A 1.26 <formula formulatype="inline"><tex Notation="TeX">$\mu{\rm W}$</tex></formula> Cytomimetic IC Emulating Complex Nonlinear Mammalian Cell Cycle Dynamics: Synthesis, Simulation and Proof-of-Concept Measured Results

Abstract

Cytomimetic circuits represent a novel, ultra low-power, continuous-time, continuous-value class of circuits, capable of mapping on silicon cellular and molecular dynamics modelled by means of nonlinear ordinary differential equations (ODEs). Such monolithic circuits are in principle able to emulate on chip, single or multiple cell operations in a highly parallel fashion. Cytomimetic topologies can be synthesized by adopting the Nonlinear Bernoulli Cell Formalism (NBCF), a mathematical framework that exploits the striking similarities between the equations describing weakly-inverted Metal-Oxide Semiconductor (MOS) devices and coupled nonlinear ODEs, typically appearing in models of naturally encountered biochemical systems. The NBCF maps biological state variables onto strictly positive subthreshold MOS circuit currents. This paper presents the synthesis, the simulation and proof-of-concept chip results corresponding to the emulation of a complex cellular network mechanism, the skeleton model for the network of Cyclin-dependent Kinases (CdKs) driving the mammalian cell cycle. This five variable nonlinear biological model, when appropriate model parameter values are assigned, can exhibit multiple oscillatory behaviors, varying from simple periodic oscillations, to complex oscillations such as quasi-periodicity and chaos. The validity of our approach is verified by simulated results with realistic process parameters from the commercially available AMS 0.35 μm technology and by chip measurements. The fabricated chip occupies an area of 2.27 mm2 and consumes a power of 1.26 μW from a power supply of 3 V. The presented cytomimetic topology follows closely the behavior of its biological counterpart, exhibiting similar time-dependent solutions of the Cdk complexes, the transcription factors and the proteins.

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

“…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.…”

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.…”

“…Such systems are power efficient, however, model adjustment is generally challenging in these circuits. Moreover, since the non-linear functions in target mathematical models are directly implemented by exploiting the inherent non-linearity of the circuit elements, very good layout is imperative in order for the resulting topologies not to suffer from variability and mismatch [11]. Another issue is raised with the realization of slow biological dynamics (such as most intercellular dynamics in CytoMimetic circuits) especially when the biological time scale must be precisely implemented (e.g.…”

Analytical study, performance optimisation and design rules for customary static and dynamic subthreshold MOS translinear topologies

“…The usefulness of subthreshold operation has been repeatedly illustrated in numerous publications in the literature. Recent, indicative, low-power biomedical examples include nonlinear cellular/molecular dynamics computation circuits [4,5,6,7,8] and linear, high-dynamic range, filtering topologies [9,10,11,12,13,14,15,16,17]. The TLP is always one of the necessary, basic tools required for the mathematical description and subsequent implementation of such circuit topologies, thanks to the flexibility that it provides when it comes to the real-time realisation of linear or nonlinear mathematical operations [18].…”