – Intensive care doctors (SCAI) – Anesthesiologists (ASA) • http: //www. cds. caltech. edu/~doyle/ASA/ • High variability in core metabolism and other examples (time permitting)

Polar Bike HR monitor Stride sensor Treadmill • Familiar modeling tools (ARMA) • But

Polar Bike HR monitor Stride sensor Treadmill • Familiar modeling tools (ARMA) • But new math to solve for models

70 HR [bpm] 70 65 60 50 “Resting” HR 60 What about this? 55

70 HR [bpm] 70 65 60 50 “Resting” HR 60 What about this? 55 50 45 40 40 35 30 0: 00 Time 0: 02: 00 Healthy mean and variance 0: 04: 00 0: 06: 00

70 HR [bpm] Healthy response 60 HR [bpm] 70 65 60 Sit 50 Stand

70 HR [bpm] Healthy response 60 HR [bpm] 70 65 60 Sit 50 Stand Sit 55 50 45 40 40 35 30 0: 00 Time 0: 02: 00 Healthy mean and variance 0: 04: 00 0: 06: 00

R-R Intervals [ms] 1600 1200 Sit Stand Sit 800 400 1 2 3 48

R-R Intervals [ms] 1600 1200 Sit Stand Sit 800 400 1 2 3 48 bpm 0: 00 0: 02: 00 0: 04: 00 0: 06: 00 Time

R-R Intervals [ms] 1600 1400 1200 1000 800 ? ? 600 400 200 0:

R-R Intervals [ms] 1600 1400 1200 1000 800 ? ? 600 400 200 0: 02: 00 0: 04: 00 0: 06: 00 Time

R-R Intervals [ms] 1600 1400 1200 1000 800 600 400 1 200 0: 00

R-R Intervals [ms] 1600 1400 1200 1000 800 600 400 1 200 0: 00 140 bpm 0: 02: 00 0: 04: 00 0: 06: 00 0: 08: 00 Mean RR down (HR up) Variance down Time 0: 10: 00

R-R Intervals [ms] 1200 Sit Stand 1600 Sit 800 400 Run 1 2 140

R-R Intervals [ms] 1200 Sit Stand 1600 Sit 800 400 Run 1 2 140 bpm 200 0: 10: 00 0: 20: 00 Diagnosis? 0: 30: 00

HR [bpm] 160 Run 120 Large variability 80 Sit 40 0: 00 0: 10:

HR [bpm] 160 Run 120 Large variability 80 Sit 40 0: 00 0: 10: 00 Large variability? 0: 20: 00 0: 30: 00

Variability: Alternative viewpoints 1. Ignore variability in physiology 2. Misinterpret variability as “emergent, chaos,

Variability: Alternative viewpoints 1. Ignore variability in physiology 2. Misinterpret variability as “emergent, chaos, criticality, scale-free” etc. , etc. 3. Properly interpret variability as the • normal healthy function • of robust, but very complex, • feedback and anticipatory control systems

Summary • Force large changes in heart rate on short timescales – Healthy subjects

Summary • Force large changes in heart rate on short timescales – Healthy subjects – Exercise load • Use control theory to interpret data • Confirm what is “well-known” to doctors, coaches, and athletes (everyone with clue) • Mimic – healthy vs ill – with fit vs unfit/fatigued

Alternative viewpoints 1. Ignore variability in physiology 2. Misinterpret variability as “emergent, chaos, criticality,

Alternative viewpoints 1. Ignore variability in physiology 2. Misinterpret variability as “emergent, chaos, criticality, scale-free” etc. , etc. 3. Properly interpret variability as the • normal healthy function • of robust, but very complex, • feedback and anticipatory control systems

Intensive Care Challenges (with increasing difficulty) 1. Reintroduce natural variability (open loop) 2. Reintroduce

Intensive Care Challenges (with increasing difficulty) 1. Reintroduce natural variability (open loop) 2. Reintroduce natural feedback control 3. Augment feedback control in regimes outside of evolutionary pressures (e. g. ICUs)

Most cited paper on HR variability 1999

Most cited paper on HR variability 1999

Nonlinear Dynamics, Fractals, and Chaos Theory: Implications for Neuroautonomic Heart Rate Control in Health

Nonlinear Dynamics, Fractals, and Chaos Theory: Implications for Neuroautonomic Heart Rate Control in Health and Disease Ary L. Goldberger http: //www. physionet. org/tutorials/ndc/ Goldberger AL, Amaral LAN, Glass L, Hausdorff JM, Ivanov PCh, Mark RG, Mietus JE, Moody GB, Peng C-K, Stanley HE. Physio. Bank, Physio. Toolkit, and Physio. Net: Components of a New Research Resource for Complex Physiologic Signals. Circulation 101(23): e 215 -e 220; 2000 (June 13)

