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Invented by Nature, Rediscovered by Man:Feedback Control Systems in Biology and Engineering                    Mustafa Kha...
Outline
Outline❖ Feedback control at the system level  ‣ Calcium homeostasis in mammals
Outline❖ Feedback control at the system level  ‣ Calcium homeostasis in mammals❖ Feedback control at the molecular level  ...
Outline❖ Feedback control at the system level  ‣ Calcium homeostasis in mammals❖ Feedback control at the molecular level  ...
Outline❖ Feedback control at the system level  ‣ Calcium homeostasis in mammals❖ Feedback control at the molecular level  ...
Outline❖ Feedback control at the system level  ‣ Calcium homeostasis in mammals❖ Feedback control at the molecular level  ...
Feedback Control at the System LevelCalcium homeostasis in mammals
Homeostasis              4
Homeostasis❖ "Homeostasis" is derived from the Greek words for "same" and  "steady."                                      ...
Homeostasis❖ "Homeostasis" is derived from the Greek words for "same" and  "steady."❖ Refers to ways the body acts to main...
Homeostasis❖ "Homeostasis" is derived from the Greek words for "same" and  "steady."❖ Refers to ways the body acts to main...
Homeostasis❖ "Homeostasis" is derived from the Greek words for "same" and  "steady."❖ Refers to ways the body acts to main...
Physiological Role of Calcium❖ Maintain the integrity of the skeleton.❖ Control of biochemical processes:  ‣ Intracellular...
Calcium Homeostasis in Mammals
Calcium Homeostasis in Mammals❖ The biochemical role of Calcium requires that its blood plasma  concentrations be precisel...
Calcium Homeostasis in Mammals❖ The biochemical role of Calcium requires that its blood plasma  concentrations be precisel...
Calcium Homeostasis in Mammals❖ The biochemical role of Calcium requires that its blood plasma  concentrations be precisel...
Calcium Homeostasis in Dairy Cows
Calcium Homeostasis in Dairy Cows                                                          Ca Clearance Rate              ...
Calcium Homeostasis in Dairy Cows                                                             Ca Clearance Rate           ...
Calcium Homeostasis in Dairy Cows                                                             Ca Clearance Rate           ...
A Disorder of Calcium Homeostasis❖ In some animals, the regulatory  mechanism fails to meet the  increased calcium demand❖...
Calcium Flow                        Milk, fetus       Formation                           FiltrationBone                  ...
Mathematical Modeling of [Ca]            Plasma
Mathematical Modeling of [Ca]Ca Total Supply Rate    VT (g/day) Intestinal Absorption                         Plasma Bone ...
Mathematical Modeling of [Ca]Ca Total Supply Rate              Total Ca Clearance Rate    VT (g/day)                      ...
Mathematical Modeling of [Ca]Ca Total Supply Rate                              Total Ca Clearance Rate    VT (g/day)      ...
in block diagram form...                 1   t        [Ca]p =        (VT − Vcl )dτ                Vol 0              Vcl  ...
VclSet point           e              VT       -                                        +            +            Control ...
Standard Model
Standard Model❖ A model describing the relation between VT and [Ca]p is given by:  Source: Ramberg, Johnson, Fargo, and Kr...
Standard Model❖ A model describing the relation between VT and [Ca]p is given by:  Source: Ramberg, Johnson, Fargo, and Kr...
Deficiencies in the Standard Model❖ From basic principles of control theory, proportional feedback alone  cannot explain: ...
Integral Feedback❖ In order to account for the zero state-state error integral feedback must  be present.❖ When combined w...
Implications of PI Feedback                      PI Feedback                                              Vcl    Set point...
Model vs. Experiment❖ Data from two groups of  normal lactating dairy  cows around the day of  calving (NADC)❖ One group w...
How Is Integral Action Realized?
How Is Integral Action Realized?❖ Our model was arrived at through necessity arguments
How Is Integral Action Realized?❖ Our model was arrived at through necessity arguments❖ Is there a plausible physiological...
How Is Integral Action Realized?❖ Our model was arrived at through necessity arguments❖ Is there a plausible physiological...
How Is Integral Action Realized?❖ Our model was arrived at through necessity arguments❖ Is there a plausible physiological...
A Two Hormone Solution…
A Two Hormone Solution…
A Two Hormone Solution…
A Two Hormone Solution…
A Two Hormone Solution…
Hormonal Regulation
Hormonal RegulationThe Parathyroid Gland monitors bloodcalcium and secretes Parathyroid Hormone(PTH) in proportion to [Ca]...
Hormonal RegulationThe Parathyroid Gland monitors bloodcalcium and secretes Parathyroid Hormone(PTH) in proportion to [Ca]...
Hormonal RegulationThe Parathyroid Gland monitors bloodcalcium and secretes Parathyroid Hormone(PTH) in proportion to [Ca]...
Hormonal RegulationThe Parathyroid Gland monitors bloodcalcium and secretes Parathyroid Hormone(PTH) in proportion to [Ca]...
Hormonal RegulationThe Parathyroid Gland monitors bloodcalcium and secretes Parathyroid Hormone(PTH) in proportion to [Ca]...
Hormonal RegulationThe Parathyroid Gland monitors bloodcalcium and secretes Parathyroid Hormone(PTH) in proportion to [Ca]...
Hormonal RegulationThe Parathyroid Gland monitors bloodcalcium and secretes Parathyroid Hormone(PTH) in proportion to [Ca]...
Hormonal RegulationThe Parathyroid Gland monitors bloodcalcium and secretes Parathyroid Hormone(PTH) in proportion to [Ca]...
Hormonal RegulationThe Parathyroid Gland monitors bloodcalcium and secretes Parathyroid Hormone(PTH) in proportion to [Ca]...
Hormonal RegulationThe Parathyroid Gland monitors bloodcalcium and secretes Parathyroid Hormone(PTH) in proportion to [Ca]...
The Integral Term• Two forms of Vitamin D: 25 (OH)D and 1,25 (OH)2 D• PTH activates 25 (OH)D in the kidney to form 1,25 OH...
23
Understanding Milk Fever ❖ The supply of calcium from the bone cannot be increased    indefinitely in response to an incre...
Breakdown Is Observed in Nonlinear Model Phase Portrait for Kp=3000, Ki=1200              Phase Portrait for Kp=5000, Ki=3...
Summary❖ Calcium homeostasis is achieved through integral feedback. Integral  action is realized by the dynamic interactio...
Control at the Molecular LevelBacterial Heat Shock Response
Gene Expression
Gene ExpressionTranscription                     mRNA      start                   DNA                                    ...
Gene ExpressionTranscription                     mRNA      start                   DNA                                    ...
Gene Expression                               Translation               proteins                             mRNATranscrip...
Gene Expression                               Translation               proteins                             mRNATranscrip...
Gene Expression                               Translation               proteins   Central Dogma of   Molecular Biology   ...
The Bug!
Cell
Cell Tempenviron
CellTemp cell         Temp        environ
CellUnfoldedProteins           Temp            cellFoldedProteins                    Temp                   environ
CellUnfoldedProteins           Aggregates                        Temp                         cellFoldedProteins          ...
Cell Loss of Protein   FunctionUnfoldedProteins                   Aggregates                                Temp          ...
Cell Loss of Protein         Network   Function               failureUnfoldedProteins                   Aggregates        ...
