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.

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.

Measuring and modeling energy and power consumption in living microbial cells with a synthetic ATP reporter.

BACKGROUND: Adenosine triphosphate (ATP) is the main energy carrier in living organisms, critical for metabolism and essential physiological processes. In humans, abnormal regulation of energy levels (ATP concentration) and power consumption (ATP consumption flux) in cells is associated with numerous diseases from cancer, to viral infection and immune dysfunction, while in microbes it influences their responses to drugs and other stresses. The measurement and modeling of ATP dynamics in cells is therefore a critical component in understanding fundamental physiology and its role in pathology. Despite the importance of ATP, our current understanding of energy dynamics and homeostasis in living cells has been limited by the lack of easy-to-use ATP sensors and the lack of models that enable accurate estimates of energy and power consumption related to these ATP dynamics. Here we describe a dynamic model and an ATP reporter that tracks ATP in E. coli over different growth phases. RESULTS: The reporter is made by fusing an ATP-sensing rrnB P1 promoter with a fast-folding and fast-degrading GFP. Good correlations between reporter GFP and cellular ATP were obtained in E. coli growing in both minimal and rich media and in various strains. The ATP reporter can reliably monitor bacterial ATP dynamics in response to nutrient availability. Fitting the dynamics of experimental data corresponding to cell growth, glucose, acetate, dissolved oxygen, and ATP yielded a mathematical and circuit model. This model can accurately predict cellular energy and power consumption under various conditions. We found that cellular power consumption varies significantly from approximately 0.8 and 0.2 million ATP/s for a tested strain during lag and stationary phases to 6.4 million ATP/s during exponential phase, indicating ~ 8-30-fold changes of metabolic rates among different growth phases. Bacteria turn over their cellular ATP pool a few times per second during the exponential phase and slow this rate by ~ 2-5-fold in lag and stationary phases. CONCLUSION: Our rrnB P1-GFP reporter and kinetic circuit model provide a fast and simple way to monitor and predict energy and power consumption dynamics in bacterial cells, which can impact fundamental scientific studies and applied medical treatments in the future.

Cytomorphic Electronic Systems: A review and perspective.

Boltzmann-exponential thermodynamic laws govern noisy molecular flux in chemical reactions as well as noisy subthreshold electron current flux in transistors. These common mathematical laws enable one to map and simulate arbitrary stochastic biochemical reaction networks in highly efficient cytomorphic systems built on subthreshold analog circuits. Such simulations can accurately model noisy, nonlinear, asynchronous, stiff, and non-modular feedback dynamics in interconnected networks in the physical circuits, automatically. The scaling in simulation time for stochastic networks with the number of reactions or molecules is constant in cytomorphic systems. In contrast, it grows rapidly in digital systems, which are not parallelizable. Therefore, cytomorphic systems enable large-scale supercomputing systems-biology simulations of arbitrary and highly computationally intensive biochemical reaction networks that can nevertheless be compiled to them via digitally programmable parameters and connectivity. We outline how cytomorphic systems can be utilized for rapid drug-cocktail formulation and discovery in future pandemics like COVID-19; can simulate networks important in cancer; and can help automate the design of synthetic biological circuits, e.g. a synthetic biological operational amplifier for robust and precise drug delivery. Thus, just as neuromorphic systems have enabled multiple applications in A.I., cytomorphic systems will enable multiple applications in biology and medicine.

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.

Can One Concurrently Record Electrical Spikes from Every Neuron in a Mammalian Brain?

The classic approach to measure the spiking response of neurons involves the use of metal electrodes to record extracellular potentials. Starting over 60 years ago with a single recording site, this technology now extends to ever larger numbers and densities of sites. We argue, based on the mechanical and electrical properties of existing materials, estimates of signal-to-noise ratios, assumptions regarding extracellular space in the brain, and estimates of heat generation by the electronic interface, that it should be possible to fabricate rigid electrodes to concurrently record from essentially every neuron in the cortical mantle. This will involve fabrication with existing yet nontraditional materials and procedures. We further emphasize the need to advance materials for improved flexible electrodes as an essential advance to record from neurons in brainstem and spinal cord in moving animals.

A Novel Bioelectronic Reporter System in Living Cells Tested with a Synthetic Biological Comparator.

