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

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• Move on to Big Picture Thinking

• Future Technologies – Synthetic Life • Ethics, Science & Society