Cell Loss of Protein         Network   Function               failure                                            DeathUnfo...
The Heat-Shock Response
The Heat-Shock Response❖ High temperatures lead to heat induced stress due to a large  increase in protein unfolding/misfo...
The Heat-Shock Response❖ High temperatures lead to heat induced stress due to a large  increase in protein unfolding/misfo...
The Heat-Shock Response❖ High temperatures lead to heat induced stress due to a large  increase in protein unfolding/misfo...
Function of the Heat-Shock Proteins
Function of the Heat-Shock ProteinsI. Protein Folding                            DnaK/J   GroEL/                          ...
Function of the Heat-Shock Proteins I. Protein Folding                                DnaK/J     GroEL/                   ...
Heat-Shock Gene Transcription   start                 DNA          end           hsp1   hsp2promoter                      ...
Heat-Shock Gene Transcription           factor            start                 DNA          end                    hsp1  ...
Heat-Shock Gene Transcription   start                 DNA          end           hsp1   hsp2promoter                      ...
Heat-Shock Gene Transcription   start                 DNA          end           hsp1   hsp2promoter                      ...
Heat-Shock Gene Transcription   start                 DNA          end           hsp1   hsp2promoter                      ...
mRNA Translation                 Heat-Shock ProteinsmRNA         ribosomes
Regulation of the Heat Shock Response    Tight regulation of σ32 at 3 levels Synthesis     Activity         StabilityFeedf...
I. Regulation of σ32 Synthesis                                 mRNA                                        mRNA
I. Regulation of σ32 SynthesisAt low temperature, mRNA has a secondary structure                                          ...
I. Regulation of σ32 SynthesisAt low temperature, mRNA has a secondary structure                                          ...
I. Regulation of σ32 SynthesisAt low temperature, mRNA has a secondary structure                                          ...
I. Regulation of σ32 SynthesisAt low temperature, mRNA has a secondary structure                                          ...
II. Regulation of σ32 Activity: A Feedback Mechanism
II. Regulation of σ32 Activity: A Feedback MechanismRNAP      hsp1       hsp2
II. Regulation of σ32 Activity: A Feedback MechanismRNAP      hsp1       hsp2                            Transcription & T...
II. Regulation of σ32 Activity: A Feedback MechanismRNAP      hsp1       hsp2                            Transcription & T...
II. Regulation of σ32 Activity: A Feedback MechanismRNAP      hsp1       hsp2                            Transcription & T...
II. Regulation of σ32 Activity: A Feedback MechanismRNAP      hsp1       hsp2                            Transcription & T...
III. Regulation of σ32 DegradationFtsH degrades sigma-32 only when bound to chaperonesRNAP      hsp1         hsp2         ...
III. Regulation of σ32 DegradationFtsH degrades sigma-32 only when bound to chaperonesRNAP          hsp1     hsp2         ...
III. Regulation of σ32 DegradationFtsH degrades sigma-32 only when bound to chaperonesRNAP          hsp1          hsp2    ...
III. Regulation of σ32 DegradationFtsH degrades sigma-32 only when bound to chaperonesRNAP          hsp1          hsp2    ...
DisturbanceFF sensor                    FB Control          sensor                                        Plant       Actu...
σ mRNA                               Heat FF sensor                             sensor   Control                          ...
Mathematical ModelProteinSynthesis
BindingEquationsMass -BalanceEquations
600                                  24000                                                                       DnaK450  ...
Analysis of the Heat-Shock System❖ What are the advantages of the different control strategies  ‣ Disturbance feedforward ...
Analysis of the Heat-Shock System❖ What are the advantages of the different control strategies  ‣ Disturbance feedforward ...
Analysis of the Heat-Shock System❖ What are the advantages of the different control strategies  ‣ Disturbance feedforward ...
Analysis of the Heat-Shock System❖ What are the advantages of the different control strategies  ‣ Disturbance feedforward ...
Analysis of the Heat-Shock System❖ What are the advantages of the different control strategies  ‣ Disturbance feedforward ...
Analysis of the Heat-Shock System❖ What are the advantages of the different control strategies  ‣ Disturbance feedforward ...
600450                 Total σ32300150                               Wild type 0            0    10          20           ...
600450                 Total σ32300150                               Wild type                                  No feedfor...
600450                 Total σ32300150                               Wild type                                  No feedfor...
600450                 Total σ32300150                               Wild type                                  No feedfor...
600450                 Total σ32300150                               Wild type                                  No feedfor...
600                              2400                                                      DnaK450                Total σ3...
600                                  2400                                                          DnaK450                ...
600                                  2400                                                                 DnaK450         ...
Analysis of the Heat-Shock System❖ What are the advantages of the different control strategies
Analysis of the Heat-Shock System❖ What are the advantages of the different control strategies – Disturbance feedforward
Analysis of the Heat-Shock System❖ What are the advantages of the different control strategies – Disturbance feedforward  ...
Analysis of the Heat-Shock System❖ What are the advantages of the different control strategies – Disturbance feedforward  ...
Analysis of the Heat-Shock System❖ What are the advantages of the different control strategies – Disturbance feedforward  ...
Analysis of the Heat-Shock System❖ What are the advantages of the different control strategies – Disturbance feedforward  ...
Analysis of the Heat-Shock System❖ What are the advantages of the different control strategies – Disturbance feedforward  ...
Analysis of the Heat-Shock System❖ What are the advantages of the different control strategies – Disturbance feedforward  ...
Analysis of the Heat-Shock System❖ What are the advantages of the different control strategies – Disturbance feedforward  ...
Is the Wild Type Optimal?
Is the Wild Type Optimal?❖ Observation: A hypothetical heat-shock response system maybe  devised to achieve  ‣ a very smal...
Is the Wild Type Optimal?❖ Observation: A hypothetical heat-shock response system maybe  devised to achieve  ‣ a very smal...
Is the Wild Type Optimal?❖ Observation: A hypothetical heat-shock response system maybe  devised to achieve  ‣ a very smal...
Is the Wild Type Optimal?❖ Observation: A hypothetical heat-shock response system maybe  devised to achieve  ‣ a very smal...
Is the Wild Type Optimal?❖ Observation: A hypothetical heat-shock response system maybe  devised to achieve  ‣ a very smal...
❖ A well-designed system would be configured to  ‣ minimize unfolded proteins  ‣ minimize the chaperones used
❖ A well-designed system would be configured to  ‣ minimize unfolded proteins  ‣ minimize the chaperones used❖ A performan...
❖ A well-designed system would be configured to    ‣ minimize unfolded proteins    ‣ minimize the chaperones used❖ A perfo...
❖ A well-designed system would be configured to    ‣ minimize unfolded proteins    ‣ minimize the chaperones used❖ A perfo...
• For a fixed α, the optimal solution yields a single optimal point:                                   t1             Unfo...
• For a fixed α, the optimal solution yields a single optimal point:                                     t1              U...
Pareto Optimal Design of the    Heat Shock System                              100                                        ...
Pareto Optimal Design of the    Heat Shock System                              100                                        ...
1                             Sensitivity of DnaK to model parametersSensitivity of DnaK   10                       0     ...
1                                     Sensitivity of DnaK to model parameters                              10The complex a...
A Bio-Inspired Engineering Application Search strategies for unmanned aerial vehicles
Bacterial ChemotaxisE. coli must swim towardsnutrients or away from repellantsBacteria are too small to sensespatial gra...