…de-complexification of systems with disease appears to be a common feature of many pathologies,

…de-complexification of systems with disease appears to be a common feature of many pathologies, as well as of aging. When physiologic systems become less complex, their information content is degraded. As a result, they are less adaptable and less able to cope with the exigencies of a constantly changing environment. To generate information, a system must be capable of behaving in an unpredictable fashion. Findings from nonlinear dynamics have also challenged conventional mechanisms of physiological control based on classical homeostasis, which presumes that healthy systems seek to attain a constant steady state. In contrast, nonlinear systems with fractal dynamics, such as the neuroautonomic mechanisms regulating heart rate variability, behave as if they were driven far from equilibrium under basal conditions. This kind of complex variability, rather than a regular homeostatic steady state, appears to define the free-running function of many biological systems.

Warren Weaver, 1948 • Warned against confusing – disorganized complexity versus – organized complexity

Warren Weaver, 1948 • Warned against confusing – disorganized complexity versus – organized complexity • Disorganized complexity dominates physical sciences (statistical physics) • Organized complexity is relevant to biology and technology • Confusion/disconnect has gotten much worse since 1948

 • Disorganized complexity – Chaos, fractals, stat mech, criticality, scale-free, … – Fun

• Disorganized complexity – Chaos, fractals, stat mech, criticality, scale-free, … – Fun topics with broad interest, applicability • Organized complexity – All of the above topics plus – Control, dynamical systems, info, comp theory – Homeostasis/Rheostasis/Allostasis/Uberstasis – Tradeoffs, robust/fragile, evolvability, optimization – Protocols, architecture, scalability, constraints, …

 • Disorganized complexity – Chaos, fractals, stat mech, criticality, scale-free, … – Fun

• Disorganized complexity – Chaos, fractals, stat mech, criticality, scale-free, … – Fun topics with broad interest, applicability – But bio and tech networks, medicine, are bewildering when viewed with only these tools – Systematic misinterpretation of high variability – Yet successful in “high impact” journals and funding • Popular applications – Self-organized critical forest fires, Internet traffic – Scale-free Internet, metabolism, protein-protein nets – Chaos, fractals, and HR variability ? ? ?

Disorganized complexity, chaos, and HR variability? Heart &Lung HR highly variable • “Resting” HR?

Disorganized complexity, chaos, and HR variability? Heart &Lung HR highly variable • “Resting” HR? – “free running” = unpredictable =chaotic?

Organized complexity, control, and HR variability? Internal Loads Heart &Lung Liver, brain, heart, kidney,

Organized complexity, control, and HR variability? Internal Loads Heart &Lung Liver, brain, heart, kidney, digestion, muscle, other… HR highly variable • “Resting” HR? ? – “free running” = unpredictable =chaotic? – or responsive to internal, fluctuating loads? • Hard to measure internal loads • Presumably fluctuating but uncertain

Control Internal Loads Heart &Lung external Skeletal Muscle HR highly variable - Error=0

Control Internal Loads Heart &Lung external Skeletal Muscle HR highly variable - Error=0

Different views on variability • Disorganized complexity – Simple systems can be unpredictable –

Different views on variability • Disorganized complexity – Simple systems can be unpredictable – (True but irrelevant, as physiology is not simple. ) • Organized complexity – Extremely robust and adaptive systems – Often require high internal complexity and organization – That results in appropriately large, adaptive, variable responses

70 HR [bpm] Healthy response 60 HR [bpm] 70 65 60 Sit 50 Stand

70 HR [bpm] Healthy response 60 HR [bpm] 70 65 60 Sit 50 Stand Sit 55 50 45 40 40 35 30 0: 00 Time 0: 02: 00 Healthy mean and variance 0: 04: 00 0: 06: 00

HR [bpm] 160 Run 120 Large variability 80 Sit 40 0: 00 0: 10:

HR [bpm] 160 Run 120 Large variability 80 Sit 40 0: 00 0: 10: 00 Large variability? 0: 20: 00 0: 30: 00

Pace [min/km] 3: 20 4: 36 7: 30 1 2 Time 0: 00 0:

Pace [min/km] 3: 20 4: 36 7: 30 1 2 Time 0: 00 0: 10: 00 0: 20: 00 0: 30: 00

 10 -20 watts “treadmillstasis”? Internal Loads Heart &Lung external Skeletal Muscle 100 -400

