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.
@cite_36: Linear I O systems are a fundamental tool in systems theory, and have been used to design complex circuits and control systems in a variety of settings. Here we present a principled design method for implementing arbitrary linear I O systems with biochemical reactions. This method relies on two levels of abstraction: first, an implementation of linear I O systems using idealised chemical reactions, and second, an approximate implementation of the ideal chemical reactions with enzyme-free, entropy-driven DNA reactions. The ideal linear dynamics are shown to be closely approximated by the chemical reactions model and the DNA implementation. We illustrate the approach with integration, gain and summation as well as with the ubiquitous robust proportional-integral controller.
@cite_27: 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.
@cite_21: Synthetic analog gene circuits can be engineered to execute logarithmically linear sensing, addition, ratiometric and power-law computations in living cells using just three transcription factors.
@cite_8: DNA circuits have been widely used to develop biological computing devices because of their high programmability and versatility. Here, we propose an architecture for the systematic construction of DNA circuits for analog computation based on DNA strand displacement. The elementary gates in our architecture include addition, subtraction, and multiplication gates. The input and output of these gates are analog, which means that they are directly represented by the concentrations of the input and output DNA strands, respectively, without requiring a threshold for converting to Boolean signals. We provide detailed domain designs and kinetic simulations of the gates to demonstrate their expected performance. On the basis of these gates, we describe how DNA circuits to compute polynomial functions of inputs can be built. Using Taylor Series and Newton Iteration methods, functions beyond the scope of polynomials can also be computed by DNA circuits built upon our architecture.
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.