New types of complex motion of a simple camphor boat.

We discuss the motion of a rectangular camphor boat, considering the position of a camphor pill in relation to the boat's stern as the control parameter. The boat moves because the pill releases surface active molecules that decrease the surface tension and support the motion. We introduce a new experimental system in which the boat rotates on a long arm around the axis located at the centre of a Petri dish; thus, the motion is restricted to a circle and can be studied under stationary conditions for a long time. The experiments confirmed two previously reported modes of motion: continuous motion when the pill was located at the boat edge and pulsating (intermittent) motion if it was close to the boat centre (Suematsu et al., J. Phys. Chem. C, 2010, 114(21), 9876-9882). For intermediate pill locations, we observed a new, unreported type of motion characterised by oscillating speed (i.e. oscillating motion). Different modes of motion can be observed for the same pill location. The experimental results are qualitatively confirmed using a simple reaction-diffusion model of the boat evolution used in the above-mentioned paper.

Dynamic ordering caused by a source-sink relation between two droplets.

Two droplets composed of different chemicals, 1-decanol and liquid paraffin, floating on the water surface show characteristic co-responsive behavior. The presence of two different types of droplets in the system imposes an asymmetry that would not be possible with single droplets alone. The self-propulsion and interactions between droplets appear because surface active 1-decanol molecules provided by the source are absorbed by the paraffin sink thus generating an asymmetric surface tension gradient. This source-sink relation between droplets stabilizes and enhances the self-propulsion, and leads to a variety of dynamic structures including oscillations in the inter-droplet distance. We found that the character of time evolution also depends on the concentration of dye, Sudan Black B, initially used just to stain the decanol droplet. A simple mathematical model explains the transition between the stationary state and the oscillations as a Hopf bifurcation.

Complexity and bifurcations in the motion of a self-propelled rectangle confined in a circular water chamber.

We consider the motion of a self-propelled object of rectangular shape inside a circular water chamber. The mathematical model of self-motion includes equations for the orientation and location of the rectangle and reaction-diffusion equation with an effective diffusion coefficient for the time evolution of the surface concentration of active molecules. Numerical simulations of motion were performed for different values of the ratio between the supply rate S and the evaporation rate a of active molecules. Treating S0 = S/a as a control parameter, we found the critical behavior in variables characterizing the trajectory and identified different types of motion. If the value of S0 is small, the rectangle rests at the chamber center. For larger S0, a reciprocal motion during which the rectangle passes through the center is observed. At yet higher supply rates, the star-polygonal motion appears, and the trajectory remains at a distance from the chamber center. In the experiments with a rectangle made of camphor-camphene-polypropylene plastic moving in a Petri dish, we observed the transition from the star-polygonal motion to the reciprocal motion in time. This transition can be understood on the basis of the developed model if we assume that the supply rate decreases in time.

Information Processing Using Networks of Chemical Oscillators.

I believe the computing potential of systems with chemical reactions has not yet been fully explored. The most common approach to chemical computing is based on implementation of logic gates. However, it does not seem practical because the lifetime of such gates is short, and communication between gates requires precise adjustment. The maximum computational efficiency of a chemical medium is achieved if the information is processed in parallel by different parts of it. In this paper, I review the idea of computing with coupled chemical oscillators and give arguments for the efficiency of such an approach. I discuss how to input information and how to read out the result of network computation. I describe the idea of top-down optimization of computing networks. As an example, I consider a small network of three coupled chemical oscillators designed to differentiate the white from the red points of the Japanese flag. My results are based on computer simulations with the standard two-variable Oregonator model of the oscillatory Belousov−Zhabotinsky reaction. An optimized network of three interacting oscillators can recognize the color of a randomly selected point with >98% accuracy. The presented ideas can be helpful for the experimental realization of fully functional chemical computing networks.

A Perfect Plastic Material for Studies on Self-Propelled Motion on the Water Surface.

We describe a novel plastic material composed of camphene, camphor, and polypropylene that seems perfectly suited for studies on self-propelled objects on the water surface. Self-motion is one of the attributes of life, and chemically propelled objects show numerous similarities with animated motion. One of important questions is the relationship between the object shape and its motility. In our previous paper, {R. Löffler et al. PCCP, 2019, 21, 24852-24856}, we presented a novel hybrid material, obtained from the solution of camphor in camphene, that allowed making objects of various shapes. This hybrid material has wax-like mechanical properties, but it has a very high tackiness. Here, we report that a small amount of polypropylene removed this undesirable feature. We investigated the properties of camphor-camphene-polypropylene plastic by performing the statistical analysis of a pill trajectory inside a Petri dish and compared them with those of camphor-camphene wax. The plastic showed the stable character of motion for over an hour-long experiment. The surface activity of objects made of plastic did not significantly depend on the weight ratios of the compounds. Such a significant increase in usefulness came from the polypropylene, which controlled the dissipation of camphor and camphene molecules.