10 -20 watts “treadmillstasis”? Internal Loads Heart &Lung external Skeletal Muscle 100 -400 watts HR highly variable - Error=0 stasis

 10 -20 watts “treadmillstasis”? Internal Loads Heart &Lung external Skeletal Muscle 100 -400

10 -20 watts “treadmillstasis”? Internal Loads Heart &Lung external Skeletal Muscle 100 -400 watts HR highly variable - Error=0 stasis

 • Disorganized complexity – Chaos, fractals, stat mech, criticality, scalefree, … Heart &Lung

• Disorganized complexity – Chaos, fractals, stat mech, criticality, scalefree, … Heart &Lung HR highly variable

 • Disorganized complexity – Chaos, fractals, stat mech, criticality, scale-free, … • Organized

• Disorganized complexity – Chaos, fractals, stat mech, criticality, scale-free, … • Organized complexity – All of the above topics plus – Control, dynamical systems, info, comp theory – Homeostasis/Rheostasis/Allostasis/Uberstasis – Tradeoffs, robust/fragile, evolvability, optimization – Protocols, architecture, scalability, constraints, … • We think it makes sense to use all of the above

Organized complexity, circa 1972 Internal Loads Heart &Lung external Skeletal Muscle HR highly variable

Organized complexity, circa 1972 Internal Loads Heart &Lung external Skeletal Muscle HR highly variable - Error=0

Control Internal Loads Heart &Lung external Skeletal Muscle HR highly variable - Error=0

Control Internal Loads Heart &Lung external Skeletal Muscle HR highly variable - Error=0

Internal Loads Heart &Lung external Skeletal Muscle HR highly variable - Bike and treadmill

Internal Loads Heart &Lung external Skeletal Muscle HR highly variable - Bike and treadmill Error=0

HR [bpm] 160 Run ramp Bike and treadmill Steady bike Run ramp Steady Run

HR [bpm] 160 Run ramp Bike and treadmill Steady bike Run ramp Steady Run Steady bike ramp bike Run ramp 160 140 120 100 80 60 80 1 0: 00 22 0: 20: 00 0: 40: 00 1: 20: 00 1: 40: 00 Time

Bike and treadmill 160 Steady bike Run ramp 140 120 100 80 60 0:

Bike and treadmill 160 Steady bike Run ramp 140 120 100 80 60 0: 40: 00 1: 40: 00

160 Steady bike Run ramp 140 120 100 80 60 45 min Run ramp

160 Steady bike Run ramp 140 120 100 80 60 45 min Run ramp

160 140 120 100 80 60 Steady bike

160 140 120 100 80 60 Steady bike

160 140 120 100 80 60 Steady bike

160 140 120 100 80 60 Steady bike

160 Steady bike @250 w 140 120 Extremely repeatable 100 80 60 40 Rest

160 Steady bike @250 w 140 120 Extremely repeatable 100 80 60 40 Rest HR 20 0 20 40 60 80 100

160 Steady bike @250 w 140 Mean HR 120 100 80 Error HR +

160 Steady bike @250 w 140 Mean HR 120 100 80 Error HR + constant 60 40 20 40 60 80 x 5 secs 100

HR [bpm] 150 11/16/2007 140 11/22/2007 130 120 110 100 8 104 bpm 90

HR [bpm] 150 11/16/2007 140 11/22/2007 130 120 110 100 8 104 bpm 90 0: 45: 00 Time 0: 50: 00 0: 55: 00 1: 05: 00

160 140 120 100 80 60 Run ramp

160 140 120 100 80 60 Run ramp

160 140 120 100 80 60 Run ramp

160 140 120 100 80 60 Run ramp

~kcal/hr ~watts Run ramp 1089 272 1023 256 944 236 883 221 810 203

~kcal/hr ~watts Run ramp 1089 272 1023 256 944 236 883 221 810 203 754 189 687 172 637 159 0 20 40 60 80 100

160 140 120 100 80 60 40 20 40 60 80 x 5 secs

160 140 120 100 80 60 40 20 40 60 80 x 5 secs 100

160 140 120 100 80 60 40 20 40 60 80 100

160 140 120 100 80 60 40 20 40 60 80 100

Run ramp 160 272 256 236 221 203 189 172 159 140 120 100

Run ramp 160 272 256 236 221 203 189 172 159 140 120 100 80 60 40 20 40 60 80 100

