Molecular Communication: From Theory to Practice Andrew W. Eckford Dept. of Electrical Engineering and Computer Science York University, Toronto, Canada

2 Molecular Communication: What, why and how?

What is molecular communication? Molecular communication = Chemical properties

Why Molecular Communication? Because it could enable “nano-networks”

Why Molecular Communication? 5 Because information theory can tell us about biology

Why Molecular Communication? Because it’s fun!

Molecular communication: How? TxRx 1, 2, 3,..., |M| M: m Tx m Noise m' m = m'? Medium

8 How do you “say it with molecules?” Transmit:

Cell 1 Cell 2 Quantity: Sending 0 Release no molecules How do you “say it with molecules?”

Cell 1 Cell 2 Quantity: Sending 1 Release lots of molecules How do you “say it with molecules?”

Cell 1 Cell 2 Quantity: Receiving Measure number arriving How do you “say it with molecules?”

Cell 1 Cell 2 Identity: Sending 0 Release type A How do you “say it with molecules?”

Cell 1 Cell 2 Identity: Sending 1 Release type B How do you “say it with molecules?”

Cell 1 Cell 2 Identity: Receiving Measure identity of arrivals How do you “say it with molecules?”

Cell 1 Cell 2 Timing: Sending 0 Release a molecule now How do you “say it with molecules?”

Cell 1 Cell 2 Timing: Sending 1 WAIT … How do you “say it with molecules?”

Cell 1 Cell 2 Timing: Sending 1 Release at time T>0 How do you “say it with molecules?”

Cell 1 Cell 2 Timing: Receiving Measure arrival time How do you “say it with molecules?”

Outline Nanonetworks: Information-theoretic models Biology: Capacity of signal transduction Just for fun (or is it?): Macroscale molecular communication

What is the best you can do?

“All models are wrong, but some are useful” -- George Box

22 Ideal System Model: Transmitter and receiver are perfectly synchronized. Transmitter perfectly controls the release times and physical state of transmitted particles. Receiver perfectly measures the arrival time and physical state of any particle that crosses the boundary. Receiver immediately absorbs (i.e., removes from the system) any particle that crosses the boundary.

23 Tx Rx d0 Two-dimensional Brownian motion First passage time is additive noise! Release: t Arrive:t + n Brownian motion as additive noise

24 Brownian motion with drift velocity v: First passage time given by inverse Gaussian (IG) distribution. IG(λ,μ) Additive Inverse Gaussian Noise (AIGN) channel

Inverse Gaussian Distribution: Examples

26 Additive Inverse Gaussian Channel

27 Let h(λ,μ) = differential entropy of IG. Additive Inverse Gaussian Channel

28 Let h(λ,μ) = differential entropy of IG. Additive Inverse Gaussian Channel

29 Additivity property: Additive Inverse Gaussian Channel If Then Let

30 Let h(λ,μ) = differential entropy of IG, E[X] ≤ m. Additive Inverse Gaussian Channel

31 Additive Inverse Gaussian Channel Let h(λ,μ) = differential entropy of IG, E[X] ≤ m.

32 Additive Inverse Gaussian Channel Let h(λ,μ) = differential entropy of IG, E[X] ≤ m.

33 Additive Inverse Gaussian Channel Let h(λ,μ) = differential entropy of IG, E[X] ≤ m.

34 Bounds on capacity subject to input constraint E[X] ≤ m: K. V. Srinivas, A. W. Eckford, and R. S. Adve, “Molecular communication in fluid media: The additive inverse Gaussian noise channel,” IEEE Trans. Info. Theory, A. W. Eckford, K. V. Srinivas, and R. S. Adve, “The peak constrained additive inverse Gaussian noise channel,” in Proc. IEEE ISIT, Additive Inverse Gaussian Channel

Capacity of intercellular signal transduction 1994, Medicine: “for their discovery of G-proteins and the role of these proteins in signal transduction in cells”

Signal transduction Cell 1 Cell 2 Ligands

Cells talk to each other using signal transduction Cell growth, differentiation, apoptosis Immune system regulation Metabolic control Multicellular organisms can’t exist without signal transduction

Signal transduction is a Markov process

Cyclic adenosine monophosphate (cAMP) – A ligand-gated receptor found in amoeba Our Example

Cell Second Messenger See also: H. C. Berg and E. M. Purcell, “Physics of chemoreception,” Biophysical Journal, vol. 20, pp. 193–219, Ligand-gated channels Second Messenger Cyclic adenosine monophosphate (cAMP)

Receptor states form a Poisson process Concentration Cyclic adenosine monophosphate (cAMP)

Receptor states form a Poisson process

Cyclic adenosine monophosphate (cAMP) Receptor states form a Poisson process

Signal transduction as a discrete time Markov chain Or, for simplicity:

Signal transduction as a discrete time Markov chain Concentration

Signal transduction as a discrete time Markov chain Concentration

Capacity of Signal Transduction Capacity is achieved with inputs only at: The lowest possible input The highest possible input P. Thomas and A. Eckford, “Capacity of a simple intercellular signal transduction channel,” arXiv: , sub. to IEEE Trans. Info. Theory.

Capacity of Signal Transduction

Input distribution depends only on previous channel output J. Chen and T. Berger, “The capacity of finite-state Markov channels with feedback,” IEEE Trans. Info. Theory, vol. 51, pp. 780–798, Mar Capacity of Signal Transduction

regardless of Capacity of Signal Transduction

regardless of Capacity of Signal Transduction

Cyclic adenosine monophosphate (cAMP) P. Thomas and A. Eckford, “Capacity of a simple intercellular signal transduction channel,” arXiv: , sub. to IEEE Trans. Info. Theory.

Signal transduction is a Markov process

“Eckford’s Law” :-) In any new field, the number of models grows linearly with the number of papers.

Closing the “model-to-experiment” gap

Try this at home! N. Farsad, W. Guo, and A. W. Eckford, “Table-top molecular communication: Text messages through chemical signals,” PLOS ONE,

Next steps … L. Wang, N. Farsad, W. Guo, S. Magierowski, and A. W. Eckford, “Molecular barcodes: Information transmission via persistent chemical tags,” in Proc. IEEE ICC, 2015.

In conclusion … There is lots of work to do in molecular communication, both in theory and in practice!

Contact & Thanks Thanks to my collaborators Tadashi Nakano, Osaka University Weisi Guo, University of Warwick Chan-Byoung Chae, Yonsei University Nariman Farsad, Stanford University (ex York University) Peter Thomas, Case Western Reserve University K. V. Srinivas and Ravi Adve, University of Toronto Sachin Kadloor, University of Illinois at Urbana-Champaign Thanks to NSERC for funding this research

Cell Light-gated channels ion current photon ion current photon Channelrhodopsin-2 (ChR2)

Receptor states form a Poisson process photon Intensity Degraded G. Nagel et al., “Channelrhodopsin-2: A directly light-gated cation-selective membrane channel,” PNAS, 2003.

Receptor states form a Poisson process Channelrhodopsin-2 (ChR2)

Receptor states form a Poisson process Channelrhodopsin-2 (ChR2)

Capacity of Signal Transduction Channelrhodopsin-2 (ChR2)

Surprisingly High Information Rates Channelrhodopsin-2 (ChR2)