As the fields of biotechnology and synthetic biology expand, cheap and sensitive tools are needed to measure increasingly complicated genetic circuits. In order to bypass some drawbacks of optical fluorescent reporting systems, we have designed and created a co-culture microbial fuel cell (MFC) system for electronic reporting. This system leverages the syntrophic growth of Escheriachia. coli (E. coli) and an electrogenic bacterium Shewanella oneidensis MR-1 (S. oneidensis). The fermentative products of E. coli provide a carbon and electron source for S. oneidensis MR-1, which then reports on such activity electrically at the anode of the MFC. To further test the capability of electrical reporting of complicated synthetic circuits, a novel synthetic biological comparator was designed and tested with both fluorescent and electrical reporting systems. The results suggest that the electrical reporting system is a good alternative to commonly used optical fluorescent reporter systems since it is a non-toxic reporting system with a much wider dynamic range.

An Artificial Tissue Homeostasis Circuit Designed via Analog Circuit Techniques.

Tissue homeostasis (feedback control) is an important mechanism that regulates the population of different cell types within a tissue. In type-1 diabetes, auto-immune attack and consequent death of pancreatic ß cells result in the failure of homeostasis and loss of organ function. Synthetically engineered adult stem cells with homeostatic control based on digital logic have been proposed as a solution for regenerating ß cells. Such previously proposed homeostatic control circuits have thus far been unable to reliably control both stem-cell proliferation and stem-cell differentiation. Using analog circuits and feedback systems analysis, we have designed an in silico circuit that performs homeostatic control by utilizing a novel scheme with both symmetric and asymmetric division of stem cells. The use of a variety of feedback systems analysis techniques, which is common in analog circuit design, including root-locus techniques, Bode plots of feedback-loop frequency response, compensation techniques for improving stability, and robustness analysis help us choose design parameters to meet desirable specifications. For example, we show that lead compensation in analog circuits instantiated as an incoherent feed-forward loop in the biological circuit improves stability, whereas simultaneously reducing steady-state tracking error. Our symmetric and asymmetric division scheme also improves phase margin in the feedback loop, and thus improves robustness. This paper could be useful in porting an analog-circuit design framework to synthetic biological applications of the future.

A Synthetic Microbial Operational Amplifier.

Synthetic biology has created oscillators, latches, logic gates, logarithmically linear circuits, and load drivers that have electronic analogs in living cells. The ubiquitous operational amplifier, which allows circuits to operate robustly and precisely has not been built with biomolecular parts. As in electronics, a biological operational-amplifier could greatly improve the predictability of circuits despite noise and variability, a problem that all cellular circuits face. Here, we show how to create a synthetic three-stage inducer-input operational amplifier with a fast CRISPR-based differential-input push-pull stage, a slow transcription-and-translation amplification stage, and a fast-enzymatic output stage. Our "Bio-OpAmp" uses only 5 proteins including dCas9. It expands the toolkit of fundamental analog circuits in synthetic biology and provides a simple circuit motif for robust and precise molecular homeostasis.

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

Prior work has shown that compact analog circuits can faithfully represent and model fundamental biomolecular circuits via efficient log-domain cytomorphic transistor equivalents. Such circuits have emphasized basis functions that are dominant in genetic transcription and translation networks and deoxyribonucleic acid (DNA)-protein binding. Here, we report a system featuring digitally programmable 0.35 µm BiCMOS analog cytomorphic chips that enable arbitrary biochemical reaction networks to be exactly represented thus enabling compact and easy composition of protein networks as well. Since all biomolecular networks can be represented as chemical reaction networks, our protein networks also include the former genetic network circuits as a special case. The cytomorphic analog protein circuits use one fundamental association-dissociation-degradation building-block circuit that can be configured digitally to exactly represent any zeroth-, first-, and second-order reaction including loading, dynamics, nonlinearity, and interactions with other building-block circuits. To address a divergence issue caused by random variations in chip fabrication processes, we propose a unique way of performing computation based on total variables and conservation laws, which we instantiate at both the circuit and network levels. Thus, scalable systems that operate with finite error over infinite time can be built. We show how the building-block circuits can be composed to form various network topologies, such as cascade, fan-out, fan-in, loop, dimerization, or arbitrary networks using total variables. We demonstrate results from a system that combines interacting cytomorphic chips to simulate a cancer pathway and a glycolysis pathway. Both simulations are consistent with conventional software simulations. Our highly parallel digitally programmable analog cytomorphic systems can lead to a useful design, analysis, and simulation tool for studying arbitrary large-scale biological networks in systems and synthetic biology.

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.

Bioelectronic measurement and feedback control of molecules in living cells.