160 1089 1023 944 883 810 754 687 637 140 120 100 80 60

160 1089 1023 944 883 810 754 687 637 140 120 100 80 60 40 20 40 60 80 100

Linear time invariant (LTI) models

Linear time invariant (LTI) models

160 140 HR 120 h(t) 100 80 60 40 20 0 100 200 300

160 140 HR 120 h(t) 100 80 60 40 20 0 100 200 300 time (seconds) 400 500

160 140 HR 120 h(t) 100 80 60 “rest HR” 40 20 0 100

160 140 HR 120 h(t) 100 80 60 “rest HR” 40 20 0 100 200 300 time (seconds) 400 500

150 Steady State HR 140 130 120 110 600 700 800 900 KCal/hr 1000

150 Steady State HR 140 130 120 110 600 700 800 900 KCal/hr 1000 1100

160 140 HR 120 h(t) 100 80 60 40 20 0 100 200 300

160 140 HR 120 h(t) 100 80 60 40 20 0 100 200 300 time (seconds) 400 500

Watts HR 130 250 120 200 110 100 150 90 100 80 70 50

Watts HR 130 250 120 200 110 100 150 90 100 80 70 50 0 0 time (secs) 1000 2000 time (min) 3000 50 0

HR 130 120 110 100 90 80 0 time (min) 40

HR 130 120 110 100 90 80 0 time (min) 40

130 120 110 100 90 80 70 60 50 HR Simple Linear Model

130 120 110 100 90 80 70 60 50 HR Simple Linear Model

130 HR Model 250 120 110 100 200 150 90 80 70 60 50

130 HR Model 250 120 110 100 200 150 90 80 70 60 50 100 50

130 HR Model 250 120 110 100 200 150 90 80 70 60 50

130 HR Model 250 120 110 100 200 150 90 80 70 60 50 100 50

130 250 120 200 110 100 150 90 80 Supply Total demand 70 50

130 250 120 200 110 100 150 90 80 Supply Total demand 70 50 60 50 100 external internal

Model

Model

130 HR Model 250 120 110 100 200 150 90 80 70 60 50

130 HR Model 250 120 110 100 200 150 90 80 70 60 50 100 50

130 120 110 100 90 80 70 60 50 noise

130 120 110 100 90 80 70 60 50 noise

130 120 110 100 90 80 70 60 50

130 120 110 100 90 80 70 60 50

150 Post-trauma 140 130 120 110 100 90 80 0 time (min) 40

150 Post-trauma 140 130 120 110 100 90 80 0 time (min) 40

150 140 130 120 Post-trauma

150 140 130 120 Post-trauma

HR [bpm] 120 Post-trauma & post-breakfast 100 80 Posttrauma 60 Healthy 40 0: 00

HR [bpm] 120 Post-trauma & post-breakfast 100 80 Posttrauma 60 Healthy 40 0: 00 0: 02: 00 0: 04: 00 0: 06: 00

500 not 400 watts 300 achievable 200 100 0 sec min Log(time) hour

500 not 400 watts 300 achievable 200 100 0 sec min Log(time) hour

500 not 400 watts 300 achievable 200 Simple 100 0 sec min Log(time) hour

500 not 400 watts 300 achievable 200 Simple 100 0 sec min Log(time) hour

Very special: • Easy forcing • 260 watts • No fatigue effects • Good

Very special: • Easy forcing • 260 watts • No fatigue effects • Good hydration • Minimal temperature effects Steady bike Run ramp 160 140 120 100 80 60 0: 40: 00 1: 40: 00

HR [bpm] 180 160 140 120 100 80 60 40 0: 00 Run Sit

HR [bpm] 180 160 140 120 100 80 60 40 0: 00 Run Sit 0: 10: 00 0: 20: 00 0: 30: 00

Pace [min/km] 3: 20 4: 36 7: 30 1 2 Time 0: 00 0:

Pace [min/km] 3: 20 4: 36 7: 30 1 2 Time 0: 00 0: 10: 00 0: 20: 00 0: 30: 00

LTI 180 Data 160 140 heart. Rate 120 100 80 60 40 20 0

LTI 180 Data 160 140 heart. Rate 120 100 80 60 40 20 0 0 500 1000 time (seconds) 1500 2000

LTI 160 140 Data 120

LTI 160 140 Data 120

LTI 160 “Fatigue effects” 140 120 Data

LTI 160 “Fatigue effects” 140 120 Data

 • Disorganized complexity – Chaos, fractals, stat mech, criticality, scalefree, … • Organized

• Disorganized complexity – Chaos, fractals, stat mech, criticality, scalefree, … • Organized complexity – All of the above topics plus – Control, dynamical systems, info, comp theory – Homeostasis/Rheostasis/Allostasis/Uberstasis – Tradeoffs, robust/fragile, evolvability, optimization – Protocols, architecture, scalability, constraints… • We think it makes sense to use all of the above

Most cited paper on HR variability 1999

Most cited paper on HR variability 1999

Disorganized complexity, chaos, and HR variability? Heart &Lung HR highly variable • “Resting” HR?

