A Digitally Programmable Cytomorphic Chip for Simulation of Arbitrary Biochemical Reaction Networks

Drug Cocktail Formulation via Circuit Design

Electronic circuits intuitively visualize and quantitatively simulate biological systems with nonlinear differential equations that exhibit complicated dynamics. Drug cocktail therapies are a powerful tool against diseases that exhibit such dynamics. We show that just six key states, which are represented in a feedback circuit, enable drug-cocktail formulation: 1) healthy cell number; 2) infected cell number; 3) extracellular pathogen number; 4) intracellular pathogenic molecule number; 5) innate immune system strength; and 6) adaptive immune system strength. To enable drug cocktail formulation, the model represents the effects of the drugs in the circuit. For example, a nonlinear feedback circuit model fits measured clinical data, represents cytokine storm and adaptive autoimmune behavior, and accounts for age, sex, and variant effects for SARS-CoV-2 with few free parameters. The latter circuit model provided three quantitative insights on the optimal timing and dosage of drug components in a cocktail: 1) antipathogenic drugs should be given early in the infection, but immunosuppressant timing involves a tradeoff between controlling pathogen load and mitigating inflammation; 2) both within and across-class combinations of drugs have synergistic effects; 3) if they are administered sufficiently early in the infection, anti-pathogenic drugs are more effective at mitigating autoimmune behavior than immunosuppressant drugs.

A Compact and Power-Efficient Noise Generator for Stochastic Simulations

This paper describes an adaptive noise generator circuit suitable for on-chip simulations of stochastic chemical kinetics. The circuit uses amplified BJT white noise and adaptive low-pass filtering to emulate the power spectrum and autocorrelation of random telegraph signals (RTS) with Poisson-distributed level transitions. A current-mode implementation in the AMS 0.35 μm BiCMOS process shows excellent agreement with theoretical results from the Gillespie stochastic simulation algorithm over a 60 dB range in mean current levels (modeling molecule count numbers). The circuit has an estimated layout area of 0.032 mm2 and typically consumes 400 μA, which are 73% and 50% less, respectively, than prior implementations. Moreover, it does not require any off-chip capacitors. Experimental results from a discrete board-level implementation of the circuit are in good agreement with theoretical predictions.

Rapid modeling of experimental molecular kinetics with simple electronic circuits instead of with complex differential equations

Kinetic modeling has relied on using a tedious number of mathematical equations to describe molecular kinetics in interacting reactions. The long list of differential equations with associated abstract variables and parameters inevitably hinders readers’ easy understanding of the models. However, the mathematical equations describing the kinetics of biochemical reactions can be exactly mapped to the dynamics of voltages and currents in simple electronic circuits wherein voltages represent molecular concentrations and currents represent molecular fluxes. For example, we theoretically derive and experimentally verify accurate circuit models for Michaelis-Menten kinetics. Then, we show that such circuit models can be scaled via simple wiring among circuit motifs to represent more and arbitrarily complex reactions. Hence, we can directly map reaction networks to equivalent circuit schematics in a rapid, quantitatively accurate, and intuitive fashion without needing mathematical equations. We verify experimentally that these circuit models are quantitatively accurate. Examples include 1) different mechanisms of competitive, noncompetitive, uncompetitive, and mixed enzyme inhibition, important for understanding pharmacokinetics; 2) product-feedback inhibition, common in biochemistry; 3) reversible reactions; 4) multi-substrate enzymatic reactions, both important in many metabolic pathways; and 5) translation and transcription dynamics in a cell-free system, which brings insight into the functioning of all gene-protein networks. We envision that circuit modeling and simulation could become a powerful scientific communication language and tool for quantitative studies of kinetics in biology and related fields.

