Search

The boltzmann-exponential thermodynamic laws govern the noisy molecular flux in chemical reactions as well as the 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 and automatically model noisy, nonlinear, asynchronous, stiff, and nonmodular feedback dynamics in interconnected networks in physical circuits. The scaling in simulation time for stochastic networks with the number of reactions or molecules is constant in cytomorphic systems. By 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 via digitally programmable parameters and connectivity. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. Author summary: 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. [ABSTRACT FROM AUTHOR]

A quasi-stable threshold voltage (V[sub t]) shift is imparted onto field-effect transistors (FETs) with organic semiconductors and polymer dielectrics. Adjustment of V[sub t] from accumulation mode to zero or depletion mode is demonstrated for both p-channel and n-channel FETs, and is accomplished by applying a depletion voltage to the gate prior to device operation. Hydrophobic dielectrics and dopant-resistant semiconductors were advantageous. A pixel circuit that utilizes this nonvolatile memory element is proposed. © 2002 American Institute of Physics. [ABSTRACT FROM AUTHOR]

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 β 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 β 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM PUBLISHER]

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. [ABSTRACT FROM PUBLISHER]

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. [ABSTRACT FROM PUBLISHER]

We describe a 0.35~\mum BiCMOS silicon chip that quantitatively models fundamental molecular circuits via efficient log-domain cytomorphic transistor equivalents. These circuits include those for biochemical binding with automatic representation of non-modular and loading behavior, e.g., in cascade and fan-out topologies; for representing variable Hill-coefficient operation and cooperative binding; for representing inducer, transcription-factor, and DNA binding; for probabilistic gene transcription with analogic representations of log-linear and saturating operation; for gain, degradation, and dynamics of mRNA and protein variables in transcription and translation; and, for faithfully representing biological noise via tunable stochastic transistor circuits. The use of on-chip DACs and ADCs enables multiple chips to interact via incoming and outgoing molecular digital data packets and thus create scalable biochemical reaction networks. The use of off-chip digital processors and on-chip digital memory enables programmable connectivity and parameter storage. We show that published static and dynamic MATLAB models of synthetic biological circuits including repressilators, feed-forward loops, and feedback oscillators are in excellent quantitative agreement with those from transistor circuits on the chip. Computationally intensive stochastic Gillespie simulations of molecular production are also rapidly reproduced by the chip and can be reliably tuned over the range of signal-to-noise ratios observed in biological cells. [ABSTRACT FROM PUBLISHER]