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Associative Learning in Single Cells
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Chrisantha Fernando & Jon Rowe1
Systems Biology Centre, 1School of Computer Science, University of Birmingham, Edgbaston, UK
Introduction
Associative learning in biology is not confined to
neurons. For example the Paramecium caudatum (a
single celled organism common in pond water) can
be classically conditioned (Hennessey, 1979).
A Potential Medical Application
A Bacterial Gene Circuit Design
More Realistic Models..
As a proof of concept, we developed designs to
construct a 3-gene circuit on a bacterial plasmid.
This should will bacteria to learn to associate two
stimuli.
reveal similar problems to when the Hebb rule is
applied to neurons, e.g. saturation of output
activity. Also we must deal with the persistence
of memory across bacterial generations. Crucial
features for a functional circuit are as follows…
Reducing the bystander effect in chemotherapy
1. P must bind linearly without saturation to the
promoters of Wi genes, for Wi to be produced
proportional to the product [P]x[Ui].
Qu i c k T i m e ™ a n d a
T I F F (Un c o m p re s s e d ) d e c o m p re s s o r
a re n e e d e d to s e e th i s p i c t u re .
3. The gain in Wj when Ui +Uj are paired must be
greater than the gain in Wj with 2Uj, if Wj > Wi
initially.
We show that gene circuits can carry out associative
(Hebbian) learning in individual cells.
One application is in gene therapy, where a gene
learns under what conditions to express itself, to suit
the patient it is in. Gene learning may be supervised
or unsupervised. The engram is inherited
epigenetically, e.g. as a transcription factor or
phosphorylated kinase concentration.
2. For rapid learning, the promoters must be
strong, thus some leakiness is likely, so [Wi] will
be non-zero, even when Ui = 0.
The circuit consists of transcription factor proteins. U1 and U2 represent
inputs (repressors), P represents the output (activator), and W1 and W2
represent the weights (activators). An inducer acting on Ui to lift its
repression, allows synthesis of P at rate UiWi. This is implemented by a simple
cooperative AND-gate promoter (Buchler, 2003) P also positively feeds back,
allowing Wi to be increased in proportion to WiP. W1 and W2 store the memory
trace by decaying slowly.
What is Hebbian Learning?
Conclusion
Hebb (1949) proposed a neural mechanism to
explain classical conditioning. Variants of Hebbian
learning are responsible for LTP, auto-associative
memory, and self-organized map formation in cortex.
Using a model similar to that of Elowitz and Leibler (2000) we see that the gain
in response to U2 (red) over one paired UCS + CS trial is reduced. There is
some response to U2 even before pairing of CS + UCS. Promoters are twice as
strong as in E&L, repression and depression is complete, TFs bind with Hill
coefficient n = 2.
Synaptic strength is
increased in proportion to
the correlated firing of the
post- and the pre-synaptic
neuron. Information is
encoded as interaction
strengths between cells
forming a neural network.
Task A
Task B1
Modelling suggests it will be possible (using
synthetic biology techniques) to construct a gene
circuit capable of associative learning within a
bacterial plasmid. If Hebbian learning can be ported
to the intra-cellular realm, then the scope of
application for existing algorithms from neural
networks and pattern classification is extended,
following which, many potential medical applications
suggest themselves.
References & Acknowledgements
The principle can be extended to any dynamical
system of the form…
xi dv = - v + w$u
dt
xw dw = u v
dt
Several ODE models of the above circuit were produced, the simplest is shown
above. W1 starts high, so U1 is the unconditioned stimulus (derepressed form)
After pairing of U1 and U2, the circuit responds to U2 alone, whereas before
pairing there was no response to U2 presented alone. The circuit learns to
associate U1 and U2.
Task A. P output for various degrees
of correlation between two Poisson
spike train inputs encoded as [U1] and
[U2], against U2 decay rate. Task B1
P output when two spikes are input,
spike U2 at time t = 20, and spike U1 at
t = Scale.i , i = {0, 40}. Task B2. As
above Scale = 32, for varying P Kd.
Hennessey, T. M., W. B. Rucker, and C. G. McDiarmid. "Classical Conditioning in
Paramecia." Animal Learning & Behavior (1979) 7:417-23.
Donald Olding Hebb, “The Organization of Behaviour” ,(1949)
Nicolas E. Buchler, Ulrich Gerland, and Terence Hwa. “On Schemes of Combinatorial
Transcription Logic” PNAS (2003), 100(9):5136-5141
Elowitz, M.B, and Leibler, S. “A synthetic oscillatory network of transcriptional
regulators.” Nature (2000), 403:335-8.
Task B2
Thanks to Lewis Bingle, Anthony Liekens, Dov Stekel, and the ESIGNET 6th Framework
Grant for Cell Signaling Network Research.