Post on 23-Dec-2021
L5.3: Cells as Biosensors II
Prof. Rickus
In this lecture
• Sensitivity
• Sensitivity Amplification
• Ultrasensitivity
Recognition Element Transducer Detector
Target
End User
Display
What is a biosensor?
SENSOR
Signal INPUT
OUTPUT Response
Sensitivity Sensitivity: The differential change in R as a ratio to the differential change in S
Res
pons
e, R
Input Signal, S
Plot the magnitude of the response magnitude as a function of the signal magnitude
slope for a linear response
slope = unit of response unit of signal
Sensitivity
Signal
sensitivity
R = mS + b
Increase the sensitivity of the sensor response background
Dynamic Range
Concentration Range for which Response is Predictably Dependent Upon the Signal Level
max min
max – usually some saturation of the response (e.g. saturated binding) min – signal lost in the noise (limit of detection)
Signal
G protein
1) 1 metarhodopsin catalyzes many GDP/GTP exchanges
2) Each phosphodiesterase can hydrolyze many molecules of cGMP
From Neuron to Brain. 4th ed. Nicholls, Martin, Wallace, Fuchs, chapter 19
Classic Example of Magnitude Amplification - Phototransduction
1 photon event results in the hydrolysis of 105 cGMPs
Whole Cell Biosensor
Signal Response
commonly genetically encoded
http://www.nobelprize.org/nobel_prizes/chemistry/laureates/2008/tsien-slides.pdf
Whole Cell Biosensor from Simple Activation
Response of the Sensor Circuit at Zero Signal Some circuits can be “leaky”. E.g. still get basal transcription with 0 activator.
Background
Transcription rate of Y
X
βo
Signal
Maximum β1
Simple activation model
response
signal
Classic Hyperbolic Response (.e. Calibration) Curve
Normalize the response and stimulus parameters Rmax: maximum response S0.5: the concentration of signal where the response is at half maximum r, s: dimensionless response (Y) and signal (X) - divide both sides by Rmax - multiply both sides by S0.5/S0.5
= 1 S0.5
= KXY = level of X signal that results in a half
maximum response (transcription rate of Y) dimensionless form
Sensitivity Amplification
An increase in the % change in response , R, relative to the % change in stimulus, S.
We define the sensitivity amplification factor, As.
Hyperbolic sensitivity classic hyperbolic calibration
Ultrasensitivity As > 1 for a range of S
Sub-sensitivity The As is never greater than 1.
Koshland, Goldbeter, Stock Science 1982
R /
R m
ax
Note the trade off between dynamic range and sensitivity.
Biological Design Approaches to Achieve Ultra-sensitivity
1.Cooperativity
2.Cascades
3.Zero-Order Ultra-sensitivity
Ultra-sensitivity – Cooperativity
f(x)
x/K
n=1 n=2 n=3 n=4
K: - units conc. - defines functional concentration range of X - may correlate with (but is not formally) the binding affinity of X to the DNA - other factors contribute to K n: - Hill coefficient - increases nonlinearity of function - increases steepness of sigmoidal - greater n, more on/off switch-like
[X] gene
x >> K ON high
x = K 0.5 ON mod
x << K 0 0 OFF
rate prob. Hill function model of gene activation
From Lecture on Simple Models of Gene Expression
hyperbolic sensitivity
Ultra-sensitivity
Sara Hooshangi et al. PNAS 2005;102:3581-3586
Ultra-sensitivity: Multi-stage Cascades
W W*
Enzyme 1
Enzyme 2
R = W* / Wtotal
S S is an activator of Enzyme, E1
E1 and E2 are enzymes that follow classic Michaelis Menton Kinetics
Ultra-sensitivity: Zero Order Sensitivity
W is some Response Signal Protein that can exist in 2 states
W W*
E1
E2
S
Structure is used widely by biology
kinase
phosphatase
P
ATP ADP
Kinases make up 1. 5 – 2.5% of all proteins in most genomes examined.
Quantitative analysis of signaling networks (2004) Herbert M. Sauroa, Boris N. Kh l d k
S
0o Ultrasensitivity Depends on Certain Conditions:
KM,1 / WT = KM,1 / WT = 0.1 equivalent hill coefficient = 2.9 KM,1 / WT = KM,1 / WT = 0.01 equivalent hill coefficient = 13
Zero Order Regime: The total amount of WT = W + W* must be very high relative to the KM’s of the reactions catalyzed by E1 and E2
W
VE1
W0.5
Zero order regime
high W levels
Cascades to Enhance 0o Ultra-sensitivity:
W W*
E1
E2
S
Z Z*
E3
E4
R1 = W*/WT R2 = Z*/ZT
1 cycle
2 cycle
Adding the 2nd cycle increases the ultrasensitivity
response Equivalent to hill coeff. of
3.6
7.5
ALBERT GOLDBETER AND DANIEL E. KOSHLAND, JR. PNAS 1981
1st cascade
2nd cascade
Engineering Design: Analogy to the Transistor
Quantitative analysis of signaling networks (2004) Herbert M. Sauroa, Boris N. Kholodenkoc
View these systems as sensors, amplifiers, or switches
Coming up …
• Move on to Big Picture Thinking
• Future Technologies – Synthetic Life • Ethics, Science & Society