Bacterial ChemotaxisE. coli must swim towardsnutrients or away from repellantsBacteria are too small to sensespatial gra...
The Flagellar MotorKeiichi NAMBA                         Francis et al., 1994
OptimotaxisAgents mimics bacteria chemotactic                            Advantages behavior with the goal of:          ...
Simulation Results Exponential turning rate model                      Different stages in optimotaxis in the presence of ...
Conclusions❖ Feedback regulation mechanisms are ubiquitous❖ A dynamical-systems and control approach can  ‣ Bring out the ...
❖ A systems approach enhances our understanding of biological  complexity  ‣ Notions such as robustness, adaptation, ampli...
Acknowledgement❖ Calcium homeostasis: Hana El-Samad (UCSF), Jess Goff (NADC)❖ Heat Shock: Hana El-Samad (UCSF), Carol Gros...
Calcium
Calcium
Calcium
Calcium
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  • in spite of environmental variations and disturbances\n Claude Bernard (1865)\n Recognized the prevalence of regulatory processes within the organisms (fixite du milieu interieur)\n Walter Cannon (1929)\n Coined the term “homeostasis” to describe the way by which the physical and chemical properties of a living organism are controlled—Wisdom of the Body\n Norbert Wiener (1948)\n Launched an important attempt for interdisciplinary coordination between system the oryand the biological sciences—Cybernetics.\n
  • in spite of environmental variations and disturbances\n Claude Bernard (1865)\n Recognized the prevalence of regulatory processes within the organisms (fixite du milieu interieur)\n Walter Cannon (1929)\n Coined the term “homeostasis” to describe the way by which the physical and chemical properties of a living organism are controlled—Wisdom of the Body\n Norbert Wiener (1948)\n Launched an important attempt for interdisciplinary coordination between system the oryand the biological sciences—Cybernetics.\n
  • in spite of environmental variations and disturbances\n Claude Bernard (1865)\n Recognized the prevalence of regulatory processes within the organisms (fixite du milieu interieur)\n Walter Cannon (1929)\n Coined the term “homeostasis” to describe the way by which the physical and chemical properties of a living organism are controlled—Wisdom of the Body\n Norbert Wiener (1948)\n Launched an important attempt for interdisciplinary coordination between system the oryand the biological sciences—Cybernetics.\n
  • in spite of environmental variations and disturbances\n Claude Bernard (1865)\n Recognized the prevalence of regulatory processes within the organisms (fixite du milieu interieur)\n Walter Cannon (1929)\n Coined the term “homeostasis” to describe the way by which the physical and chemical properties of a living organism are controlled—Wisdom of the Body\n Norbert Wiener (1948)\n Launched an important attempt for interdisciplinary coordination between system the oryand the biological sciences—Cybernetics.\n
  • 99% of all calcium is in the skeleton (1.5% of body weight)\n1% in body fluids. Blood coagulation, muscle contraction, nerve function\n
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  • (daily need is typically less than 20g/day)\n (up to 50 additional g/day)\n
  • (daily need is typically less than 20g/day)\n (up to 50 additional g/day)\n
  • (daily need is typically less than 20g/day)\n (up to 50 additional g/day)\n
  • (daily need is typically less than 20g/day)\n (up to 50 additional g/day)\n
  • (daily need is typically less than 20g/day)\n (up to 50 additional g/day)\n
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  • RNAP slides rapidly along DNA…Latches tightly when it encounters the promoter (sequence of nucleotides signifying start region)…Subunit of RNAP called sigma factor recognises promoter sequence…Opens up double helix, exposes nucleotides…One of the two DNA strands acts as a template for base pairing\nBy incoming ribonucleatides (AGCU). A medium sized gene ~1500 nucleotide pairs requires 50 seconds for transcription.\nThere maybe 15 RNAP for on one gene. Error rate is 10^-4 compared to 10^-7 in DNA replication.\nRNAP acts as a reading head.\n
  • RNAP slides rapidly along DNA…Latches tightly when it encounters the promoter (sequence of nucleotides signifying start region)…Subunit of RNAP called sigma factor recognises promoter sequence…Opens up double helix, exposes nucleotides…One of the two DNA strands acts as a template for base pairing\nBy incoming ribonucleatides (AGCU). A medium sized gene ~1500 nucleotide pairs requires 50 seconds for transcription.\nThere maybe 15 RNAP for on one gene. Error rate is 10^-4 compared to 10^-7 in DNA replication.\nRNAP acts as a reading head.\n
  • RNAP slides rapidly along DNA…Latches tightly when it encounters the promoter (sequence of nucleotides signifying start region)…Subunit of RNAP called sigma factor recognises promoter sequence…Opens up double helix, exposes nucleotides…One of the two DNA strands acts as a template for base pairing\nBy incoming ribonucleatides (AGCU). A medium sized gene ~1500 nucleotide pairs requires 50 seconds for transcription.\nThere maybe 15 RNAP for on one gene. Error rate is 10^-4 compared to 10^-7 in DNA replication.\nRNAP acts as a reading head.\n
  • RNAP slides rapidly along DNA…Latches tightly when it encounters the promoter (sequence of nucleotides signifying start region)…Subunit of RNAP called sigma factor recognises promoter sequence…Opens up double helix, exposes nucleotides…One of the two DNA strands acts as a template for base pairing\nBy incoming ribonucleatides (AGCU). A medium sized gene ~1500 nucleotide pairs requires 50 seconds for transcription.\nThere maybe 15 RNAP for on one gene. Error rate is 10^-4 compared to 10^-7 in DNA replication.\nRNAP acts as a reading head.\n
  • RNAP slides rapidly along DNA…Latches tightly when it encounters the promoter (sequence of nucleotides signifying start region)…Subunit of RNAP called sigma factor recognises promoter sequence…Opens up double helix, exposes nucleotides…One of the two DNA strands acts as a template for base pairing\nBy incoming ribonucleatides (AGCU). A medium sized gene ~1500 nucleotide pairs requires 50 seconds for transcription.\nThere maybe 15 RNAP for on one gene. Error rate is 10^-4 compared to 10^-7 in DNA replication.\nRNAP acts as a reading head.\n
