Robustness in protein circuits: adaptation in bacterial chemotaxis 1 Information in Biology 2008 Oren Shoval

Outline Noise is a part of life Overview of bacterial chemotaxis Internal mechanism of chemotaxis control The robust model of perfect adaptation Perfect adaptation and control theory 2

Outline Noise is a part of life Overview of bacterial chemotaxis Internal mechanism of chemotaxis control The robust model of perfect adaptation Perfect adaptation and control theory 3

Many biological processes are robust to external and internal fluctuations Internal protein levels vary significantly between genetically identical cells Humans keep body temperature at 36.7° despite: – External noise of surrounding temperature – Internal noise of body weight, size, food intake 4 Elowitz et al., Science, 2002

Sensitivity to noise is a measure of biological system performance Sensitivity is the change in system output (Y) due to changes in the internal parameter (  ) Robustness means zero sensitivity For example, dependence of body temperature on body weight: Savageau, Nature, Robust

Outline Noise is a part of life Overview of bacterial chemotaxis Internal mechanism of chemotaxis control The robust model of perfect adaptation Perfect adaptation and control theory 6

Chemotaxis: Bacteria can “swim” towards an attractant and away from a repellent 7 Repellant (poison) Attractant (food)

Swimming is done by a spiraling motor (flagella) Flagella can rotate in two directions: Speed of about 50  m/sec. Is this fast? 8 Clock wise (advancing ~sec) Counter clock wise (tumble ~0.1sec) OrganismKilometers per hourBody lengths per second Cheetah11125 Human - Michael Johnson Bacteria

Bacteria find their way up a nutrient gradient by changing the tumbling rate Bacteria are too small to measure gradient Gradient found by temporal change during running Positive Gradient Biased random walk 9 Berg, Nature, 1972 Lower tumbling rate Continue in correct direction

Automated analysis of the bacteria trails enables extracting the chemotaxis parameters 10 Berg, Nature, 1972 Parameters: Mean free path Tumbling rate

Tumbling rate shows exact adaptation to nutrient level addition of nutrient bacteria stop tumbling Adaptation: slowly return to a steady state tumbling Adaptation is commonly found in sensory systems Adaptation is the focus of Barkai’s paper 11 Addition of attractant reduces tumbling immediately Adaptation Steady state tumbling rate

Adaptation increases the dynamic range of sensors Adaptation keeps sensor sensitive to changes regardless of average stimulus Bacteria without adaptation show <1% chemotaxis ability 12 Possible stimulus range System dynamic range Stimulus level System unable to sense changes

Outline Noise is a part of life Overview of bacterial chemotaxis Internal mechanism of chemotaxis control The robust model of perfect adaptation Perfect adaptation and control theory 13

Motor control by a two component system: receptor and regulator Receptor without an attractant Activate Y by adding a P Y-P binds to motor Increase rate of tumbling Shorter runs 14 Y Y Y Y P P Removal of P at constant rate Motor more tumbling Receptor Sensor activity level

An attractant inhibits the receptor, thus reducing motor activity Adding attractant Less receptor activity Less Y-P is created Reduced tumbling Longer runs 15 Y Y Y Y P P Removal of P at constant rate Motor Less tumbling Receptor Sugar Sensor activity level Fast process (miliseconds)

Again: 16 Y Y Y Y P P Removal of P at constant rate Motor Less tumbling Receptor Sugar Sensor activity level Y Y Y Y P P Removal of P at constant rate Motor more tumbling Receptor Sensor activity level Less sugar Shorter runsMore sugar Longer runs

Adaptation is achieved by reactivating the receptor Adding M (Methylation) overcomes deactivation due to sugar R add M, B removes M 17 Sensor activity level Reactivation (R) M M Negative feedback Deactivation (B) M M Slow process (minutes)

The adaptation cycle: 18 Steady State Tumbling Sugar addition Receptor activity decreases Tumbling decreases (running) Receptor reactivation (methylation) Tumbling increases Fast (miliseconds) Slow (minutes)

Outline Noise is a part of life Overview of bacterial chemotaxis Internal mechanism of chemotaxis control The robust model of perfect adaptation Perfect adaptation and control theory 19

Is adaptation accuracy sensitive or robust to internal protein levels? 20 Example: If the level of protein R (reactivation) changes by 20%, will we still have adaptation? Two mechanisms for adaptation

Barkai proposed a robust model of adaptation that depends on two assumptions 1.Methylation (R) works at maximum rate (saturation) 2.Demethylation (B) occurs only on activated receptors Barkai, Nature, CheR

Let’s have fun with some equations The attractant governs the active vs. inactive ratio: Methylation rate: At steady state: 22 CheR Adaptation is robust!

Experiments can measure the sensitivity of chemotaxis parameters to internal protein level 23 Alon experimentally varied the level of proteins that make up chemotaxis Three parameters were extracted for each mutant: Adaptation time Adaptation precision Steady state tumbling Alon et al., Nature, 1999

Experiments have proven that adaptation precision is robust to variations in protein levels Alon et al., Nature, x3 receptors x0.5 CheY x0 CheZ x12 CheB Adaptation is precise in all cases Steady state tumbling rate and adaptation time change Adaptation is precise in all cases Steady state tumbling rate and adaptation time change x50 CheR

Perfect adaptation is important, so the network is designed to keep it robust Partial adaptation leads to <1% of wild- type chemotaxis ability Changing the tumbling frequency and adaptation time does not affect chemotaxis ability Exact adaptation is displayed in taxis of many other bacterial species (B. subtillis, R. sphaeroides) 25 However, nonessential features are sensitive to protein levels

Outline Noise is a part of life Overview of bacterial chemotaxis Internal mechanism of chemotaxis control The robust model of perfect adaptation Perfect adaptation and control theory 26

Robust adaptation in chemotaxis is an example of integral feedback control Error A Yi et al., PNAS,

Summary Biochemical networks need to cope with noise Chemotaxis is the ability of bacteria to swim towards an attractant Chemotaxis adaptation is robust to internal protein levels 28