Disorganized complexity, chaos, and HR variability? Heart &Lung HR highly variable • “Resting” HR? – “free running” = unpredictable =chaotic?

Organized complexity, control, and HR variability? Internal Loads Heart &Lung Liver, brain, heart, kidney,

Organized complexity, control, and HR variability? Internal Loads Heart &Lung Liver, brain, heart, kidney, digestion, muscle, other… HR highly variable • “Resting” HR? ? – “free running” = unpredictable =chaotic? – or responsive to internal, fluctuating loads? • Hard to measure internal loads • Presumably fluctuating but uncertain

Control Internal Loads Heart &Lung external Skeletal Muscle HR highly variable - Error=0

Control Internal Loads Heart &Lung external Skeletal Muscle HR highly variable - Error=0

 • Disorganized complexity – No external demand – Health=“complexity” (fractals, chaos, etc) –

• Disorganized complexity – No external demand – Health=“complexity” (fractals, chaos, etc) – Illness= “loss of complexity” • Organized complexity – Coherent response to varying demand – Health= “simple” behavior, complex implementation – Illness= loss of coherent response 500 watts achievable Simple 0 sec min hour Log(time)

Medical challenges (increasing difficulty) 1. Reintroduce natural variability (open loop) 2. Reintroduce natural feedback

Medical challenges (increasing difficulty) 1. Reintroduce natural variability (open loop) 2. Reintroduce natural feedback control 3. Augment feedback control in regimes outside of evolutionary pressures (e. g. ICUs)

Carriers Metabolites 3 Catabolism Precursors 10 Rank all metabolites 33 65 78 2 10

Carriers Metabolites 3 Catabolism Precursors 10 Rank all metabolites 33 65 78 2 10 Amino acids 132 152 Carriers Nucleotides 1 10 Lipids & fatty acids 0 184 204 236 251 10 Number of reactions H. Pylori 100 Cofactors Reactions 313 58 133 190 240

Power laws are ubiquitous Mo re n Low variability orm al t han No

Power laws are ubiquitous Mo re n Low variability orm al t han No rma l High variability Gaussian Exponential Power law Central Limit Theorem (CLT) Marginalization (Markov property) CLT Marginalization Maximization Mixtures

Convergent moments Low variability Gaussian Exponential Divergent moments High variability Power law

Convergent moments Low variability Gaussian Exponential Divergent moments High variability Power law

Power Mlaws are ubiquitous ore no rm a l th an No • Power

Power Mlaws are ubiquitous ore no rm a l th an No • Power laws have extremely strong statistical invariants • The should naturally arise whenever there is high variability • High variability is everywhere in nature and technology and has nothing to do with any particular mechanism rm al High variability Power law CLT Marginalization Maximization Mixtures

Power laws are unexceptional Mo re n Low variability orm al t han No

Power laws are unexceptional Mo re n Low variability orm al t han No rma l High variability Gaussian Exponential Power law Central Limit Theorem (CLT) Marginalization (Markov property) CLT Marginalization Maximization Mixtures

High variability and power laws • • • High variability is more fundamental, And

High variability and power laws • • • High variability is more fundamental, And is ubiquitous, Particularly in highly engineered/evolved systems. • • • Power laws are “more normal than Normal” And not a “signature” of specific mechanisms Any more than Gaussians are

Highly variable highly confused • • Extreme statistical features of power laws… …means they

Highly variable highly confused • • Extreme statistical features of power laws… …means they are “discovered” where they are absent… …yet high variability is ignored even when abundant. And high variability is very abundant in networks. Major errors are typical in “high impact” journals 1. Finding power laws in low variability data 2. Badly misestimating slope –α 3. Badly misunderstanding origins of high variability in “robust yet fragile” (RYF) systems.

