You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
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.

Cited Abstract(s):
[1]: The programming of biological cells by genetic circuit engineering is enabling the development of man-made devices and systems in the biochemical environment, with applications in the areas of biomedicine, security, and environmental sensing and control, amongst others. The exchange of information through biochemical reactions and molecule transport, i.e., Molecular Communication (MC), stands as one of the foundational paradigms for the design and characterization of these systems. In a previous work, the same authors developed an analog soft decoder design for MC based on biological circuits inspired by the analog information processing in biochemical reactions. While such a design was optimized for an MC channel affected by Gaussian noise, realistic noise models in molecule transport processes and biochemical reactions tend to deviate from this assumption. In this paper, these models are discussed, together with the validity of their Gaussian approximations, in light of the performance of the log-likelihood ratio calculation of the aforementioned design, numerically evaluated through biochemical simulation. These models, which are directly derived from the theory of molecular diffusion and stochastic chemical reaction analysis, are formulated with a general validity with respect to any future MC system design based on biological circuits.

[2]: The design of communication systems capable of processing and exchanging information through molecules and chemical processes is a rapidly growing interdisciplinary field, which holds the promise to revolutionize how we realize computing and communication devices. While molecular communication (MC) theory has had major developments in recent years, more practical aspects in the design and prototyping of components capable of MC functionalities remain less explored. In this paper, motivated by a bulk of MC literature on information transmission via molecular pulse modulation, the design of a pulse generator is proposed as an MC component able to output a predefined pulse-shaped molecular concentration upon a triggering input. The chemical processes at the basis of this pulse generator are inspired by how cells generate pulse-shaped molecular signals in biology. At the same time, the slow-speed, unreliability, and non-scalability of these processes in cells are overcome with a microfluidic-based implementation based on standard reproducible components with well-defined design parameters. Mathematical models are presented to demonstrate the analytical tractability of each component, and are validated against a numerical finite element simulation. Finally, the complete pulse generator design is implemented and simulated in a standard engineering software framework, where the predefined nature of the output pulse shape is demonstrated together with its dependence on practical design parameters.

[3]: Abstract Recent advances in synthetic biology, in particular towards the engineering of DNA-based circuits, are providing tools to program man-designed functions within biological cells, thus paving the way for the realization of biological nanoscale devices, known as nanomachines. By stemming from the way biological cells communicate in the nature, Molecular Communication (MC), i.e., the exchange of information through the emission, propagation, and reception of molecules, has been identified as the key paradigm to interconnect these biological nanomachines into nanoscale networks, or nanonetwork. The design of MC nanonetworks built upon biological circuits is particularly interesting since cells possess many of the elements required to realize this type of communication, thus enabling the design of cooperative functions in the biological environment. In this paper, a systems-theoretic modeling is realized by analyzing a minimal subset of biological circuit elements necessary to be included in an MC nanonetwork design where the message-bearing molecules are propagated via free diffusion between two cells. The obtained system-theoretic models stem from the biochemical processes underlying cell-to-cell MC, and are analytically characterized by their transfer functions, attenuation and delay experienced by an information signal exchanged by the communicating cells. Numerical results are presented to evaluate the obtained analytical expressions as functions of realistic biological parameters.

[4]: Molecular Communication (MC) is an enabling paradigm for the interconnection of future devices and networks in the biological environment, with applications ranging from bio-medicine to environmental monitoring and control. The engineering of biological circuits, which allows to manipulate the molecular information processing abilities of biological cells, is a candidate technology for the realization of MC-enabled devices. In this paper, inspired by recent studies favoring the efficiency of analog computation over digital in biological cells, an analog decoder design is proposed based on biological circuit components. In particular, this decoder computes the a-posteriori log-likelihood ratio of parity-check-encoded bits from a binary-modulated concentration of molecules. The proposed design implements the required L-value and the box-plus operations entirely in the biochemical domain by using activation and repression of gene expression, and reactions of molecular species. Each component of the circuit is designed and tuned in this paper by comparing the resulting functionality with that of the corresponding analytical expression. Despite evident differences with classical electronics, biochemical simulation data of the resulting biological circuit demonstrate very close performance in terms of Mean Squared Error (MSE) and Bit Error Rate (BER), and validate the proposed approach for the future realization of MC components.
There were other examples of using molecular circuits for molecular communication. The paper [3] presented a biological circuit for molecular communication from a system-theoretic perspective. There was also work on using analog circuits for soft detection [1] and parity check decoder [4] . The key difference between these few pieces of work and ours is that they use one sample point per symbol. Lastly, there is also work on using chemical reactions to produce transmission signals for molecular communication, see [2] .