This work is a first step towards a long-term goal of understanding computations occurring in the brain and using those principles to make more efficient machines. The traditional computing paradigm calls for using digital supercomputers to simulate large scale brain-like neural networks resulting in large power consumption which limits scalability or model detail. For example, IBM's digital simulation of a cat brain with simplistic neurons and synapses consumes power equivalent to that of a thousand houses! Instead of digital methods, this work uses analog processing concepts to develop scalable, low-power silicon models of neurons which have been shown to be around ten thousand times more power efficient. This has been achieved by modeling the dynamical behavior of Hodgkin-Huxley (H-H) or Morris-Lecar type equations instead of modeling the exact equations themselves. In particular, the two silicon neuron designs described exhibit a Hopf and a saddle-node bifurcation. Conditions for the bifurcations allow the identification of correct biasing regimes for the neurons. Also, since the hardware neurons compute in real time, they can be used for dynamic clamp protocols in addition to computational experiments. To empower this analog implementation with the flexibility of a digital simulation, a family of field programmable analog array (FPAA) architectures have been developed in 0.35 um CMOS that provide reconfigurability in the network of neurons as well as tunability of individual neuron parameters. This programmability is obtained using floating-gate (FG) transistors. The neurons are organized in blocks called computational analog blocks (CAB) which are embedded in a programmable switch matrix. An unique feature of the architecture is that the switches, being FG elements, can be used also for computation leading to more than 50,000 analog parameters in 9 sq. mm. Several neural systems including central pattern generators and coincidence detectors are demonstrated. Also, a separate chip that is capable of implementing signal processing algorithms has been designed by modifying the CAB elements to include transconductors, multipliers etc. Several systems including an AM demodulator and a speech processor are presented. An important contribution of this work is developing an architecture for programming the FG elements over a wide dynamic range of currents. An adaptive logarithmic transimpedance amplifier is used for this purpose. This design provides a general solution for wide dynamic range current measurement with a low power dissipation and has been used in imaging chips too. A new generation of integrated circuits have also been designed that are 25 sq. mm in area and contain several new features including adaptive synapses and support for smart sensors. These designs and the previous ones should allow prototyping and rapid development of several neurally inspired systems and pave the path for the design of larger and more complex brain like adaptive neural networks.

Chemical reactions involving small number of reacting molecules are noisy processes. They are simulated using stochastic simulation algorithms like the Gillespie SSA, which are valid when the reaction environment is well-mixed. This is not the case in reactions occuring on biological media like cell membranes, where alternative simulation methods have to be used to account for the crowded nature of the reacting environment. Ion channels, which are membrane proteins controlling the flow of ions into and out of the cell, offer excellent single molecule conditions to test stochastic simulation schemes in crowded biological media. Single molecule reactions are of great importance in determining the functions of biological molecules. Access to their experimental data have increased the scope of com-putational modeling of biological processes. Recently, single molecule experiments have revealed the non-Markovian nature of chemical reactions, due to a phenomenon called `dynamic disorder', which makes the rate constants a deterministic function of time or a random process. This happens when there are additional slow scale conformational transitions, giving the molecule a memory of its previous states. In a previous work, the hTREK1 two pore domain potassium channel was revealed to have long term memory in its kinetics, prompting alternate non-Markovian schemes to analyze its gating. Traditionally, ion channel gating is modeled as Markovian transitions between fixed states. In this work, we have used single channel data from hTREK1 ion channel and have provided a simple diffusion model for its gating. The main assumption of this model is that the ion channel diffuses through a continuum of states on its potential energy landscape, which is derived from the steady state probability distribution of ionic current recorded from patch clamp experiments. A stochastic differential equation (SDE) driven by Gaussian white noise is proposed to model this motion in an asymmetric double well potential. The method is computationally very simple and efficient and reproduces the amplitude histogram very well. For the case when ligands are added, leading to incorporation of long term memory in the kinetics, the SDE is modified to run on coloured noise. This has been done by introducing an auxiliary variable into the equation. It has been shown that increasing the noise correlation with ligand concentration improves the fits to the experimental data. This has been validated for several datasets. These methods are more advantageous for simulation than the Markovian models as they are true to the physical picture of gating and also computationally very efficient. Reproducing the whole raw data trace takes no more than a few seconds with our scheme, with the only input being the amplitude histogram and four parameters. Finally a quantitative model based on a modified version of the Chemical Langevin equation is given, which works on random rate parameters. This model is computationally simple to implement and reproduces the catalytic activity of the channel as a function of time. From the computational analysis undertaken in this work, we can infer that ion channel activity can be modeled using the framework of non-Markovian processes, lending credence to the recent understanding that single molecule reactions are basically processes with long-term memory. Since the ion channel is basically a protein, we can also hypothesize that the some of the properties that make proteins so vital to living organ-isms could be attributed to long-term memory in their folding kinetics, giving them the ability to sample specific regions of their conformation space, which are of interest to biological functions.

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