Chemical Boltzmann Machines

Poole, William; Ortiz-Muñoz, Andrés; Behera, Abhishek; Jones, Nick; Ouldridge, Thomas E.; Winfree, Erik; Gopalkrishnan, Manoj

doi:10.1007/978-3-319-66799-7_14

Cited by 28 publications

(29 citation statements)

References 45 publications

(68 reference statements)

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“…In biochemical information-handling systems [48,70,74,75] and chemical computing [76], information is stored and processed at the molecular level. Conservation laws play a crucial role since they enable to store information in the form of nontrivial probability distributions [77] (see e.g. Eq.…”

Section: Discussionmentioning

confidence: 99%

Conservation laws and work fluctuation relations in chemical reaction networks

Rao

Esposito

2018

The Journal of Chemical Physics

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We formulate a nonequilibrium thermodynamic description for open chemical reaction networks (CRN) described by a chemical master equation. The topological properties of the CRN and its conservation laws are shown to play a crucial role. They are used to decompose the entropy production into a potential change and two work contributions, the first due to time dependent changes in the externally controlled chemostats concentrations and the second due to flows maintained across the system by nonconservative forces. These two works jointly satisfy a Jarzynski and Crooks fluctuation theorem. In absence of work, the potential is minimized by the dynamics as the system relaxes to equilibrium and its equilibrium value coincides with the maximum entropy principle. A generalized Landauer's principle also holds: the minimal work needed to create a nonequilibrium state is the relative entropy of that state to its equilibrium value reached in absence of any work.

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Section: Discussionmentioning

confidence: 99%

Conservation laws and work fluctuation relations in chemical reaction networks

Rao

Esposito

2018

The Journal of Chemical Physics

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“…Poole et al [43] have described Chemical Boltzmann Machines, which are reaction network schemes whose dynamics reconstructs inference in Boltzmann Machines. This inference can be viewed as a version of E projection.…”

Section: Related Workmentioning

confidence: 99%

A Reaction Network Scheme Which Implements Inference and Learning for Hidden Markov Models

Singh

Wiuf

Behera

et al. 2019

Lecture Notes in Computer Science

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With a view towards molecular communication systems and molecular multi-agent systems, we propose the Chemical Baum-Welch Algorithm, a novel reaction network scheme that learns parameters for Hidden Markov Models (HMMs). Each reaction in our scheme changes only one molecule of one species to one molecule of another. The reverse change is also accessible but via a different set of enzymes, in a design reminiscent of futile cycles in biochemical pathways. We show that every fixed point of the Baum-Welch algorithm for HMMs is a fixed point of our reaction network scheme, and every positive fixed point of our scheme is a fixed point of the Baum-Welch algorithm. We prove that the "Expectation" step and the "Maximization" step of our reaction network separately converge exponentially fast. We simulate mass-action kinetics for our network on an example sequence, and show that it learns the same parameters for the HMM as the Baum-Welch algorithm.

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“…Conversely, some computational schemes are possible with stochastic CRNs but not with deterministic CRNs. For example, stochastic CRNs can directly represent complex probability distributions [23], perform probabilistic inference [24], and use the CRN's inherent stochasticity to help solve combinatorial search problems [25].…”

Section: Introductionmentioning

confidence: 99%

Programming and simulating chemical reaction networks on a surface

Clamons

Qian

Winfree

2020

J. R. Soc. Interface.

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Models of well-mixed chemical reaction networks (CRNs) have provided a solid foundation for the study of programmable molecular systems, but the importance of spatial organization in such systems has increasingly been recognized. In this paper, we explore an alternative chemical computing model introduced by Qian & Winfree in 2014, the surface CRN, which uses molecules attached to a surface such that each molecule only interacts with its immediate neighbours. Expanding on the constructions in that work, we first demonstrate that surface CRNs can emulate asynchronous and synchronous deterministic cellular automata and implement continuously active Boolean logic circuits. We introduce three new techniques for enforcing synchronization within local regions, each with a different trade-off in spatial and chemical complexity. We also demonstrate that surface CRNs can manufacture complex spatial patterns from simple initial conditions and implement interesting swarm robotic behaviours using simple local rules. Throughout all example constructions of surface CRNs, we highlight the trade-off between the ability to precisely place molecules and the ability to precisely control molecular interactions. Finally, we provide a Python simulator for surface CRNs with an easy-to-use web interface, so that readers may follow along with our examples or create their own surface CRN designs.

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Chemical Boltzmann Machines

Cited by 28 publications

References 45 publications

Conservation laws and work fluctuation relations in chemical reaction networks

Conservation laws and work fluctuation relations in chemical reaction networks

A Reaction Network Scheme Which Implements Inference and Learning for Hidden Markov Models

Programming and simulating chemical reaction networks on a surface

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