A Poisson Process Generator Based on Multiple Thermal Noise Amplifiers for Parallel Stochastic Simulation of Biochemical Reactions

In this paper, we propose a novel Poisson process generator that uses multiple thermal noise amplifiers (TNAs) as a source of randomness and controls its event rate via a frequency-locked loop (FLL). The increase in the number of TNAs extends the effective bandwidth of amplified thermal noise and hence enhances the maximum event rate the proposed architecture can generate. Verilog-A simulation of the proposed Poisson process generator shows that its maximum event rate can be increased by a factor of 26.5 when the number of TNAs increases from 1 to 10. In order to realize parallel stochastic simulations of the biochemical reaction network, we present a fundamental reaction building block with continuous-time multiplication and addition using an AND gate and a 1-bit current-steering digital-to-analog converter, respectively. Stochastic biochemical reactions consisting of the fundamental reaction building blocks are simulated in Verilog-A, demonstrating that the simulation results are consistent with those of conventional Gillespie algorithm. An increase in the number of TNAs to accelerate the Poisson events and the use of digital AND gates for robust reaction rate calculations allow for faster and more accurate stochastic simulations of biochemical reactions than previous parallel stochastic simulators.

Markov Chain Abstractions of Electrochemical Reaction-Diffusion in Synaptic Transmission for Neuromorphic Computing

Progress in computational neuroscience toward understanding brain function is challenged both by the complexity of molecular-scale electrochemical interactions at the level of individual neurons and synapses and the dimensionality of network dynamics across the brain covering a vast range of spatial and temporal scales. Our work abstracts an existing highly detailed, biophysically realistic 3D reaction-diffusion model of a chemical synapse to a compact internal state space representation that maps onto parallel neuromorphic hardware for efficient emulation at a very large scale and offers near-equivalence in input-output dynamics while preserving biologically interpretable tunable parameters.

The Merging of Biological and Electronic Circuits

Biological circuits and systems within even a single cell need to be represented by large-scale feedback networks of nonlinear, stochastic, stiff, asynchronous, non-modular coupled differential equations governing complex molecular interactions. Thus, rational drug discovery and synthetic biological design is difficult. We suggest that a four-pronged interdisciplinary approach merging biology and electronics can help: (1) The mapping of biological circuits to electronic circuits via quantitatively exact schematics; (2) The use of existing electronic circuit software for hierarchical modeling, design, and analysis with such schematics; (3) The use of cytomorphic electronic hardware for rapid stochastic simulation of circuit schematics and associated parameter discovery to fit measured biological data; (4) The use of bio-electronic reporting circuits rather than bio-optical circuits for measurement. We suggest how these approaches can be combined to automate design, modeling, analysis, simulation, and quantitative fitting of measured data from a synthetic biological operational amplifier circuit in living microbial cells.

A compiler for biological networks on silicon chips

The explosive growth in semiconductor integrated circuits was made possible in large part by design automation software. The design and/or analysis of synthetic and natural circuits in living cells could be made more scalable using the same approach. We present a compiler which converts standard representations of chemical reaction networks and circuits into hardware configurations that can be used to simulate the network on specialized cytomorphic hardware. The compiler also creates circuit–level models of the target configuration, which enhances the versatility of the compiler and enables the validation of its functionality without physical experimentation with the hardware. We show that this compiler can translate networks comprised of mass–action kinetics, classic enzyme kinetics (Michaelis–Menten, Briggs–Haldane, and Botts–Morales formalisms), and genetic repressor kinetics, thereby allowing a large class of models to be transformed into a hardware representation. Rule–based models are particularly well–suited to this approach, as we demonstrate by compiling a MAP kinase model. Development of specialized hardware and software for simulating biological networks has the potential to enable the simulation of larger kinetic models than are currently feasible or allow the parallel simulation of many smaller networks with better performance than current simulation software.

We present a “silicon compiler” that is capable of translating biochemical models encoded in the SBML standard into specialized analog cytomorphic hardware and transfer function–level simulations of such hardware. We show how the compiler and hardware address challenges in analog computing: 1) We ensure that the integration of errors due to the mismatch between analog circuit parameters does not become infinite over time but always remains finite via the use of total variables (the solution of the “divergence problem”); 2) We describe the compilation process through a series of examples using building blocks of biological networks, and show the results of compiling two SBML models from the literature: the Elowitz repressilator model and a rule–based model of a MAP kinase cascade. Source code for the compiler is available at https://doi.org/10.5281/zenodo.3948393.