  • RNAP slides rapidly along DNA…Latches tightly when it encounters the promoter (sequence of nucleotides signifying start region)…Subunit of RNAP called sigma factor recognises promoter sequence…Opens up double helix, exposes nucleotides…One of the two DNA strands acts as a template for base pairing\nBy incoming ribonucleatides (AGCU). A medium sized gene ~1500 nucleotide pairs requires 50 seconds for transcription.\nThere maybe 15 RNAP for on one gene. Error rate is 10^-4 compared to 10^-7 in DNA replication.\nRNAP acts as a reading head.\n
  • RNAP slides rapidly along DNA…Latches tightly when it encounters the promoter (sequence of nucleotides signifying start region)…Subunit of RNAP called sigma factor recognises promoter sequence…Opens up double helix, exposes nucleotides…One of the two DNA strands acts as a template for base pairing\nBy incoming ribonucleatides (AGCU). A medium sized gene ~1500 nucleotide pairs requires 50 seconds for transcription.\nThere maybe 15 RNAP for on one gene. Error rate is 10^-4 compared to 10^-7 in DNA replication.\nRNAP acts as a reading head.\n
  • RNAP slides rapidly along DNA…Latches tightly when it encounters the promoter (sequence of nucleotides signifying start region)…Subunit of RNAP called sigma factor recognises promoter sequence…Opens up double helix, exposes nucleotides…One of the two DNA strands acts as a template for base pairing\nBy incoming ribonucleatides (AGCU). A medium sized gene ~1500 nucleotide pairs requires 50 seconds for transcription.\nThere maybe 15 RNAP for on one gene. Error rate is 10^-4 compared to 10^-7 in DNA replication.\nRNAP acts as a reading head.\n
  • RNAP slides rapidly along DNA…Latches tightly when it encounters the promoter (sequence of nucleotides signifying start region)…Subunit of RNAP called sigma factor recognises promoter sequence…Opens up double helix, exposes nucleotides…One of the two DNA strands acts as a template for base pairing\nBy incoming ribonucleatides (AGCU). A medium sized gene ~1500 nucleotide pairs requires 50 seconds for transcription.\nThere maybe 15 RNAP for on one gene. Error rate is 10^-4 compared to 10^-7 in DNA replication.\nRNAP acts as a reading head.\n
  • RNAP slides rapidly along DNA…Latches tightly when it encounters the promoter (sequence of nucleotides signifying start region)…Subunit of RNAP called sigma factor recognises promoter sequence…Opens up double helix, exposes nucleotides…One of the two DNA strands acts as a template for base pairing\nBy incoming ribonucleatides (AGCU). A medium sized gene ~1500 nucleotide pairs requires 50 seconds for transcription.\nThere maybe 15 RNAP for on one gene. Error rate is 10^-4 compared to 10^-7 in DNA replication.\nRNAP acts as a reading head.\n
  • RNAP slides rapidly along DNA…Latches tightly when it encounters the promoter (sequence of nucleotides signifying start region)…Subunit of RNAP called sigma factor recognises promoter sequence…Opens up double helix, exposes nucleotides…One of the two DNA strands acts as a template for base pairing\nBy incoming ribonucleatides (AGCU). A medium sized gene ~1500 nucleotide pairs requires 50 seconds for transcription.\nThere maybe 15 RNAP for on one gene. Error rate is 10^-4 compared to 10^-7 in DNA replication.\nRNAP acts as a reading head.\n
  • RNAP slides rapidly along DNA…Latches tightly when it encounters the promoter (sequence of nucleotides signifying start region)…Subunit of RNAP called sigma factor recognises promoter sequence…Opens up double helix, exposes nucleotides…One of the two DNA strands acts as a template for base pairing\nBy incoming ribonucleatides (AGCU). A medium sized gene ~1500 nucleotide pairs requires 50 seconds for transcription.\nThere maybe 15 RNAP for on one gene. Error rate is 10^-4 compared to 10^-7 in DNA replication.\nRNAP acts as a reading head.\n
  • RNAP slides rapidly along DNA…Latches tightly when it encounters the promoter (sequence of nucleotides signifying start region)…Subunit of RNAP called sigma factor recognises promoter sequence…Opens up double helix, exposes nucleotides…One of the two DNA strands acts as a template for base pairing\nBy incoming ribonucleatides (AGCU). A medium sized gene ~1500 nucleotide pairs requires 50 seconds for transcription.\nThere maybe 15 RNAP for on one gene. Error rate is 10^-4 compared to 10^-7 in DNA replication.\nRNAP acts as a reading head.\n
  • RNAP slides rapidly along DNA…Latches tightly when it encounters the promoter (sequence of nucleotides signifying start region)…Subunit of RNAP called sigma factor recognises promoter sequence…Opens up double helix, exposes nucleotides…One of the two DNA strands acts as a template for base pairing\nBy incoming ribonucleatides (AGCU). A medium sized gene ~1500 nucleotide pairs requires 50 seconds for transcription.\nThere maybe 15 RNAP for on one gene. Error rate is 10^-4 compared to 10^-7 in DNA replication.\nRNAP acts as a reading head.\n
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  • Transcript of "Calcium"

    1. 1. Invented by Nature, Rediscovered by Man:Feedback Control Systems in Biology and Engineering Mustafa Khammash University of California, Santa Barbara
    2. 2. Outline
    3. 3. Outline❖ Feedback control at the system level ‣ Calcium homeostasis in mammals
    4. 4. Outline❖ Feedback control at the system level ‣ Calcium homeostasis in mammals❖ Feedback control at the molecular level ‣ The bacterial Heat-Shock Response
    5. 5. Outline❖ Feedback control at the system level ‣ Calcium homeostasis in mammals❖ Feedback control at the molecular level ‣ The bacterial Heat-Shock Response❖ A Bio-Inspired Engineering Application ‣ Search strategies for unmanned aerial vehicles
    6. 6. Outline❖ Feedback control at the system level ‣ Calcium homeostasis in mammals❖ Feedback control at the molecular level ‣ The bacterial Heat-Shock Response❖ A Bio-Inspired Engineering Application ‣ Search strategies for unmanned aerial vehicles❖ Challenges and opportunities
    7. 7. Outline❖ Feedback control at the system level ‣ Calcium homeostasis in mammals❖ Feedback control at the molecular level ‣ The bacterial Heat-Shock Response❖ A Bio-Inspired Engineering Application ‣ Search strategies for unmanned aerial vehicles❖ Challenges and opportunities❖ Conclusions
    8. 8. Feedback Control at the System LevelCalcium homeostasis in mammals
    9. 9. Homeostasis 4
    10. 10. Homeostasis❖ "Homeostasis" is derived from the Greek words for "same" and "steady." 4
    11. 11. Homeostasis❖ "Homeostasis" is derived from the Greek words for "same" and "steady."❖ Refers to ways the body acts to maintain a stable internal environment. 4