Inversion probability of three-bladed self-propelled rotors after forced stops of different durations.

We investigated self-propelled rotation of a symmetric three-bladed rotor on water under periodic halt and release operations. The rotation was driven by the difference in the surface tension around the blades of the rotor because camphor molecules developed from three camphor disks glued at the blade ends. Spontaneous inversion of rotation direction was observed after a forced stop of the rotor and the subsequent release. The probability of such inversion decreased with an increase in the halting time. The asymmetric distribution of camphor molecules around the blades was also inverted after the forced stop and the degree of asymmetry increased with an increase in the angular velocity characterizing the stationary rotation of the rotor. Our experimental results for rotors with different shapes indicate that there is a strong correlation between the stationary angular velocity of the rotor and the maximum time duration of the forced stop for which a high probability of inversion is observed.

On a simple model that explains inversion of a self-propelled rotor under periodic stop-and-release-operations.

We propose a simple mathematical model that describes the time evolution of a self-propelled object on a liquid surface using variables such as object location, surface concentration of active molecules, and hydrodynamic surface flow. The model is applied to simulate the time evolution of a rotor composed of a polygonal plate with camphor pills at its corners. We have qualitatively reproduced results of experiments, in which the inversion of rotational direction under periodic stop-and-release-operations was investigated. The model correctly describes the probability of the inversion as a function of the duration of the phase when the rotor is stopped. Moreover, the model allows to introduce the rotor asymmetry unavoidable in real experiments and study its influence on the studied phenomenon. Our numerical simulations have revealed that the probability of the inversion of rotational direction is determined by the competition among the transport of the camphor molecules by the flow, the intrinsic asymmetry of the rotor, and the noise amplitude.

Applications of Information Theory Methods for Evolutionary Optimization of Chemical Computers.

It is commonly believed that information processing in living organisms is based on chemical reactions. However, the human achievements in constructing chemical information processing devices demonstrate that it is difficult to design such devices using the bottom-up strategy. Here I discuss the alternative top-down design of a network of chemical oscillators that performs a selected computing task. As an example, I consider a simple network of interacting chemical oscillators that operates as a comparator of two real numbers. The information on which of the two numbers is larger is coded in the number of excitations observed on oscillators forming the network. The parameters of the network are optimized to perform this function with the maximum accuracy. I discuss how information theory methods can be applied to obtain the optimum computing structure.

A hybrid camphor-camphene wax material for studies on self-propelled motion.

A new material that combines the self-propelling properties of camphor with the malleability of camphene is reported. It has wax-like mechanical properties at room temperature and can be formed into required shapes. The speed of the self-propelled objects and the trajectory depend on the shape and camphor-camphene weight ratio.

Bifurcation in the angular velocity of a circular disk propelled by symmetrically distributed camphor pills.

We studied rotation of a disk propelled by a number of camphor pills symmetrically distributed at its edge. The disk was put on a water surface so that it could rotate around a vertical axis located at the disk center. In such a system, the driving torque originates from surface tension difference resulting from inhomogeneous surface concentration of camphor molecules released from the pills. Here, we investigated the dependence of the stationary angular velocity on the disk radius and on the number of pills. The work extends our previous study on a linear rotor propelled by two camphor pills [Y. Koyano et al., Phys. Rev. E 96, 012609 (2017)]. It was observed that the angular velocity dropped to zero after a critical number of pills was exceeded. Such behavior was confirmed by a numerical model of time evolution of the rotor. The model predicts that, for a fixed friction coefficient, the speed of pills can be accurately represented by a function of the linear number density of pills. We also present bifurcation analysis of the conditions at which the transition between a standing and a rotating disk appears.

Chemical memory with states coded in light controlled oscillations of interacting Belousov-Zhabotinsky droplets.

The information storing potential of droplets, in which an oscillatory, photosensitive Belousov-Zhabotinsky (BZ) reaction proceeds, is investigated experimentally. We consider coupled oscillations in pairs and triplets of droplets. Droplets are surrounded by a solution of lipids in decane. Oscillations synchronize via diffusion of an activator through a lipid bilayer. The reaction in each droplet can be individually controlled by illumination with blue light through an optical fiber. We found that in pairs of BZ droplets, only the in-phase and the forcing oscillation modes are stable, however switching between these modes is not reliable. In triplets of droplets, switching between two different, stable rotational modes (clockwise and anticlockwise) can be easily implemented. Therefore, such a system is an excellent candidate for a light controlled, reliable, one bit chemical memory unit.

Cancer classification with a network of chemical oscillators.