Finding power laws in low variability data High variability Low variability Gaussian Exponential Power

Finding power laws in low variability data High variability Low variability Gaussian Exponential Power law data models

Finding power laws in low variability data 10 10 3 2 rank 10 10

Finding power laws in low variability data 10 10 3 2 rank 10 10 1 0 50 degree Numerically generated random “data” n=1 e 3; yu=rand(1, n); ye=10*(-1+log(yu)); 100 y=-sort(ceil(ye)); semilogy(y, 1: n, 'k. ');

rank frequency u=unique(y); nu=length(u); g=0*u; for k=1: nu g(k)=sum(y==u(k)); end figure(2); loglog(u, g, 'bo‘);

rank frequency u=unique(y); nu=length(u); g=0*u; for k=1: nu g(k)=sum(y==u(k)); end figure(2); loglog(u, g, 'bo‘);

2 10 α=1. 5 1+α=2. 5 1 10 u=unique(y); nu=length(u); g=0*u; for k=1: nu

2 10 α=1. 5 1+α=2. 5 1 10 u=unique(y); nu=length(u); g=0*u; for k=1: nu g(k)=sum(y==u(k)); end figure(2); loglog(u, g, 'bo‘); frequency 0 10 1 10 degree 10 2

2 10 α=1. 5 1+α=2. 5 1 10 frequency 0 10 1 10 degree

2 10 α=1. 5 1+α=2. 5 1 10 frequency 0 10 1 10 degree 10 2

10 3 2 10 10 α=1. 5 2 rank 10 1 frequency 10 0

10 3 2 10 10 α=1. 5 2 rank 10 1 frequency 10 0 0 50 degree 100 10 1 10 degree 10 2

Systematic errors in “high impact” journals • • • Protein-Protein Interaction (PPI) networks Power

Systematic errors in “high impact” journals • • • Protein-Protein Interaction (PPI) networks Power grid Internet router “graph” WWW “graph” Metabolic networks

Protein-Protein Interaction (PPI) networks Node degree distribution of all interactions in 'filtered yeast interactome'

Protein-Protein Interaction (PPI) networks Node degree distribution of all interactions in 'filtered yeast interactome' 3 10 α=1 2 10 frequency Han, J. -D et al (2004). Evidence for dynamically organized modularity in the yeast protein-protein interaction network. Nature, 430, 88 -93. 1 10 1+α=2 0 10 10 0 1 10 degree

(PPI) networks 3 10 α=1 2 10 frequency 1 1 10 10 Roughly exponential

(PPI) networks 3 10 α=1 2 10 frequency 1 1 10 10 Roughly exponential 0 10 20 30 10 0 1 10 degree

( from Science) α=3 α=1. 1 WWW Power Grid

( from Science) α=3 α=1. 1 WWW Power Grid

( from Science) 10 4 rank 10 10 2 Power Grid Clearly exponential 0

( from Science) 10 4 rank 10 10 2 Power Grid Clearly exponential 0 0 5 10 15 degree 20

frequency 10 0 10 -2 10 -4 10 -6 10 -8 -10 10 α=1.

frequency 10 0 10 -2 10 -4 10 -6 10 -8 -10 10 α=1. 1 WWW Logarithmic binning =2. 1 α=1. 1 0 10 1 10 2 10 3 10 4 10 degree replot to check the method

Wrong α α=1. 1 10 rank 10 10 10 6 α=1. 7 5 WWW

Wrong α α=1. 1 10 rank 10 10 10 6 α=1. 7 5 WWW 4 3 2 α=1. 1 1 0 10 10 1 2 10 3 10 degree 10 4

Internet Router Data (Mercator Data Set) 6 10 5 10 Router Size-Frequency Plot (Mercator

Internet Router Data (Mercator Data Set) 6 10 5 10 Router Size-Frequency Plot (Mercator Data Set) 4 10 3 10 2 10 1 10 0 10 1 10 2 10 3 10

5 10 4 10 freq 6 10 3 10 5 10 2 α=1. 4

5 10 4 10 freq 6 10 3 10 5 10 2 α=1. 4 10 1 10 3 10 Binned Size. Frequency Plot 0 10 2 10 1 10 0 10 1 10 2 10 3 10 size 2 10

5 10 4 10 freq 3 10 2 α=1. 4 10 1 10 0

5 10 4 10 freq 3 10 2 α=1. 4 10 1 10 0 10 1 10 size 2 10

Size-Rank Plot (Log-Linear Scale) 5 10 4 10 freq 6 10 3 10 2

Size-Rank Plot (Log-Linear Scale) 5 10 4 10 freq 6 10 3 10 2 α=1. 4 10 rank 1 10 0 10 2 10 1 10 0 100 size 200 300 size 2 10

Size-Rank Plot (Log-Linear Scale) 6 10 Mean size lowered by “excess” small degree routers

Size-Rank Plot (Log-Linear Scale) 6 10 Mean size lowered by “excess” small degree routers 4 10 rank 2 10 Clearly exponential 0 100 size 200 300

Size-Rank Plot (Log-Linear Scale) 5 10 4 10 freq 6 10 3 10 2

Size-Rank Plot (Log-Linear Scale) 5 10 4 10 freq 6 10 3 10 2 10 4 α=1. 4 1 10 10 rank 0 10 2 10 Clearly exponential 0 100 size 200 300 1 10 size 2 10

High variability Major errors are typical in “high impact” journals 1. Finding power laws

High variability Major errors are typical in “high impact” journals 1. Finding power laws in low variability data 2. Badly misestimating slope –α 3. Badly misunderstanding origins of high variability in “robust yet fragile” (RYF) systems.