    12. 12. Homeostasis❖ "Homeostasis" is derived from the Greek words for "same" and "steady."❖ Refers to ways the body acts to maintain a stable internal environment.❖ The body is endowed with a multitude of automatic mechanisms of feedback that counteract influences tending toward disequilibrium. 4
    13. 13. Homeostasis❖ "Homeostasis" is derived from the Greek words for "same" and "steady."❖ Refers to ways the body acts to maintain a stable internal environment.❖ The body is endowed with a multitude of automatic mechanisms of feedback that counteract influences tending toward disequilibrium.❖ In history: ‣ Claude Bernard (1865) -- Fixité du milieu intérieur ‣ Walter Cannon (1929) -- Homeostasis ‣ Norbert Wiener (1948) -- Cybernetics 4
    14. 14. Physiological Role of Calcium❖ Maintain the integrity of the skeleton.❖ Control of biochemical processes: ‣ Intracellular: - Activity of a large number of enzymes - Conveying information from the surface to the interior of the cell ‣ Extracellular: - Muscle and nerve function - Blood clotting
    15. 15. Calcium Homeostasis in Mammals
    16. 16. Calcium Homeostasis in Mammals❖ The biochemical role of Calcium requires that its blood plasma concentrations be precisely controlled
    17. 17. Calcium Homeostasis in Mammals❖ The biochemical role of Calcium requires that its blood plasma concentrations be precisely controlled❖ Normal concentration of about 9 mg/dl must be maintained within small tolerances despite ‣ variations in dietary calcium levels ‣ variation in demand for calcium
    18. 18. Calcium Homeostasis in Mammals❖ The biochemical role of Calcium requires that its blood plasma concentrations be precisely controlled❖ Normal concentration of about 9 mg/dl must be maintained within small tolerances despite ‣ variations in dietary calcium levels ‣ variation in demand for calcium❖ Humans and other mammals have an effective feedback mechanism for regulating plasma concentration of calcium [Ca]p
    19. 19. Calcium Homeostasis in Dairy Cows
    20. 20. Calcium Homeostasis in Dairy Cows Ca Clearance Rate 100 90❖ Plasma concentrations are 80 70 easily maintained during g/day 60 periods of nonlactation 50 40 30 20 10 0 10 12 14 16 18 20 22 time (days) Plasma Ca Concentration 0.1 0.095 0.09 0.085 g/l 0.08 0.075 0.07 0.065 0.06 0.055 0.05 10 12 14 16 18 20 22 time (days) Parturition
    21. 21. Calcium Homeostasis in Dairy Cows Ca Clearance Rate 100 90❖ Plasma concentrations are 80 70 easily maintained during g/day 60 periods of nonlactation 50 40 30❖ An especially large loss of 20 plasma calcium to milk takes 10 0 10 12 14 16 18 20 22 place during lactation time (days) Plasma Ca Concentration 0.1 0.095 0.09 0.085 g/l 0.08 0.075 0.07 0.065 0.06 0.055 0.05 10 12 14 16 18 20 22 time (days) Parturition
    22. 22. Calcium Homeostasis in Dairy Cows Ca Clearance Rate 100 90❖ Plasma concentrations are 80 70 easily maintained during g/day 60 periods of nonlactation 50 40 30❖ An especially large loss of 20 plasma calcium to milk takes 10 0 10 12 14 16 18 20 22 place during lactation time (days) Plasma Ca Concentration❖ Most animals adapt to the 0.1 0.095 onset of lactation 0.09 0.085 g/l 0.08 0.075 0.07 0.065 0.06 0.055 0.05 10 12 14 16 18 20 22 time (days) Parturition
    23. 23. A Disorder of Calcium Homeostasis❖ In some animals, the regulatory mechanism fails to meet the increased calcium demand❖ Animals become hypocalcemic ‣ Results in disruption of muscle and nerve function ‣ Leads to recumbency❖ The clinical syndrome is Parturient Paresis (Milk Fever)❖ Affects 6% of the dairy cows in the US
    24. 24. Calcium Flow Milk, fetus Formation FiltrationBone Calcium pool Kidney Resorption reabsorption Secretion Absorption Intestine
    25. 25. Mathematical Modeling of [Ca] Plasma
    26. 26. Mathematical Modeling of [Ca]Ca Total Supply Rate VT (g/day) Intestinal Absorption Plasma Bone Resorption
    27. 27. Mathematical Modeling of [Ca]Ca Total Supply Rate Total Ca Clearance Rate VT (g/day) Vcl (g/day) Intestinal Absorption Plasma Milk, fetus, urine, etc. Bone Resorption
    28. 28. Mathematical Modeling of [Ca]Ca Total Supply Rate Total Ca Clearance Rate VT (g/day) Vcl (g/day) Intestinal Absorption Plasma Milk, fetus, urine, etc. Bone Resorption Vol = Plasma Volume (l) [Ca]p = Plasma Concentration (g/l)
    29. 29. in block diagram form... 1 t [Ca]p = (VT − Vcl )dτ Vol 0 Vcl - VT + k
    30. 30. VclSet point e VT - + + Control - e = error (g/l) what is f (·) ?
    31. 31. Standard Model
    32. 32. Standard Model❖ A model describing the relation between VT and [Ca]p is given by: Source: Ramberg, Johnson, Fargo, and Kronfeld, “Calcium homeostasis in cows, with special reference to parturient hypocalcemia,” Am. J. Physiol. , 1984.
    33. 33. Standard Model❖ A model describing the relation between VT and [Ca]p is given by: Source: Ramberg, Johnson, Fargo, and Kronfeld, “Calcium homeostasis in cows, with special reference to parturient hypocalcemia,” Am. J. Physiol. , 1984. This is proportional feedback! VT = Kp e
    34. 34. Deficiencies in the Standard Model❖ From basic principles of control theory, proportional feedback alone cannot explain: ‣ The observed zero steady-state error (Perfect Adaptation) ‣ The shape of the time response of [Ca]p following increased Calcium clearance at calving
    35. 35. Integral Feedback❖ In order to account for the zero state-state error integral feedback must be present.❖ When combined with Proportional Feedback, Integral Feedback will account for ‣ The zero steady-state error in response to Ca clearance ‣ The second order shape of the [Ca]p time response❖ We propose the feedback:
    36. 36. Implications of PI Feedback PI Feedback Vcl Set point e VT + - + + -❖ Supply rate depends on both the level and duration of calcium deficiency prior to and until the time of interest.❖ Understanding the dynamics of the system is unavoidable.
    37. 37. Model vs. Experiment❖ Data from two groups of normal lactating dairy cows around the day of calving (NADC)❖ One group was used to determine model parameters❖ The model prediction was compared against data from the second group (20 animals) 17
    38. 38. How Is Integral Action Realized?
    39. 39. How Is Integral Action Realized?❖ Our model was arrived at through necessity arguments
    40. 40. How Is Integral Action Realized?❖ Our model was arrived at through necessity arguments❖ Is there a plausible physiological basis?
    41. 41. How Is Integral Action Realized?❖ Our model was arrived at through necessity arguments❖ Is there a plausible physiological basis?❖ Given that calcium is hormonally regulated, what is the mechanism through which integration is realized?
