4 Positive feedback Flashcards
What is a network?
Nodes connected by edges
Define edges in a network
Edges connect nodes = it is an action that occurs
Give 4 examples of different networks and what their nodes and edges are
Cell: node = enzymes, substrates, proteins
edges = activation, suppression, cascade
Species interaction: node = organism/species
edges = feeding
Social network: node = people/IDs
edges = info flowing from one person to another
Artificial neural network
What is a network motif?
Basic interaction patterns that recur throughout biological networks, much more often than in random networks
Motifs can generate predictable outputs
Motifs are building blocks of networks
Define a node
One or more nodes that are interconnected in a specific way with predictive outcome
What is the equation for negative autoregulation?
A dot = -rA
Describe the graph of negative autoregulation
Exponential decay
Degradation of protein or death of animal = how things disappear on itself over time
What is the equation for a self-suppressing gene and why?
A dot = +s - rA
This is because the +s is the external signal to activate the gene A
This signal doesn’t depend on how strong/amount of rA
Product of gene A suppresses its own expression at rate r>0
What is the fixed point for A dot = +s - rA?
A* = s/r
Stable fixed point = the rate you get something / rate you lost something
What is the outcome of negative autoregulation on response time?
Negative autoregulation ACCELERATES response time
What does integrating negative autoregulation equation tell us?
The expression of gene A saturates over time
What are the limits for the integration of A dot = +s -rA?
t»_space;> infinity
A»_space;> s/r
What factors affect expression level and response time?
s = external stimuli alters level of steady state
Lower expression level at steady state A* = s/r
Stronger auto-suppression = larger r
Leads to faster response time = gene A reaches steady state faster
How to ensure both high expression level and fast response time?
High expression level = when s is large
Fast response time = when r is large
What is positive autoregulation also called?
Autoactivation
What is the Hill Function, give the equation?
Generalized logistic equation
f((x) = x^n / k^n + x^n
What are the equations for positive autoregulation, exponential and logistic?
Exponential: A dot = +rA
Logistic: A dot = +rA (K - A)
What does k stand for in the Hill function?
Level at which the function f(x) reaches 50% of the max
What does n stand for in the Hill function?
Hill coefficient = represents level of association
What happens when ‘n’ is large in the Hill function?
Ultrasensitivity
For high n, reaction rate increases drastically
Until it becomes a STEP FUNCTION when n = infinity
What happens when k = 1 in the hill equation?***
f(x) is the same as x dot
x dot = x^n / 1 + x^n
Reaction reaches 50% of max rate when x dot = 1 at the same conc of x = 1
What does it mean when n=1 as opposed to n= 2? ***
n = 1 means autoactivation only needs one copy of itself
n = 2 means that it could need a dimer to autoactivate
What can ultrasensitivity and degradation (removal) enable?
Bistability
If n =1 there is one steady state = constant expression rate of A (LINEAR)
If n>1 (ultrasensitive autoactivation) there are two steady states = eitehr constant expression rate or no expression at all (ON/OFF switch)
NON-LINEAR = S-curve
What is cooperativeness and what can it induce? ***
Cooperativeness = when X^n (n>1)
Cooperativeness can induce ultrasensitivity in autoactivation
What are the nullclines and trajectories for linear positive feedback?
A dot = +/- rB
B dot = +/- sA
Nullclines: A* and B* = 0
Vectors on nullclines (0, +/-sA) (+/-rB,0)
What does linear positive feedback generate with the eigenvectors?
Saddle point = unstable fixed points/nodes
Happens in both mutual activation and mutual repression
Examples of mutual activation and repression
Activation = amplification
Repression = exclusion