Carriers Metabolites 3 Catabolism Precursors 10 Rank all metabolites 33 65 78 2 10

Carriers Metabolites 3 Catabolism Precursors 10 Rank all metabolites 33 65 78 2 10 Amino acids 132 152 Carriers Nucleotides 1 10 Lipids & fatty acids 0 184 204 236 251 10 Number of reactions H. Pylori 100 Cofactors Reactions 313 58 133 190 240

10 10 3 All Metabolites 2 100 Rank 10 10 3 1 1 10

10 10 3 All Metabolites 2 100 Rank 10 10 3 1 1 10 1 Number of reactions 10 2 2 (ADP) 1 (ATP)

10 10 3 All Metabolites 2 100 Rank 10 10 3 1 1 10

10 10 3 All Metabolites 2 100 Rank 10 10 3 1 1 10 1 Number of reactions 10 2 2 (ADP) 1 (ATP)

10 Rank 10 3 All Metabolites 2 Exponential Others Carriers 10 Exponential Precursors Exponential

10 Rank 10 3 All Metabolites 2 Exponential Others Carriers 10 Exponential Precursors Exponential 1 1 10 1 Number of reactions 10 2 0 20 40 60 Number of reactions

Mixture 10 2 Most are in only a few reactions All Metabolites Rank 10

Mixture 10 2 Most are in only a few reactions All Metabolites Rank 10 3 High variability of metabolite degree 10 1 1 Number of reactions 10 1 10 2 A few metabolites are in many reactions

Mixture 10 All Metabolites Rank 10 Other metabolites 3 2 High variability due to

Mixture 10 All Metabolites Rank 10 Other metabolites 3 2 High variability due to structure of metabolic network Precursors 10 Carriers 1 1 Number of reactions 10 1 10 2

Mixture 10 32 Other metabolites 3 86 106 138 158 190 Rank 10 2

Mixture 10 32 Other metabolites 3 86 106 138 158 190 Rank 10 2 All Metabolites 205 10 267 Precursors Carriers 1 276 289 58 1 Number of reactions 10 1 10 2 133 190 240 Reactions

10 Rank 10 Component degrees are roughly exponential 3 All Metabolites 2 Exponential Others

10 Rank 10 Component degrees are roughly exponential 3 All Metabolites 2 Exponential Others Carriers Exponential 10 Precursors Exponential 1 1 10 1 Number of reactions 10 2 0 20 40 60 Number of reactions

E Coli 2 10 Rank -5/4 1 10 0 10 1 10 Degree 2

E Coli 2 10 Rank -5/4 1 10 0 10 1 10 Degree 2 10 20 40 60 Degree 80 100 120

Autocatalytic feedback Polymerization and complex assembly gar u S cids a y t t

Autocatalytic feedback Polymerization and complex assembly gar u S cids a y t t a F Co-factors Amin o Aci ds Nu cle Carriers otid es Precursors Catabolism Core metabolisms Genes DNA replication Regulation & control Trans* Proteins Nutrients Taxis and transport Metabolism, biosynthesis, assembly

Autocatalytic feedback Polymerization and complex assembly gar u S cids a y t t

Autocatalytic feedback Polymerization and complex assembly gar u S cids a y t t a F Co-factors Amin o Aci ds Nu cle Carriers otid es Precursors Catabolism Core metabolisms Genes DNA replication Trans* Proteins Nutrients Taxis and transport Metabolism, biosynthesis, assembly The architecture of stoichiometry.

gar u S cids a y t t a F Co-factors Amin o Aci

gar u S cids a y t t a F Co-factors Amin o Aci ds Nu cle Carriers otid es Precursors Catabolism Core metabolisms Genes DNA replication Trans* Proteins Nutrients Autocatalytic feedback

Bacterial cell Autocatalytic feedback Core metabolisms Precursors Catabolism Nutrients Environment Genes DNA replication Huge

Bacterial cell Autocatalytic feedback Core metabolisms Precursors Catabolism Nutrients Environment Genes DNA replication Huge Variety Trans* Proteins gar u S cids a y t t a Environment F Co-factors Amin o Aci ds Nu cle Carriers otid es Huge Variety