    42. 42. How Is Integral Action Realized?❖ Our model was arrived at through necessity arguments❖ Is there a plausible physiological basis?❖ Given that calcium is hormonally regulated, what is the mechanism through which integration is realized? Can a single hormone be at work? • P feedback: • PI feedback:
    43. 43. A Two Hormone Solution…
    44. 44. A Two Hormone Solution…
    45. 45. A Two Hormone Solution…
    46. 46. A Two Hormone Solution…
    47. 47. A Two Hormone Solution…
    48. 48. Hormonal Regulation
    49. 49. Hormonal RegulationThe Parathyroid Gland monitors bloodcalcium and secretes Parathyroid Hormone(PTH) in proportion to [Ca] deficiency
    50. 50. Hormonal RegulationThe Parathyroid Gland monitors bloodcalcium and secretes Parathyroid Hormone(PTH) in proportion to [Ca] deficiency
    51. 51. Hormonal RegulationThe Parathyroid Gland monitors bloodcalcium and secretes Parathyroid Hormone(PTH) in proportion to [Ca] deficiency
    52. 52. Hormonal RegulationThe Parathyroid Gland monitors bloodcalcium and secretes Parathyroid Hormone(PTH) in proportion to [Ca] deficiency
    53. 53. Hormonal RegulationThe Parathyroid Gland monitors bloodcalcium and secretes Parathyroid Hormone(PTH) in proportion to [Ca] deficiencyPTH stimulates renal calciumreabsorption and bone resorption
    54. 54. Hormonal RegulationThe Parathyroid Gland monitors bloodcalcium and secretes Parathyroid Hormone(PTH) in proportion to [Ca] deficiencyPTH stimulates renal calciumreabsorption and bone resorption
    55. 55. Hormonal RegulationThe Parathyroid Gland monitors bloodcalcium and secretes Parathyroid Hormone(PTH) in proportion to [Ca] deficiencyPTH stimulates renal calciumreabsorption and bone resorption(1,25 OH2 D3) Hormone stimulatescalcium absorption from the intestine
    56. 56. Hormonal RegulationThe Parathyroid Gland monitors bloodcalcium and secretes Parathyroid Hormone(PTH) in proportion to [Ca] deficiencyPTH stimulates renal calciumreabsorption and bone resorption(1,25 OH2 D3) Hormone stimulatescalcium absorption from the intestine
    57. 57. Hormonal RegulationThe Parathyroid Gland monitors bloodcalcium and secretes Parathyroid Hormone(PTH) in proportion to [Ca] deficiencyPTH stimulates renal calciumreabsorption and bone resorption(1,25 OH2 D3) Hormone stimulatescalcium absorption from the intestineBone resporption and intestinal absorptionaccount for the entire calcium supply
    58. 58. Hormonal RegulationThe Parathyroid Gland monitors bloodcalcium and secretes Parathyroid Hormone(PTH) in proportion to [Ca] deficiencyPTH stimulates renal calciumreabsorption and bone resorption(1,25 OH2 D3) Hormone stimulatescalcium absorption from the intestineBone resporption and intestinal absorptionaccount for the entire calcium supply
    59. 59. The Integral Term• Two forms of Vitamin D: 25 (OH)D and 1,25 (OH)2 D• PTH activates 25 (OH)D in the kidney to form 1,25 OH2 D PTH 25 (OH)D 1,25 (OH)2D For a given [25 (OH)D]:
    60. 60. 23
    61. 61. Understanding Milk Fever ❖ The supply of calcium from the bone cannot be increased indefinitely in response to an increases in [PTH] ❖ Absorption is transiently reduced as a result of low calcium VclSet point e VT - + + + - x
    62. 62. Breakdown Is Observed in Nonlinear Model Phase Portrait for Kp=3000, Ki=1200 Phase Portrait for Kp=5000, Ki=3000 Initial condition (low clearance EP) Breakdown Homeostasis is achieved
    63. 63. Summary❖ Calcium homeostasis is achieved through integral feedback. Integral action is realized by the dynamic interaction among 1,25 (OH)2D and PTH❖ Sequence of discovery: Perfect adaptation necessity of integral action  specific action at molecular level❖ The dynamic interactions give a new perspective on calcium homeostasis disorders and disease trajectories❖ Future work: ‣ Other homeostatic mechanisms, e.g. blood sugar, diabetes ‣ Osteoporosis 26
    64. 64. Control at the Molecular LevelBacterial Heat Shock Response
    65. 65. Gene Expression
    66. 66. Gene ExpressionTranscription mRNA start DNA end promoter RNA polymerase
    67. 67. Gene ExpressionTranscription mRNA start DNA mRNA end promoter RNA polymerase DNA
    68. 68. Gene Expression Translation proteins mRNATranscription ribosomes mRNA start DNA mRNA end promoter RNA polymerase DNA
    69. 69. Gene Expression Translation proteins mRNATranscription ribosomes mRNA protein start DNA mRNA end promoter RNA polymerase DNA
    70. 70. Gene Expression Translation proteins Central Dogma of Molecular Biology mRNATranscription ribosomes mRNA protein start DNA mRNA end promoter RNA polymerase DNA
    71. 71. The Bug!
    72. 72. Cell
    73. 73. Cell Tempenviron
    74. 74. CellTemp cell Temp environ
    75. 75. CellUnfoldedProteins Temp cellFoldedProteins Temp environ
    76. 76. CellUnfoldedProteins Aggregates Temp cellFoldedProteins Temp environ
    77. 77. Cell Loss of Protein FunctionUnfoldedProteins Aggregates Temp cellFoldedProteins Temp environ
    78. 78. Cell Loss of Protein Network Function failureUnfoldedProteins Aggregates Temp cellFoldedProteins Temp environ
    79. 79. Cell Loss of Protein Network Function failure DeathUnfoldedProteins Aggregates Temp cellFoldedProteins Temp environ
    80. 80. The Heat-Shock Response
    81. 81. The Heat-Shock Response❖ High temperatures lead to heat induced stress due to a large increase in protein unfolding/misfolding
    82. 82. The Heat-Shock Response❖ High temperatures lead to heat induced stress due to a large increase in protein unfolding/misfolding❖ The heat-shock response is a protective cellular response to deal with heat-induced protein damage.
    83. 83. The Heat-Shock Response❖ High temperatures lead to heat induced stress due to a large increase in protein unfolding/misfolding❖ The heat-shock response is a protective cellular response to deal with heat-induced protein damage.❖ It involves building and dispatching heat-shock proteins (HSPs) ‣ Chaperones: refold denatured proteins ‣ Proteases: degrade aggregated proteins
    84. 84. Function of the Heat-Shock Proteins
    85. 85. Function of the Heat-Shock ProteinsI. Protein Folding DnaK/J GroEL/ GroESUnfolded/partially folded Proteins Folded Proteins
    86. 86. Function of the Heat-Shock Proteins I. Protein Folding DnaK/J GroEL/ GroES Unfolded/partially folded ProteinsII. Protein Degradation Proteases Folded Amino Acids ProteinsProteins Aggregates
    87. 87. Heat-Shock Gene Transcription start DNA end hsp1 hsp2promoter terminator
    88. 88. Heat-Shock Gene Transcription factor start DNA end hsp1 hsp2 promoter terminatorRNA Polymerase
    89. 89. Heat-Shock Gene Transcription start DNA end hsp1 hsp2promoter terminator
    90. 90. Heat-Shock Gene Transcription start DNA end hsp1 hsp2promoter terminator
    91. 91. Heat-Shock Gene Transcription start DNA end hsp1 hsp2promoter terminator
    92. 92. mRNA Translation Heat-Shock ProteinsmRNA ribosomes
    93. 93. Regulation of the Heat Shock Response Tight regulation of σ32 at 3 levels Synthesis Activity StabilityFeedforward Feedback
    94. 94. I. Regulation of σ32 Synthesis mRNA mRNA
    95. 95. I. Regulation of σ32 SynthesisAt low temperature, mRNA has a secondary structure mRNA mRNA
    96. 96. I. Regulation of σ32 SynthesisAt low temperature, mRNA has a secondary structure mRNA Heat mRNA
    97. 97. I. Regulation of σ32 SynthesisAt low temperature, mRNA has a secondary structure mRNA Heat mRNA
    98. 98. I. Regulation of σ32 SynthesisAt low temperature, mRNA has a secondary structure mRNA Translation Heat mRNA
    99. 99. II. Regulation of σ32 Activity: A Feedback Mechanism
    100. 100. II. Regulation of σ32 Activity: A Feedback MechanismRNAP hsp1 hsp2
    101. 101. II. Regulation of σ32 Activity: A Feedback MechanismRNAP hsp1 hsp2 Transcription & Translation Chaperones
    102. 102. II. Regulation of σ32 Activity: A Feedback MechanismRNAP hsp1 hsp2 Transcription & Translation Chaperones Heat
    103. 103. II. Regulation of σ32 Activity: A Feedback MechanismRNAP hsp1 hsp2 Transcription & Translation Chaperones Heat
    104. 104. II. Regulation of σ32 Activity: A Feedback MechanismRNAP hsp1 hsp2 Transcription & Translation Chaperones Heat
    105. 105. III. Regulation of σ32 DegradationFtsH degrades sigma-32 only when bound to chaperonesRNAP hsp1 hsp2 Transcription & Translation Chaperones Heat
    106. 106. III. Regulation of σ32 DegradationFtsH degrades sigma-32 only when bound to chaperonesRNAP hsp1 hsp2 Transcription & Translation Proteases Chaperones Heat FtsH FtsH FtsH
    107. 107. III. Regulation of σ32 DegradationFtsH degrades sigma-32 only when bound to chaperonesRNAP hsp1 hsp2 Transcription & Translation Proteases Chaperones Heat FtsH FtsH FtsH FtsH
    108. 108. III. Regulation of σ32 DegradationFtsH degrades sigma-32 only when bound to chaperonesRNAP hsp1 hsp2 Transcription & Translation Proteases Chaperones Heat FtsH FtsH FtsH FtsH
    109. 109. DisturbanceFF sensor FB Control sensor Plant Actuator A control theorist’s view. What is the relation to the HS system?
