Associative Learning in Single Cells

1
Associative Learning in Single Cells
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). 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.
A Potential Medical Application
A Bacterial Gene Circuit Design 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.

• More Realistic Models..
• 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
• P must bind linearly without saturation to the
  promoters of Wi genes, for Wi to be produced
  proportional to the product PxUi.
• For rapid learning, the promoters must be strong,
  thus some leakiness is likely, so Wi will be
  non-zero, even when Ui 0.
• The gain in Wj when Ui Uj are paired must be
  greater than the gain in Wj with 2Uj, if Wj gt Wi
  initially.

Reducing the bystander effect in chemotherapy
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? 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.
The principle can be extended to any
dynamical system of the form
Conclusion 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.
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 EL, 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
References Acknowledgements Hennessey, T. M.,
W. B. Rucker, and C. G. McDiarmid. "Classical
Conditioning in Paramecia." Animal Learning
Behavior (1979) 7417-23. 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),
403335-8. Thanks to Lewis Bingle, Anthony
Liekens, Dov Stekel, and the ESIGNET 6th
Framework Grant for Cell Signaling Network
Research.
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.
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 B2