Hu Va ge riet y Precursors Nutrients Taxis and transport Same 12 in all

Hu Va ge riet y Precursors Nutrients Taxis and transport Same 12 in all Core metabolism cells rs a g Su cids A o n i m A Nucleotides Catabolism Fatty acid s Cofact ors Carriers Same 8 in all cells 0 0 1 me a ll s s n a sm i ni a g or

Proteins Core metabolism s ar g Su cids A o n i Am Nucleotides

Proteins Core metabolism s ar g Su cids A o n i Am Nucleotides Catabolism Fatty acids Cofact ors Carriers Precursors Nutrients Taxis and transport Polymerization and complex Autocatalytic feedback assembly Regulation Trans* & control Genes Regulation & control DNA replication The architecture of the cell.

Precursors Core metabolism rs a g Su cids A o n i m A

Precursors Core metabolism rs a g Su cids A o n i m A Nucleotides Catabolism Fatty acid s Cofact ors Carriers Nested bowties

Precursors Catabolism Carriers rs a g Su ds i c A o Amin Nucleotides

Precursors Catabolism Carriers rs a g Su ds i c A o Amin Nucleotides Fatty aci ds Cofact ors

Precursors Catabolism Carriers

Precursors Catabolism Carriers

Gly G 1 P G 6 P F 1 -6 BP Catabolism Gly 3

Gly G 1 P G 6 P F 1 -6 BP Catabolism Gly 3 p 13 BPG ATP 3 PG 2 PG NADH Oxa PEP Pyr ACA TCA Cit

Gly Precursors G 1 P G 6 P F 1 -6 BP Gly 3

Gly Precursors G 1 P G 6 P F 1 -6 BP Gly 3 p 13 BPG 3 PG 2 PG Oxa PEP Pyr ACA TCA Cit

Gly Precursors G 1 P G 6 P F 6 P Autocatalytic F 1

Gly Precursors G 1 P G 6 P F 6 P Autocatalytic F 1 -6 BP Gly 3 p Carriers ATP 13 BPG 3 PG 2 PG NADH Oxa PEP Pyr ACA TCA Cit

Gly G 1 P G 6 P Regulatory F 6 P F 1 -6

Gly G 1 P G 6 P Regulatory F 6 P F 1 -6 BP Gly 3 p ATP 13 BPG 3 PG 2 PG NADH Oxa PEP Pyr ACA TCA Cit

Gly G 1 P G 6 P F 1 -6 BP Gly 3 p

Gly G 1 P G 6 P F 1 -6 BP Gly 3 p 13 BPG 3 PG 2 PG Oxa PEP Pyr ACA TCA Cit

If we drew the feedback loops the diagram would be unreadable. Gly G 1

If we drew the feedback loops the diagram would be unreadable. Gly G 1 P G 6 P F 1 -6 BP Gly 3 p ATP 13 BPG 3 PG 2 PG Oxa PEP Pyr ACA TCA NADH Cit

Stoichiometry plus regulation Matrix of integers “Simple, ” can be known exactly Amenable to

Stoichiometry plus regulation Matrix of integers “Simple, ” can be known exactly Amenable to high throughput assays and manipulation Bowtie architecture Vector of (complex? ) functions Difficult to determine and manipulate Effected by stochastics and spatial/mechanical structure Hourglass architecture Can be modeled by optimal controller (? !? )

Precursors Catabolism Carriers rs a g Su ds i c A o Amin Nucleotides

Precursors Catabolism Carriers rs a g Su ds i c A o Amin Nucleotides Fatty aci ds Cofact ors

Component degrees are roughly exponential H Pylori 10 Rank 10 3 All Metabolites 2

Component degrees are roughly exponential H Pylori 10 Rank 10 3 All Metabolites 2 Exponential Others Carriers Exponential 10 Precursors Exponential 1 1 10 1 Number of reactions 10 2 0 20 40 60 Number of reactions

E Coli 2 10 Others Rank -5/4 Carriers 1 10 Precursors 0 10 1

E Coli 2 10 Others Rank -5/4 Carriers 1 10 Precursors 0 10 1 10 Degree 2 10 20 40 60 Degree 80 100 120

Precursors Catabolism 2 10 Others Rank -5/4 Carriers 1 10 Precursors 0 10 1

Precursors Catabolism 2 10 Others Rank -5/4 Carriers 1 10 Precursors 0 10 1 10 Degree 2 10 s r a g Su ds i c A o Amin Nucleotides Fatty aci ds Cofact ors