We discuss chemical information processing considering dataset classifiers formed with a network of interacting droplets. Our arguments are based on computer simulations of droplets in which a photosensitive variant of the Belousov-Zhabotinsky (BZ) reaction proceeds. By applying optical control we can adjust the time evolution of individual droplets and prepare the network to perform a specific computational task. We demonstrate that chemical classifiers made of droplets can be designed in computer simulations based on evolutionary algorithms. The mutual information between the dataset and the observed time evolution of droplets in the network is taken as the fitness function in the optimization process. We show that a classifier of the Wisconsin Breast Cancer Dataset made of a relatively small number of droplets can distinguish between malignant and benign forms of cancer with an accuracy exceeding 97%. The reliability of the optimized chemical classifiers of this dataset as a function of optimization time, number of droplets involved in data processing and the method of extracting the output information is discussed.

Unidirectional motion of a camphor disk on water forced by interactions between surface camphor concentration and dynamically changing boundaries.

We study the motion of a camphor disk on the water surface in a system with flexible boundaries. The boundaries can be dynamically modified by non-uniform surface tension resulting from the nonhomogeneous surface concentration of the camphor molecules dissipated by the disk. We investigate the geometry of the boundaries that forces unidirectional motion of the disk. The studied system can be regarded as a signal diode if the presence or absence of a camphor disk at a specific point is interpreted as the binary TRUE and FALSE variables. The diode can be incorporated into more complex devices, like a ring that imposes unidirectional rotation of camphor disks.

Evolutionary Design of Classifiers Made of Droplets Containing a Nonlinear Chemical Medium.

Unconventional computing devices operating on nonlinear chemical media offer an interesting alternative to standard, semiconductor-based computers. In this work we study in-silico a chemical medium composed of communicating droplets that functions as a database classifier. The droplet network can be "programmed" by an externally provided illumination pattern. The complex relationship between the illumination pattern and the droplet behavior makes manual programming hard. We introduce an evolutionary algorithm that automatically finds the optimal illumination pattern for a given classification problem. Notably, our approach does not require us to prespecify the signals that represent the output classes of the classification problem, which is achieved by using a fitness function that measures the mutual information between chemical oscillation patterns and desired output classes. We illustrate the feasibility of our approach in computer simulations by evolving droplet classifiers for three machine learning datasets. We demonstrate that the same medium composed of 25 droplets located on a square lattice can be successfully used for different classification tasks by applying different illumination patterns as its externally supplied program.

How many enzyme molecules are needed for discrimination oriented applications?

Chemical reactions establish a molecular mechanism for information processing in living organisms. Here we consider a simple enzymatic reaction model that can be used to discriminate parameters characterizing periodic reagent inflow. Numerical simulations based on the kinetic equations show that there exist a range of inflow frequencies and amplitudes in which the time evolution of the system is very sensitive to small changes in the values of these parameters. However, the kinetic equations are derived for the thermodynamic limit, whereas in a real biological medium, like a cell, the number of enzyme molecules is an integer and finite. We use stochastic simulations to estimate discriminator reliability as a function of the number of enzyme molecules involved. For systems with 10 000 molecules the functionality predicted by kinetic equations is confirmed. If the number of molecules is decreased to 100, discrimination becomes unreliable.

Discrimination of time-dependent inflow properties with a cooperative dynamical system.

Many physical, chemical, and biological systems exhibit a cooperative or sigmoidal response with respect to the input. In biochemistry, such behavior is called an allosteric effect. Here, we demonstrate that a system with such properties can be used to discriminate the amplitude or frequency of an external periodic perturbation. Numerical simulations performed for a model sigmoidal kinetics illustrate that there exists a narrow range of frequencies and amplitudes within which the system evolves toward significantly different states. Therefore, observation of system evolution should provide information about the characteristics of the perturbation. The discrimination properties for periodic perturbation are generic. They can be observed in various dynamical systems and for different types of periodic perturbation.

Communication: relative diffusion in two dimensions: breakdown of the standard diffusive model for simple liquids.

Using molecular dynamics simulations for a liquid of identical soft spheres we analyze the relative diffusion constant DΣn(r) and the self diffusion constant Dn where r is the interparticle distance and n = 2, 3 denotes the dimensionality. We demonstrate that for the periodic boundary conditions, Dn is a function of the system size and the relation: DΣn(r = L/2) ≅ 2Dn(L), where L is the length of the cubic box edge, holds both for n = 2 and 3. For n = 2 both DΣ2(r) and D2(L) increase logarithmically with its argument. However, it was found that the diffusive process for large two dimensional systems is very sensitive to perturbations. The sensitivity increases with L and even a very low perturbation limits the increase of D2(L → ∞). Nevertheless, due to the functional form of DΣ2(r) the standard assumption for the Smoluchowski type models of reaction kinetics at three dimensions:DΣn(r) ≈ 2Dn leads to giant errors if applied for n = 2.

