Publications about 'Boolean circuits' |
Articles in journal or book chapters |
A design for genetically-encoded counters is proposed via repressor-based circuits. An N-bit counter reads sequences of input pulses and displays the total number of pulses, modulo $2^N$. The design is based on distributed computation, with specialized cell types allocated to specific tasks. This allows scalability and bypasses constraints on the maximal number of circuit genes per cell due to toxicity or failures due to resource limitations. The design starts with a single-bit counter. The N-bit counter is then obtained by interconnecting (using diffusible chemicals) a set of N single-bit counters and connector modules. An optimization framework is used to determine appropriate gate parameters and to compute bounds on admissible pulse widths and relaxation (inter-pulse) times, as well as to guide the construction of novel gates. This work can be viewed as a step toward obtaining circuits that are capable of finite-automaton computation, in analogy to digital central processing units. |
An important goal of synthetic biology is to build biosensors and circuits with well-defined input-output relationships that operate at speeds found in natural biological systems. However, for molecular computation, most commonly used genetic circuit elements typically involve several steps from input detection to output signal production: transcription, translation, and post-translational modifications. These multiple steps together require up to several hours to respond to a single stimulus, and this limits the overall speed and complexity of genetic circuits. To address this gap, molecular frameworks that rely exclusively on post-translational steps to realize reaction networks that can process inputs at a time scale of seconds to minutes have been proposed. Here, we build mathematical models of fast biosensors capable of producing Boolean logic functionality. We employ protease-based chemical and light-induced switches, investigate their operation, and provide selection guidelines for their use as on-off switches. As a proof of concept, we implement a rapamycin-induced switch in vitro and demonstrate that its response qualitatively agrees with the predictions from our models. We then use these switches as elementary blocks, developing models for biosensors that can perform OR and XOR Boolean logic computation while using reaction conditions as tuning parameters. We use sensitivity analysis to determine the time-dependent sensitivity of the output to proteolytic and protein-protein binding reaction parameters. These fast protease-based biosensors can be used to implement complex molecular circuits with a capability of processing multiple inputs controllably and algorithmically. Our framework for evaluating and optimizing circuit performance can be applied to other molecular logic circuits. |
Starting in the early 2000s, sophisticated technologies have been developed for the rational construction of synthetic genetic networks that implement specified logical functionalities. Despite impressive progress, however, the scaling necessary in order to achieve greater computational power has been hampered by many constraints, including repressor toxicity and the lack of large sets of mutually-orthogonal repressors. As a consequence, a typical circuit contains no more than roughly seven repressor-based gates per cell. A possible way around this scalability problem is to distribute the computation among multiple cell types, which communicate among themselves using diffusible small molecules (DSMs) and each of which implements a small sub-circuit. Examples of DSMs are those employed by quorum sensing systems in bacteria. This paper focuses on systematic ways to implement this distributed approach, in the context of the evaluation of arbitrary Boolean functions. The unique characteristics of genetic circuits and the properties of DSMs require the development of new Boolean synthesis methods, distinct from those classically used in electronic circuit design. In this work, we propose a fast algorithm to synthesize distributed realizations for any Boolean function, under constraints on the number of gates per cell and the number of orthogonal DSMs. The method is based on an exact synthesis algorithm to find the minimal circuit per cell, which in turn allows us to build an extensive database of Boolean functions up to a given number of inputs. For concreteness, we will specifically focus on circuits of up to 4 inputs, which might represent, for example, two chemical inducers and two light inputs at different frequencies. Our method shows that, with a constraint of no more than seven gates per cell, the use of a single DSM increases the total number of realizable circuits by at least 7.58-fold compared to centralized computation. Moreover, when allowing two DSM's, one can realize 99.995\% of all possible 4-input Boolean functions, still with at most 7 gates per cell. The methodology introduced here can be readily adapted to complement recent genetic circuit design automation software. |
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