We describe an electrochemical measurement technique that enables bioelectronic measurements of reporter proteins in living cells as an alternative to traditional optical fluorescence. Using electronically programmable microfluidics, the measurement is in turn used to control the concentration of an inducer input that regulates production of the protein from a genetic promoter. The resulting bioelectronic and microfluidic negative-feedback loop then serves to regulate the concentration of the protein in the cell. We show measurements wherein a user-programmable set-point precisely alters the protein concentration in the cell with feedback-loop parameters affecting the dynamics of the closed-loop response in a predictable fashion. Our work does not require expensive optical fluorescence measurement techniques that are prone to toxicity in chronic settings, sophisticated time-lapse microscopy, or bulky/expensive chemo-stat instrumentation for dynamic measurement and control of biomolecules in cells. Therefore, it may be useful in creating a: cheap, portable, chronic, dynamic, and precise all-electronic alternative for measurement and control of molecules in living cells.

Synthetic Biology: A Unifying View and Review Using Analog Circuits.

We review the field of synthetic biology from an analog circuits and analog computation perspective, focusing on circuits that have been built in living cells. This perspective is well suited to pictorially, symbolically, and quantitatively representing the nonlinear, dynamic, and stochastic (noisy) ordinary and partial differential equations that rigorously describe the molecular circuits of synthetic biology. This perspective enables us to construct a canonical analog circuit schematic that helps unify and review the operation of many fundamental circuits that have been built in synthetic biology at the DNA, RNA, protein, and small-molecule levels over nearly two decades. We review 17 circuits in the literature as particular examples of feedforward and feedback analog circuits that arise from special topological cases of the canonical analog circuit schematic. Digital circuit operation of these circuits represents a special case of saturated analog circuit behavior and is automatically incorporated as well. Many issues that have prevented synthetic biology from scaling are naturally represented in analog circuit schematics. Furthermore, the deep similarity between the Boltzmann thermodynamic equations that describe noisy electronic current flow in subthreshold transistors and noisy molecular flux in biochemical reactions has helped map analog circuit motifs in electronics to analog circuit motifs in cells and vice versa via a `cytomorphic' approach. Thus, a body of knowledge in analog electronic circuit design, analysis, simulation, and implementation may also be useful in the robust and efficient design of molecular circuits in synthetic biology, helping it to scale to more complex circuits in the future.

Synthetic analog computation in living cells.

A central goal of synthetic biology is to achieve multi-signal integration and processing in living cells for diagnostic, therapeutic and biotechnology applications. Digital logic has been used to build small-scale circuits, but other frameworks may be needed for efficient computation in the resource-limited environments of cells. Here we demonstrate that synthetic analog gene circuits can be engineered to execute sophisticated computational functions in living cells using just three transcription factors. Such synthetic analog gene circuits exploit feedback to implement logarithmically linear sensing, addition, ratiometric and power-law computations. The circuits exhibit Weber's law behaviour as in natural biological systems, operate over a wide dynamic range of up to four orders of magnitude and can be designed to have tunable transfer functions. Our circuits can be composed to implement higher-order functions that are well described by both intricate biochemical models and simple mathematical functions. By exploiting analog building-block functions that are already naturally present in cells, this approach efficiently implements arithmetic operations and complex functions in the logarithmic domain. Such circuits may lead to new applications for synthetic biology and biotechnology that require complex computations with limited parts, need wide-dynamic-range biosensing or would benefit from the fine control of gene expression.

Efficient universal computing architectures for decoding neural activity.

The ability to decode neural activity into meaningful control signals for prosthetic devices is critical to the development of clinically useful brain- machine interfaces (BMIs). Such systems require input from tens to hundreds of brain-implanted recording electrodes in order to deliver robust and accurate performance; in serving that primary function they should also minimize power dissipation in order to avoid damaging neural tissue; and they should transmit data wirelessly in order to minimize the risk of infection associated with chronic, transcutaneous implants. Electronic architectures for brain- machine interfaces must therefore minimize size and power consumption, while maximizing the ability to compress data to be transmitted over limited-bandwidth wireless channels. Here we present a system of extremely low computational complexity, designed for real-time decoding of neural signals, and suited for highly scalable implantable systems. Our programmable architecture is an explicit implementation of a universal computing machine emulating the dynamics of a network of integrate-and-fire neurons; it requires no arithmetic operations except for counting, and decodes neural signals using only computationally inexpensive logic operations. The simplicity of this architecture does not compromise its ability to compress raw neural data by factors greater than [Formula: see text]. We describe a set of decoding algorithms based on this computational architecture, one designed to operate within an implanted system, minimizing its power consumption and data transmission bandwidth; and a complementary set of algorithms for learning, programming the decoder, and postprocessing the decoded output, designed to operate in an external, nonimplanted unit. The implementation of the implantable portion is estimated to require fewer than 5000 operations per second. A proof-of-concept, 32-channel field-programmable gate array (FPGA) implementation of this portion is consequently energy efficient. We validate the performance of our overall system by decoding electrophysiologic data from a behaving rodent.

