Single-electron circuits performing dendritic pattern formation with nature-inspired cellular automata

We propose a novel semiconductor device in which electronic-analogue dendritic trees grow on multilayer single-electron circuits. A simple cellular-automaton circuit was designed for generating dendritic patterns by utilizing the physical properties of single-electron devices, i.e. quantum and thermal effects in tunneling junctions. We demonstrate typical operations of the proposed circuit through extensive numerical simulations

Dendritic gates for signal integration with excitability-dependent responsiveness.

The shape and excitability of neuronal dendrites are expected to be responsible for the functional characteristics of information processing in the brain. In the present study, we proposed that excitable media with branching patterns mimicked the multi-signal integration of neuronal computation. We initially examined the conditions of the coincidence detection of two inputs as the simplest form of signal integration. We considered a gate with two channels that was bound by a circular joint with uniform excitability and demonstrated that the time window for the coincidence detection was controlled by the geometry and excitability of the gate. The functions of the gate were due to the unique property of the excitation waves, known as the curvature effect. The expanded spatial spread diluted the incoming excitation signals to insufficient levels to sustain wave advancement. Next, we applied dendritic gates that were reminiscent of neuronal dendrites for multi-signal integration. The irregular dendritic patterns were produced by a cellular automaton model of self-organizing pattern formation that adopted the semi-random grid in numerical simulations. We demonstrated that the threshold operation for multiple inputs was conducted by the dendritic pattern. The thresholds varied among gates owing to their irregular patterns, and were adjusted by changing the excitability without changing the gate geometry. The materializable model may provide a novel biomimetic approach for developing fuzzy hardware with adjustable responsiveness

On digital VLSI circuits exploiting collision-based fusion gates

Abstract. Collision-based reaction-diffusion computing (RDC) represents information quanta as traveling chemical wave fragments on an excitable medium. Although the medium’s computational ability is certainly increased by utilizing its spatial degrees of freedom [2], our interpretation of collision-based RDC in this paper is that wave fragments travel along ‘limited directions ’ ‘instantaneously ’ as a result of the ‘fusion of particles’. We do not deal with collision-based computing here, but will deal with conventional silicon architectures of a ‘fusion gate ’ inspired by collision-based RDC. The hardware is constructed of a population of collision points, i.e., fusion gates, of electrically equivalent wave fragments and physical wires that connect the fusion gates to each other. We show that i) fundamental logic gates can be constructed by a small number of fusion gates, ii) multiple-input logic gates are constructed in a systematic manner, and iii) the number of transistors in specific logic gates constructed by the proposed method is significantly smaller than that of conventional logic gates while maintaining high-speed and low-power operations.

Apex of a V-shaped cut field acts as a pacemaker on an oscillatory system

The generation and propagation of chemical waves in the Belousov–Zhabotinsky (BZ) reaction were investigated using a cation-exchange membrane embedded with a metal catalyst as a 2-dimensional oscillatory/active field. We found that a target pattern is generated from the top of a V-shape, indicating that the apex on the boundary between active and passive fields behaves as a pacemaker. A Plausible mechanism for this phenomenon is proposed based on a reaction–diffusion equation

Global genetic response in a cancer cell: self-organized coherent expression dynamics.

Understanding the basic mechanism of the spatio-temporal self-control of genome-wide gene expression engaged with the complex epigenetic molecular assembly is one of major challenges in current biological science. In this study, the genome-wide dynamical profile of gene expression was analyzed for MCF-7 breast cancer cells induced by two distinct ErbB receptor ligands: epidermal growth factor (EGF) and heregulin (HRG), which drive cell proliferation and differentiation, respectively. We focused our attention to elucidate how global genetic responses emerge and to decipher what is an underlying principle for dynamic self-control of genome-wide gene expression. The whole mRNA expression was classified into about a hundred groups according to the root mean square fluctuation (rmsf). These expression groups showed characteristic time-dependent correlations, indicating the existence of collective behaviors on the ensemble of genes with respect to mRNA expression and also to temporal changes in expression. All-or-none responses were observed for HRG and EGF (biphasic statistics) at around 10-20 min. The emergence of time-dependent collective behaviors of expression occurred through bifurcation of a coherent expression state (CES). In the ensemble of mRNA expression, the self-organized CESs reveals distinct characteristic expression domains for biphasic statistics, which exhibits notably the presence of criticality in the expression profile as a route for genomic transition. In time-dependent changes in the expression domains, the dynamics of CES reveals that the temporal development of the characteristic domains is characterized as autonomous bistable switch, which exhibits dynamic criticality (the temporal development of criticality) in the genome-wide coherent expression dynamics. It is expected that elucidation of the biophysical origin for such critical behavior sheds light on the underlying mechanism of the control of whole genome

Schematic illustration of genetic criticality in DEAB of the expression.

<p>The putative genetic energy potential (15 min: blue; 20 min: red) with a fixed change in the expression (see the main text) describes the arrangement of mRNA expression in a transcriptional system, where the profile of the potential is anticipated from the scaling exponent of the frequency distribution of the expression (histograms: right panel; blue: 15 min; red: 20 min; gray: overlapped). The potential profile follows a change from single-well to double-well through a flattening profile as the <i>rmsf</i> is decreased (black arrow). The picture exhibits genetic criticality (details in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0097411#pone-0097411-t001" target="_blank">Table 1</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0097411#pone.0097411.s001" target="_blank">File S1</a>) as interpreted by the Landau theory <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0097411#pone.0097411-Landau1" target="_blank">[28]</a> on characteristic expression domains for the HRG genomic response: dynamic (dark red), transit (dark blue), and static (black) domains represent above-, near- and below-criticality, respectively. In the above-criticality, due to the unimodal to bimodal shift of the frequency distribution (see also <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0097411#pone-0097411-g006" target="_blank">Figure 6A</a>), the energy potential should also be shifted; in the near-criticality and below-criticality due to the overlapping frequency distributions between 15 min and 20 min, the energy potential should be (almost) temporally invariant. Note that, in the double-well potential (below-criticality), instead of generating two independent Boltzmann distributions (two equilibrium states), the frequency distribution shows broken distributions, which suggests non-linear interaction between coherent expression states in a non-equilibrium system.</p

Bifurcation of CESs in DEAB of the expression.