Cytomorphic Electronics With Memristors for Modeling Fundamental Genetic Circuits

Cytomorphic engineering attempts to study the cellular behavior of biological systems using electronics. As such, it can be considered analogous to the study of neurobiological concepts for neuromorphic engineering applications. To date, digital and analog translinear electronics have commonly been used in the design of cytomorphic circuits; Such circuits could greatly benefit from lowering the area of the digital memory via memristive circuits. In this article, we propose a novel approach that utilizes the Boltzmann-exponential stochastic transport of ionic species through insulators to naturally model the nonlinear and stochastic behavior of biochemical reactions. We first show that two-terminal memristive devices can capture the non-linear and stochastic behavior of biochemical reactions. Then, we present the design of several building blocks based on analog memristive circuits that inherently model the biophysical mechanisms of gene expression. The circuits model induction by small molecules, activation and repression by transcription factors, biological promoters, cooperative binding, and transcriptional and translational regulation of gene expression. Finally, we utilize the building blocks to form complex mixed-signal networks that can simulate the delay-induced oscillator and the p53-mdm2 interaction in the cancer signaling pathway. Our approach can provide a fast and simple emulative framework for studying genetic circuits and arbitrary large-scale biological networks in systems and synthetic biology. Some challenges may be that memristive devices with frequent learning and programming do not have the same longevity as traditional transistor-based electron-transport devices, and operate with significantly slower time constants, which can limit emulation speed.

Pathways to cellular supremacy in biocomputing

Synthetic biology uses living cells as the substrate for performing human-defined computations. Many current implementations of cellular computing are based on the “genetic circuit” metaphor, an approximation of the operation of silicon-based computers. Although this conceptual mapping has been relatively successful, we argue that it fundamentally limits the types of computation that may be engineered inside the cell, and fails to exploit the rich and diverse functionality available in natural living systems. We propose the notion of “cellular supremacy” to focus attention on domains in which biocomputing might offer superior performance over traditional computers. We consider potential pathways toward cellular supremacy, and suggest application areas in which it may be found.

Synthetic biology uses cells as its computing substrate, often based on the genetic circuit concept. In this Perspective, the authors argue that existing synthetic biology approaches based on classical models of computation limit the potential of biocomputing, and propose that living organisms have under-exploited capabilities.

Fast and Precise Emulation of Stochastic Biochemical Reaction Networks With Amplified Thermal Noise in Silicon Chips

The analysis and simulation of complex interacting biochemical reaction pathways in cells is important in all of systems biology and medicine. Yet, the dynamics of even a modest number of noisy or stochastic coupled biochemical reactions is extremely time consuming to simulate. In large part, this is because of the expensive cost of random number and Poisson process generation and the presence of stiff, coupled, nonlinear differential equations. Here, we demonstrate that we can amplify inherent thermal noise in chips to emulate randomness physically, thus alleviating these costs significantly. Concurrently, molecular flux in thermodynamic biochemical reactions maps to thermodynamic electronic current in a transistor such that stiff nonlinear biochemical differential equations are emulated exactly in compact, digitally programmable, highly parallel analog "cytomorphic" transistor circuits. For even small-scale systems involving just 80 stochastic reactions, our 0.35-μm BiCMOS chips yield a 311× speedup in the simulation time of Gillespie's stochastic algorithm over COPASI, a fast biochemical-reaction software simulator that is widely used in computational biology; they yield a 15 500× speedup over equivalent MATLAB stochastic simulations. The chip emulation results are consistent with these software simulations over a large range of signal-to-noise ratios. Most importantly, our physical emulation of Poisson chemical dynamics does not involve any inherently sequential processes and updates such that, unlike prior exact simulation approaches, they are parallelizable, asynchronous, and enable even more speedup for larger-size networks.