A glucose fuel cell for implantable brain-machine interfaces.

We have developed an implantable fuel cell that generates power through glucose oxidation, producing 3.4 µW cm(-2) steady-state power and up to 180 µW cm(-2) peak power. The fuel cell is manufactured using a novel approach, employing semiconductor fabrication techniques, and is therefore well suited for manufacture together with integrated circuits on a single silicon wafer. Thus, it can help enable implantable microelectronic systems with long-lifetime power sources that harvest energy from their surrounds. The fuel reactions are mediated by robust, solid state catalysts. Glucose is oxidized at the nanostructured surface of an activated platinum anode. Oxygen is reduced to water at the surface of a self-assembled network of single-walled carbon nanotubes, embedded in a Nafion film that forms the cathode and is exposed to the biological environment. The catalytic electrodes are separated by a Nafion membrane. The availability of fuel cell reactants, oxygen and glucose, only as a mixture in the physiologic environment, has traditionally posed a design challenge: Net current production requires oxidation and reduction to occur separately and selectively at the anode and cathode, respectively, to prevent electrochemical short circuits. Our fuel cell is configured in a half-open geometry that shields the anode while exposing the cathode, resulting in an oxygen gradient that strongly favors oxygen reduction at the cathode. Glucose reaches the shielded anode by diffusing through the nanotube mesh, which does not catalyze glucose oxidation, and the Nafion layers, which are permeable to small neutral and cationic species. We demonstrate computationally that the natural recirculation of cerebrospinal fluid around the human brain theoretically permits glucose energy harvesting at a rate on the order of at least 1 mW with no adverse physiologic effects. Low-power brain-machine interfaces can thus potentially benefit from having their implanted units powered or recharged by glucose fuel cells.

An energy-efficient, adiabatic electrode stimulator with inductive energy recycling and feedback current regulation.

In this paper, we present a novel energy-efficient electrode stimulator. Our stimulator uses inductive storage and recycling of energy in a dynamic power supply. This supply drives an electrode in an adiabatic fashion such that energy consumption is minimized. It also utilizes a shunt current-sensor to monitor and regulate the current through the electrode via feedback, thus enabling flexible and safe stimulation. Since there are no explicit current sources or current limiters, wasteful energy dissipation across such elements is naturally avoided. The dynamic power supply allows efficient transfer of energy both to and from the electrode and is based on a DC-DC converter topology that we use in a bidirectional fashion in forward-buck or reverse-boost modes. In an exemplary electrode implementation intended for neural stimulation, we show how the stimulator combines the efficiency of voltage control and the safety and accuracy of current control in a single low-power integrated-circuit built in a standard .35 µm CMOS process. This stimulator achieves a 2x-3x reduction in energy consumption as compared to a conventional current-source-based stimulator operating from a fixed power supply. We perform a theoretical analysis of the energy efficiency that is in accord with experimental measurements. This theoretical analysis reveals that further improvements in energy efficiency may be achievable with better implementations in the future. Our electrode stimulator could be widely useful for neural, cardiac, retinal, cochlear, muscular and other biomedical implants where low power operation is important.

An area and power-efficient analog li-ion battery charger circuit.

The demand for greater battery life in low-power consumer electronics and implantable medical devices presents a need for improved energy efficiency in the management of small rechargeable cells. This paper describes an ultra-compact analog lithium-ion (Li-ion) battery charger with high energy efficiency. The charger presented here utilizes the tanh basis function of a subthreshold operational transconductance amplifier to smoothly transition between constant-current and constant-voltage charging regimes without the need for additional area- and power-consuming control circuitry. Current-domain circuitry for end-of-charge detection negates the need for precision-sense resistors in either the charging path or control loop. We show theoretically and experimentally that the low-frequency pole-zero nature of most battery impedances leads to inherent stability of the analog control loop. The circuit was fabricated in an AMI 0.5-µm complementary metal-oxide semiconductor process, and achieves 89.7% average power efficiency and an end voltage accuracy of 99.9% relative to the desired target 4.2 V, while consuming 0.16 mm(2) of chip area. To date and to the best of our knowledge, this design represents the most area-efficient and most energy-efficient battery charger circuit reported in the literature.