Motivated by the fact that living cells use molecular circuits (i.e., a set of chemical reactions) for information processing, this paper investigates the problem of designing molecular circuits for demodulation. In our earlier work, we use a Markovian approach to derive a demodulator for diffusion-based molecular communication. The demodulation filters take the form of an ordinary differential equation, which computes the log-posteriori probability of a transmission symbol being sent. This paper considers the realization of these demodulation filters using molecular circuits assuming the transmission symbols are rectangular pulses of the same duration but different amplitudes, i.e., concentration modulation. This paper makes a number of contributions. First, we use time-scale separation and renewal theory to analytically derive an approximation of the demodulation filter from our earlier work. Second, we present a method to turn this approximation into a molecular circuit. By using simulations, we show that the output of the derived molecular circuit is approximately equal to the log-posteriori probability calculated by the exact demodulation filter if the log-posteriori probability is positive. Third, we demonstrate that a biochemical circuit in yeast behaves similarly to the derived molecular demodulation filter and is therefore a candidate for implementing the derived filter.
The use of chemical reactions to implement analog computation is an active area of research in molecular computing and synthetic biology, see @cite_21 @cite_36 @cite_27 @cite_8 . However, the problem of using chemical reactions to implement an analog filter based demodulator does not seem to have been done before.
@cite_36 @cite_27 @cite_21 @cite_8
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Advances in the field of synthetic biology have been key to demonstration of molecular computing systems in general and DNA in particular. This paper presents an overview of how continuous-time, discrete-time, and digital signal processing systems can be implemented using molecular reactions and DNA. In this paper, discrete-time systems refer to sampled signals with continuous signal amplitude. Signals that are sampled in discrete time steps with digital amplitude are referred to as digital signals. Delay elements in sampled signals are implemented using molecular reactions in the form of molecular transfer reactions. Completion of all phases of transfer reactions once corresponds to a computation cycle. These molecular systems can be implemented in a fully-synchronous, globally-synchronous locally-asynchronous or fully-asynchronous manner. The paper also presents molecular sensing systems where molecular reactions are used to implement analog-to-digital converters (ADCs) and digital-to-analog converters (DACs). Molecular implementations of digital logic systems are presented. A complete example of the addition of two molecules using digital implementation is described where the concentrations of two molecules are converted to digital by two 3-bit ADCs, and the 4-bit output of the digital adder is converted to analog by a 4-bit DAC. This system is demonstrated using both molecular reactions and DNA. A brief comparison of molecular and electronic systems is also presented. We analyse the pros and cons of analog versus digital computation in living cells. Our analysis is based on fundamental laws of noise in gene and protein expression, which set limits on the energy, time, space, molecular count and part-count resources needed to compute at a given level of precision. We conclude that analog computation is significantly more efficient in its use of resources than deterministic digital computation even at relatively high levels of precision in the cell. Based on this analysis, we conclude that synthetic biology must use analog, collective analog, probabilistic and hybrid analog–digital computational approaches; otherwise, even relatively simple synthetic computations in cells such as addition will exceed energy and molecular-count budgets. We present schematics for efficiently representing analog DNA–protein computation in cells. Analog electronic flow in subthreshold transistors and analog molecular flux in chemical reactions obey Boltzmann exponential laws of thermodynamics and are described by astoundingly similar logarithmic electrochemical potentials. Therefore, cytomorphic circuits can help to map circuit designs between electronic and biochemical domains. We review recent work that uses positive-feedback linearization circuits to architect wide-dynamic-range logarithmic analog computation in Escherichia coli using three transcription factors, nearly two orders of magnitude more efficient in parts than prior digital implementations. Chemical synthesis generally requires labor-intensive, sometimes tedious trial-and-error optimization of reaction conditions. Here, we describe a plug-and-play, continuous-flow chemical synthesis system that mitigates this challenge with an integrated combination of hardware, software, and analytics. The system software controls the user-selected reagents and unit operations (reactors and separators), processes reaction analytics (high-performance liquid chromatography, mass spectrometry, vibrational spectroscopy), and conducts automated optimizations. The capabilities of this system are demonstrated in high-yielding implementations of C-C and C-N cross-coupling, olefination, reductive amination, nucleophilic aromatic substitution (S N Ar), photoredox catalysis, and a multistep sequence. The graphical user interface enables users to initiate optimizations, monitor progress remotely, and analyze results. Subsequent users of an optimized procedure need only download an electronic file, comparable to a smartphone application, to implement the protocol on their own apparatus. This paper considers a diffusion-based molecular communication system, where the transmitter uses reaction shift keying (RSK) as the modulation scheme. We focus on the demodulation of RSK signal at the receiver. The receiver consists of a front-end molecular circuit and a back-end demodulator. The front-end molecular circuit is a set of chemical reactions consisting of multiple chemical species. The optimal demodulator computes the posteriori probability of the transmitted symbols given the history of the observation. The derivation of the optimal demodulator requires the solution to a specific Bayesian filtering problem. The solution to this Bayesian filtering problem had been derived for a few specific molecular circuits and specific choice(s) of observed chemical species. The derivation of such solution is also lengthy. The key contribution of this paper is to present a general solution to this Bayesian filtering problem, which can be applied to any molecular circuit and any choice of observed species.