Circuit Modeling of Biology

Circuits provide an intuitive and rigorous framework for representing and analyzing complex nonlinear dynamical systems and networks with lots of interactions amongst their pieces. Mechanical systems in biology such as the heart, lungs, ear, and vocal tract are easily modeled by circuits with pressure represented by voltage, volume velocity represented by current, mechanical impedances represented by electrical impedances, and valves represented by diodes. Chemical computation in biology can be well modeled by representing the chemical concentration of a species by a voltage and molecular flows by currents. Neuronal systems are electrochemical and naturally modeled by hybrid analog-digital circuits. Circuits can provide insight into the operation of biological systems that tedious algebraic modeling and simulation of nonlinear differential equations obscures. Bio-inspired design and circuit modeling of biology are often synergistic and lead to applications in engineering.

A circuit model of the biological cochlea from our lab suggested how it may possible to amplify at 100kHz even though the bandwidth of amplifying outer hair cells in the cochlea is less than 1kHz, a mystery in hearing for decades: We showed that, in a closed-loop feedback system like the cochlea, it is the gain-bandwidth product that determines the closed-loop bandwidth for amplification, not the open-loop bandwidth. Therefore, given reasonable parameters for the cochlea, the closed-loop bandwidth and quality factor could be significantly higher than open-loop values permitting amplification. Circuits are good ways of adding insight into such 'network' and 'feedback' effects that arise collectively from many local units in the network. The latter work was done in collaboration with Professor Peter Dallos of Northwestern University, a leading authority on the biophysics of hearing.

An electronic model of feedback networks in the brain, developed in collaboration with Professor Sebastian Seung of MIT, showed how it was possible to have simultaneous digital selection of inputs and analog amplification in such networks. Work on comparing analog versus digital circuits suggested that an important and underappreciated reason for the efficiency of the brain, which only consumes 12W of power, was its hybrid analog-digital and distributed architecture. Work on spike-based hybrid computation suggested how neurons could simultaneously exploit analog timing and digital count information to perform signal restoration and computation in scalable networks. The latter work led to the notion of a hybrid state machine, a generalization of finite state machines to the hybrid analog-digital domain. Current work in the lab is focusing on hybrid analog-digital control systems for building very energy-efficient feedback amplifiers and hybrid analog-digital cellular computational systems inspired by DNA-protein networks.

Selected Publications

1. T. Lu, S. Zhak, P. Dallos, and R. Sarpeshkar, “Fast Cochlear Amplification with Slow Outer Hair Cells”, Hearing Research, Vol. 214, Issues 1-2, pp. 45-67, April 2006.

2. R. Hahnloser, R. Sarpeshkar, M. Mahowald, R. Douglas, and S. Seung, “Digital Selection and Analogue Amplification Coexist in a cortex-inspired silicon circuit,” NATURE, Cover article, Vol. 405, pp. 947-951, 22 June 2000.

3. R. Sarpeshkar, “Analog Versus Digital:  Extrapolating from Electronics to Neurobiology,”Neural Computation, Vol. 10, pp. 1601-1638, 1998.

4. R. Sarpeshkar and M. O’Halloran, “Scalable Hybrid Computation with Spikes,” Neural Computation, Vol. 14, No. 9, pp. 2003-2024, September 2002.

5. R. Sarpeshkar, L. Watts, and C.A. Mead, “Refractory Neuron Circuits,” Computation and Neural Systems Technical Report, CNS TR-92-08, California Institute of Technology, 29 pages, 1992.

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