Mercury and selenium in the muscle of piscivorous common mergansers (Mergus merganser) from a selenium-deficient European country.

Although the relationship between mercury (Hg) and selenium (Se) has been studied in wild birds in areas with sufficient or excessive Se levels, little is known about this relationship in areas where the supply of Se is limited. As Hg detoxification is based on the production of biologically inactive Hg-Se complexes, the aim of this study was to investigate the relationships between the concentrations of total mercury (THg), methylmercury (MeHg), inorganic mercury (InHg=THg-MeHg), percent MeHg of THg, Se and molar ratios (THg:Se, MeHg:Se, InHg:Se) in the breast muscle (n=16) of the piscivorous common mergansers (Mergus merganser) from a Se-deficient and moderately Hg-polluted area in Poland. Mergansers were divided into two groups differing in condition (A-very good condition; C-moderate condition). Concentrations of THg, MeHg and Se were determined by atomic absorption spectrometry, modified gas chromatography atomic fluorescence spectroscopy, and spectrofluorometric methods, respectively. In all studied mergansers, mean concentrations of THg, MeHg, InHg, and Se in muscle were 2.63, 1.92, 0.46, and 0.54µgg(-1)dw, respectively. THg and MeHg concentrations in the muscle of group A mergansers were greater than in group C. The ratio of THg:Se was higher in group A than in group C (2.32 vs 1.36; p<0.01), as well as the molar ratio of MeHg:Se (A vs C: 1.98 vs 1.03; p<0.05). Comparisons between mergansers from Poland and Canada showed similar THg and percent MeHg in the muscle, but mergansers from Poland had several times lower Se levels and higher THg:Se ratios (>2.0) than the Canadian mergansers and other European and North American waterbirds. We found statistically significant positive correlations (MeHg-THg, percent MeHg/THg-MeHg, percent InHg/THg-InHg, THg:Se-THg, MeHg:Se-THg, THg:Se-MeHg, MeHg:Se-MeHg, InHg:Se-InHg, MeHg:Se-THg:Se) and some negative correlations (percent InHg/THg-MeHg, percent MeHg/THg-InHg, THg:Se-Se, MeHg:Se-Se). As THg and percent MeHg in the studied mergansers were similar to populations living in non-Se-deficient areas, it is likely that different mechanisms of muscle Hg detoxification have evolved in mergansers populations living in Se-deficient areas.

Total and methylmercury in soft tissues of white-tailed eagle (Haliaeetus albicilla) and Osprey (Pandion haliaetus) collected in Poland.

Mercury (Hg) contamination in piscivorous birds, especially methylmercury (MeHg), has been drawing much attention worldwide in regard to its bioaccumulation and biomagnification in food chains. In this study on Hg in the soft tissues of white-tailed eagles (n = 22) and ospreys (n = 2) from Poland, total Hg (THg) range was 0.15-47.6 while MeHg range was 0.11-8.05 mg kg⁻¹ dry weight. In both species, median THg and MeHg concentrations were lower in the muscle and brain than in the liver and kidney. Median nephric residues were just under 3 and 5 mgTHg kg⁻¹ or 0.9 and 3.7 mgMeHg kg⁻¹ for white-tailed eagle and osprey, respectively. In Norwegian data from the 1970s and in our results, MeHg in the muscle of white-tailed eagle was ~60 % THg (%MeHg = MeHg/THg × 100), lower than in other piscivorous birds. A clear similarity in THg tissue levels was found between Polish and German populations of white-tailed eagles.

Chemical Memory with Discrete Turing Patterns Appearing in the Glycolytic Reaction.

Memory is an essential element in information processing devices. We investigated a network formed by just three interacting nodes representing continuously stirred tank reactors (CSTRs) in which the glycolytic reaction proceeds as a potential realization of a chemical memory unit. Our study is based on the 2-variable computational model of the reaction. The model parameters were selected such that the system has a stable limit cycle and several distinct, discrete Turing patterns characterized by stationary concentrations at the nodes. In our interpretation, oscillations represent a blank memory unit, and Turing patterns code information. The considered memory can preserve information on one of six different symbols. The time evolution of the nodes was individually controlled by the inflow of ATP. We demonstrate that information can be written with a simple and short perturbation of the inflow. The perturbation applies to only one or two nodes, and it is symbol specific. The memory can be erased with identical inflow perturbation applied to all nodes. The presented idea of pattern-coded memory applies to other reaction networks that allow for discrete Turing patterns. Moreover, it hints at the experimental realization of memory in a simple system with the glycolytic reaction.