<p>The bifurcations of CESs in DEAB of the expression for 15–20 min are examined with an incremental change in a segment, <i>v</i> < <i>rmsf</i> < <i>v</i> + <i>r,</i> as an extension of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0097411#pone-0097411-g004" target="_blank">Figure 4</a>, where the range <i>r</i> is set to 0.4 and <i>v</i> is a variable of <i>rmsf</i>. The bifurcation diagrams of the expression (<i>v</i> against the expression; first row) at <i>t</i> = 20 min, and the expression change (<i>v</i> against the change in the expression for 15–20 min; second row) are plotted for HRG (left panel) and EGF (right). The bifurcation diagram of the expression defines the expression level at <i>ln</i>(<i>ε</i>)  = 2.075 (lower: low- and upper: high-expression) because of the existence of a valley, which separates the low and high CESs (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0097411#pone-0097411-g006" target="_blank">Figure 6</a>), whereas the bifurcation diagram of the expression change shows three activity levels of CES: ON (positive change in the expression), EQ (near zero) and OFF (negative change in the expression). The bifurcation diagrams clearly show distinct characteristic expression domains between HRG and EGF: static, transit and dynamic domains for <i>rmsf</i> <0.21, 0.21< <i>rmsf</i> <0.42, and 0.42< <i>rmsf</i> for HRG, and static and transit domains for <i>rmsf</i> <0.16 and 0.16< <i>rmsf</i> for EGF (see details in the main text).</p

Dynamic motion of the characteristic HRG domains in DEAB of the expression change.

<p>The coordinated expression dynamics around an equilibrated high-expression state exhibit the pendulum oscillation of CES (autonomous bistable switch) between different time periods (10–15 min, 15 min–20 min, and 20–30 min): A) in the static domain (9059 mRNAs) LES1 shows ON-OFF-EQ oscillation around HES1(EQ) through a unimodal shift, and B) in the dynamic domain (3269 mRNAs) the bifurcation of LES2 at 15 min shows a dynamic change from LES2(ON) to HES2(ON) through a unimodal to bimodal profile at 20 min, and the annihilation of HES2 through a bimodal to unimodal profile at 20–30 min around HES2(EQ). The annihilation of HES2 reveals a short-lived dynamic domain. First row: frequency distribution of the expression change. Second row: the genetic landscapes of A) the static domain and B) the dynamic domain from the top view with density color bars.</p

Unimodal to bimodal frequency distribution for DEAB of the expression.

<p>The profiles of the frequency distribution of the expression (<i>ln</i>(<i>ε</i>(<i>t</i>))) from 15 min to 20 min change from unimodal to bimodal for A) high-variance expression (the root mean square fluctuation, <i>rmsf</i> >0.42) and B) low-variance expression (<i>rmsf</i> <0.42). First row: the HRG response for <i>rmsf</i> >0.42 shows a peak-shift of unimodal profiles from <i>t = </i>15 min (blue histogram) to <i>t</i> = 20 min (red) with a change in the lower to higher value of the expression, while binomial frequency distributions between 15 min (blue polygonal line) and 20 min (red histogram) almost perfectly overlap each other for <i>rmsf</i> <0.42. Second row: the EGF response shows almost the perfect overlap of profiles for both unimodal (<i>rmsf</i> >0.42) and bimodal (<i>rmsf</i> <0.42) distributions, which suggests that there is no temporal averaging response, consistent with DEAB of the expression for the EGF response (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0097411#pone-0097411-g001" target="_blank">Figure 1A</a>). For all histograms in this report, the bin size is set to 0.05.</p

Schematic illustration of autonomous bistable switch (ABS) with genetic ‘energy profile’ in DEAB of the expression change.

<p>First row: the schematic illustration depicts the temporal development of ABS showing the opposite changes of pendulum oscillation of CES between the static and dynamic domains (refer to <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0097411#pone-0097411-g007" target="_blank">Figure 7</a>). In the HRG static domain (left panel), the temporal change of CES (LES1) occurs without the bifurcation of CES; in the dynamic domain (right), the pendulum oscillation occurs through the dynamic bifurcation of CES: bifurcation of a low-expression state with a change in a putative potential profile from single- to double-well at 15 min, a change from the low- to the high-expression state at 20 min (refer to <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0097411#pone-0097411-g006" target="_blank">Figure 6A</a>) with a single-well potential shift (small dashed box), and annihilation of the high-expression state with a change from double- to single-well at 20–30 min. Second row: schematic illustration describes the dynamics of the genetic energy potential as a function of the expression change (with a fixed expression; see details in the main text): 1. purple line: 10–15 min (at 15 min); 2. blue: 15–20 min (at 15 min); 3. red: 15–20 min (at 20 min); 4. black: 20–30 min (at 30 min). The picture shows the energy flow between the pendulum motions, which reflects the non-equilibrium dynamics of CES.</p