    110. 110. σ mRNA Heat FF sensor sensor Control PlantRNAP FtsH Actuator RNAP hsp1 hsp2
    111. 111. Mathematical ModelProteinSynthesis
    112. 112. BindingEquationsMass -BalanceEquations
    113. 113. 600 24000 DnaK450 Total σ32 16000 16000300 12000150 0 8000 0 10 20 0 10 20 0 Time (min) 30 42o 30 42o o o 8 E+ 06 6 4 Free σ32 Unfolded Proteins 2 0 0 0 10 20 0 0 10 20 Time (min) Time (min)
    114. 114. Analysis of the Heat-Shock System❖ What are the advantages of the different control strategies ‣ Disturbance feedforward ‣ Activity feedback loop ‣ Degradation feedback loop ‣ High sigma-32 flux❖ What lies behind the complexity?
    115. 115. Analysis of the Heat-Shock System❖ What are the advantages of the different control strategies ‣ Disturbance feedforward ‣ Activity feedback loop ‣ Degradation feedback loop ‣ High sigma-32 flux❖ What lies behind the complexity?Analysis Tools
    116. 116. Analysis of the Heat-Shock System❖ What are the advantages of the different control strategies ‣ Disturbance feedforward ‣ Activity feedback loop ‣ Degradation feedback loop ‣ High sigma-32 flux❖ What lies behind the complexity?Analysis Tools ‣ Dynamic analysis and simulations
    117. 117. Analysis of the Heat-Shock System❖ What are the advantages of the different control strategies ‣ Disturbance feedforward ‣ Activity feedback loop ‣ Degradation feedback loop ‣ High sigma-32 flux❖ What lies behind the complexity?Analysis Tools ‣ Dynamic analysis and simulations ‣ Sensitivity/robustness analysis
    118. 118. Analysis of the Heat-Shock System❖ What are the advantages of the different control strategies ‣ Disturbance feedforward ‣ Activity feedback loop ‣ Degradation feedback loop ‣ High sigma-32 flux❖ What lies behind the complexity?Analysis Tools ‣ Dynamic analysis and simulations ‣ Sensitivity/robustness analysis ‣ Sum-of-Squares tools
    119. 119. Analysis of the Heat-Shock System❖ What are the advantages of the different control strategies ‣ Disturbance feedforward ‣ Activity feedback loop ‣ Degradation feedback loop ‣ High sigma-32 flux❖ What lies behind the complexity?Analysis Tools ‣ Dynamic analysis and simulations ‣ Sensitivity/robustness analysis ‣ Sum-of-Squares tools ‣ Optimal control
    120. 120. 600450 Total σ32300150 Wild type 0 0 10 20 0 Time (min) 30o 42o
    121. 121. 600450 Total σ32300150 Wild type No feedforward 0 0 10 20 0 Time (min) 30o 42o
    122. 122. 600450 Total σ32300150 Wild type No feedforward 0 0 10 20 0 No DnaK interaction Time (min) 30o 42o
    123. 123. 600450 Total σ32300150 Wild type No feedforward 0 0 10 20 0 No DnaK interaction Time (min) Constitutive σ32 degradation 30o 42o
    124. 124. 600450 Total σ32300150 Wild type No feedforward 0 0 10 20 0 No DnaK interaction Time (min) Constitutive σ32 degradation 30o 42o Low σ32 flux
    125. 125. 600 2400 DnaK450 Total σ32 1600300 1600 1200150 Wild type No feedforward 800 0 0 10 20 0 10 No DnaK interaction 20 0 Time (min) Constitutive σ32 degradation 30 42o Low σ32 flux o
    126. 126. 600 2400 DnaK450 Total σ32 1600300 1600 1200150 Wild type No feedforward 800 0 0 10 20 0 10 No DnaK interaction 20 0 Time (min) Constitutive σ32 degradation 30 42o Low σ32 flux o 8 6 4 Free σ32 2 0 10 20 0 0 Time (min)
    127. 127. 600 2400 DnaK450 Total σ32 1600300 1600 1200150 Wild type No feedforward 800 0 0 10 20 0 10 No DnaK interaction 20 0 Time (min) Constitutive σ32 degradation 30 42o Low σ32 flux o 8 E+ 06 6 4 Free σ32 Unfolded Proteins 2 0 0 0 10 20 0 0 10 20 Time (min) Time (min)
    128. 128. Analysis of the Heat-Shock System❖ What are the advantages of the different control strategies
    129. 129. Analysis of the Heat-Shock System❖ What are the advantages of the different control strategies – Disturbance feedforward
    130. 130. Analysis of the Heat-Shock System❖ What are the advantages of the different control strategies – Disturbance feedforward Fast response
    131. 131. Analysis of the Heat-Shock System❖ What are the advantages of the different control strategies – Disturbance feedforward Fast response – Activity feedback loop
    132. 132. Analysis of the Heat-Shock System❖ What are the advantages of the different control strategies – Disturbance feedforward Fast response – Activity feedback loop Robustness, efficiency
    133. 133. Analysis of the Heat-Shock System❖ What are the advantages of the different control strategies – Disturbance feedforward Fast response – Activity feedback loop Robustness, efficiency – Degradation feedback loop
    134. 134. Analysis of the Heat-Shock System❖ What are the advantages of the different control strategies – Disturbance feedforward Fast response – Activity feedback loop Robustness, efficiency – Degradation feedback loop Fast response, noise suppression
    135. 135. Analysis of the Heat-Shock System❖ What are the advantages of the different control strategies – Disturbance feedforward Fast response – Activity feedback loop Robustness, efficiency – Degradation feedback loop Fast response, noise suppression – High sigma-32 flux
    136. 136. Analysis of the Heat-Shock System❖ What are the advantages of the different control strategies – Disturbance feedforward Fast response – Activity feedback loop Robustness, efficiency – Degradation feedback loop Fast response, noise suppression – High sigma-32 flux Fast response
    137. 137. Is the Wild Type Optimal?
