Systematic Computation of Nonlinear Cellular and Molecular Dynamics with Low-Power CytoMimetic Circuits: A Simulation Study

Abstract

This paper presents a novel method for the systematic implementation of low-power microelectronic circuits aimed at computing nonlinear cellular and molecular dynamics. The method proposed is based on the Nonlinear Bernoulli Cell Formalism (NBCF), an advanced mathematical framework stemming from the Bernoulli Cell Formalism (BCF) originally exploited for the modular synthesis and analysis of linear, time-invariant, high dynamic range, logarithmic filters. Our approach identifies and exploits the striking similarities existing between the NBCF and coupled nonlinear ordinary differential equations (ODEs) typically appearing in models of naturally encountered biochemical systems. The resulting continuous-time, continuous-value, low-power CytoMimetic electronic circuits succeed in simulating fast and with good accuracy cellular and molecular dynamics. The application of the method is illustrated by synthesising for the first time microelectronic CytoMimetic topologies which simulate successfully: 1) a nonlinear intracellular calcium oscillations model for several Hill coefficient values and 2) a gene-protein regulatory system model. The dynamic behaviours generated by the proposed CytoMimetic circuits are compared and found to be in very good agreement with their biological counterparts. The circuits exploit the exponential law codifying the low-power subthreshold operation regime and have been simulated with realistic parameters from a commercially available CMOS process. They occupy an area of a fraction of a square-millimetre, while consuming between 1 and 12 microwatts of power. Simulations of fabrication-related variability results are also presented.

Systematic Computation of Nonlinear Bilateral Dynamical Systems With a Novel Low-Power Log-Domain Circuit

“…The mathematical models describing the dynamical systems can be simulated with the use of powerful software such as MATLAB, however, for large-scale simulations software begins to collapse. Besides, computer-based simulations are not always suitable for interfacing with biological/physical systems where continuous monitoring with low power and area consumption might be required [1].…”

“…On the other hand, other research efforts have focused on the synthesis and study of intra/extracellular chemical dynamics demonstrating a bold shift of emphasis from the neural system. For example, in [1][2] and [13][14] cytomorphic/cytomimetic electronics are introduced. The logarithmic behaviour [15][16][17][18][19][20][21][22] of weakly inverted MOS devices is exploited.…”

“…Log-domain circuits have been shown able to produce a variety of nonlinear dynamics [23][24]. However, the systematic synthesis tool (NBCF) presented in [1] and [13], though directly applicable for cellular dynamics with strictly positive variables, does not level itself naturally to the realization of bilateral dynamical systems such as neuronal dynamics [25].…”

A Compact Synchronous Cellular Model of Nonlinear Calcium Dynamics: Simulation and FPGA Synthesis Results

“…replacement of a biological system by an electronic circuit), 3) the development of such platforms benefiting from new principles of bio-inspired massively parallel computation can be useful in engineering applications such as new devices capable of learning and independent decision making. A number of solutions for implementing such systems have been devised so far, ranging from time-continuous low power analog circuits to time-discrete massively parallel digital ones [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Here, we summarize the main solutions:…”

“…• Analog CMOS platforms are considered to be the main choice for the direct implementation of intra-and extracellular biological dynamics [7][8][9][10][11][12]. Such systems are power efficient, however, model adjustment is generally challenging in these circuits.…”