    138. 138. Is the Wild Type Optimal?❖ Observation: A hypothetical heat-shock response system maybe devised to achieve ‣ a very small number of unfolded proteins ‣ minimal complexity (no feedback necessary)
    139. 139. Is the Wild Type Optimal?❖ Observation: A hypothetical heat-shock response system maybe devised to achieve ‣ a very small number of unfolded proteins ‣ minimal complexity (no feedback necessary)❖ E.g. over-expressing chaperones & eliminating feedback
    140. 140. Is the Wild Type Optimal?❖ Observation: A hypothetical heat-shock response system maybe devised to achieve ‣ a very small number of unfolded proteins ‣ minimal complexity (no feedback necessary)❖ E.g. over-expressing chaperones & eliminating feedback❖ However… chaperone over-expression ‣ a high metabolic cost ‣ is toxic to the cell
    141. 141. Is the Wild Type Optimal?❖ Observation: A hypothetical heat-shock response system maybe devised to achieve ‣ a very small number of unfolded proteins ‣ minimal complexity (no feedback necessary)❖ E.g. over-expressing chaperones & eliminating feedback❖ However… chaperone over-expression ‣ a high metabolic cost ‣ is toxic to the cell❖ The existing design appears to achieve a tradeoff: good folding achieved with minimal number of chaperones
    142. 142. Is the Wild Type Optimal?❖ Observation: A hypothetical heat-shock response system maybe devised to achieve ‣ a very small number of unfolded proteins ‣ minimal complexity (no feedback necessary)❖ E.g. over-expressing chaperones & eliminating feedback❖ However… chaperone over-expression ‣ a high metabolic cost ‣ is toxic to the cell❖ The existing design appears to achieve a tradeoff: good folding achieved with minimal number of chaperones❖ How optimal is the WT design?
    143. 143. ❖ A well-designed system would be configured to ‣ minimize unfolded proteins ‣ minimize the chaperones used
    144. 144. ❖ A well-designed system would be configured to ‣ minimize unfolded proteins ‣ minimize the chaperones used❖ A performance index that captures how well this is achieved: α reflects the relative importance between unfolded proteins and DnaK
    145. 145. ❖ A well-designed system would be configured to ‣ minimize unfolded proteins ‣ minimize the chaperones used❖ A performance index that captures how well this is achieved: α reflects the relative importance between unfolded proteins and DnaK❖ depends on the system parameters . An optimally designed θ system would minimize €
    146. 146. ❖ A well-designed system would be configured to ‣ minimize unfolded proteins ‣ minimize the chaperones used❖ A performance index that captures how well this is achieved: α reflects the relative importance between unfolded proteins and DnaK❖ depends on the system parameters . An optimally designed θ system would minimize❖ We solve this optimization problem in silico: €
    147. 147. • For a fixed α, the optimal solution yields a single optimal point: t1 Unfolded proteins : ∫ [P un ]2 dt t0 € t1 2 cost of chaperones : ∫ [DnaK ] dt t0 €
    148. 148. • For a fixed α, the optimal solution yields a single optimal point: t1 Unfolded proteins : ∫ [P un ]2 dt t0 € t1 2 cost of chaperones : ∫ [DnaK ] dt t0• If we solve the optimization for all α>0, we get an optimal curv € t1 Unfolded proteins : ∫ [P un ]2 dt t0 Non-optimal Optimal designs € unachievable t1 2 cost of chaperones : ∫ [DnaK ] dt t0
    149. 149. Pareto Optimal Design of the Heat Shock System 100 P areto O ptimal curve 80 Cost of u nfolded proteins 60 40 20 W ild type heat shock 0 10 11 12 t1 Cost of chape rones ∫ [DnaK ]2 dt t0
    150. 150. Pareto Optimal Design of the Heat Shock System 100 P areto O ptimal curve 80 Cost of u nfolded proteins various nonoptimal values 60 of parameters 40 20 W ild type heat shock 0 10 11 12 t1 Cost of chape rones ∫ [DnaK ]2 dt t0
    151. 151. 1 Sensitivity of DnaK to model parametersSensitivity of DnaK 10 0 10 -1 10 -2 10 -3 10 -4 10 -5 10 100 200 300 400 500 600 700 800 Time (min)
    152. 152. 1 Sensitivity of DnaK to model parameters 10The complex architecture is a necessary Sensitivity of DnaK 0 10outcome of robustness and performance -1 10 requirements to survive heat-shock -2 10 -3 10 -4 10 -5 10 100 200 300 400 500 600 700 800 Time (min)
    153. 153. A Bio-Inspired Engineering Application Search strategies for unmanned aerial vehicles
    154. 154. Bacterial ChemotaxisE. coli must swim towardsnutrients or away from repellantsBacteria are too small to sensespatial gradientsInstead they rely on a veryeffective stochastic strategy Movie by P. Cluzel Run and tumble: Run  Swim with a constant direction (runs)  Changing their direction at random times (tumbles)  Frequency of tumbling depends on the Tumble sensed concentration Correlation between swimming behavior and flagellar rotation in E. coli (Cell Project)
    155. 155. Bacterial ChemotaxisE. coli must swim towardsnutrients or away from repellantsBacteria are too small to sensespatial gradientsInstead they rely on a veryeffective stochastic strategy Movie by P. Cluzel Run and tumble: Run  Swim with a constant direction (runs)  Changing their direction at random times (tumbles)  Frequency of tumbling depends on the Tumble sensed concentration Correlation between swimming behavior and flagellar rotation in E. coli (Cell Project)
    156. 156. The Flagellar MotorKeiichi NAMBA Francis et al., 1994
    157. 157. OptimotaxisAgents mimics bacteria chemotactic Advantages behavior with the goal of:  Agents simplicity, low cost  Finding the maximum of a measured quantity; or  Increasedprobability of finding the  Finding the spatial distribution of a global maximum due to randomness measured quantity.  Robustness to exogenous disturbances in the agents orientation. Chemical plume from BP-Amoco refinery explosion [courtesy of Los Alamos National Laboratory] Flapping wingAgents features Micro aerial vehicle (MAV) [courtesy of K. Jones, NPS]  Constant velocity  No position or velocity sensors required  No communication needed  Agents can be “seen” by a supervisor
    158. 158. Simulation Results Exponential turning rate model Different stages in optimotaxis in the presence of two maxima Mesquita et. al., Hybrid Systems: Computation and Control, No. 4981 in Lect. Notes in Comput. Science, 2008.
    159. 159. Conclusions❖ Feedback regulation mechanisms are ubiquitous❖ A dynamical-systems and control approach can ‣ Bring out the dynamic nature of biochemical interactions ‣ Explain interactions in the context of regulation ‣ Identify functional biological modules❖ Control theoretic notions ‣ Reveal structural constraints on the dynamics ‣ Structural constraints impose functional requirements on biological modules
    160. 160. ❖ A systems approach enhances our understanding of biological complexity ‣ Notions such as robustness, adaptation, amplification, isolation, and nonlinearity are required for a deeper understanding of biological function❖ Leads to a better understanding of the trajectory of disease ‣ suggest more effective courses of treatment❖ Many similarities with engineering systems❖ New challenges and opportunities for dynamics and control scientists
    161. 161. Acknowledgement❖ Calcium homeostasis: Hana El-Samad (UCSF), Jess Goff (NADC)❖ Heat Shock: Hana El-Samad (UCSF), Carol Gross (UCSF), John Doyle (Caltech), Hiro Kurata (KIT, Japan)❖ UAV search (Joao Hespanha, Alexandre Mesquita (UCSB))❖ Funding: ‣ National Science Foundation
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