Applied Soft Computing 13 (2013) 527–538
Contents lists available at SciVerse ScienceDirect
Applied Soft Computing
journal homepage: www.elsevier.com/locate/asoc
Euglena-based neurocomputing with two-dimensional optical feedback on
swimming cells in micro-aquariums
Kazunari Ozasa a,∗ , Jeesoo Lee b , Simon Song b , Masahiko Hara a , Mizuo Maeda a
a
b
RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
Department of Mechanical Engineering, Hanyang University, 17 Haendang-dong, Seongdong-gu, Seoul 133-791, Republic of Korea
a r t i c l e
i n f o
Article history:
Received 21 October 2011
Received in revised form 7 June 2012
Accepted 7 September 2012
Available online 17 September 2012
Keywords:
Natural computing
Soft computing
Biocomputing
Microbe-based neurocomputing
Neural network algorithm
Traveling salesman problem (TSP)
Euglena gracilis
Micro-aquarium
Microfluidic device
Optical feedback
Phototaxis
Flagellate microbial cells
Noise oscillator
a b s t r a c t
We report on neurocomputing performed with real Euglena cells confined in micro-aquariums, on which
two-dimensional optical feedback is applied using the Hopfield–Tank algorithm. Trace momentum, an
index of swimming activity of Euglena cells, is used as the input/output signal for neurons in the neurocomputation. Feedback as blue-light illumination results in temporal changes in trace momentum
according to the photophobic reactions of Euglena. Combinatorial optimization for a four-city traveling
salesman problem is achieved with a high occupation ratio of the best solutions. Two characteristics of
Euglena-based neurocomputing desirable for combinatorial optimization are elucidated: (1) attaining one
of the best solutions to the problem, and (2) searching for a number of solutions via dynamic transition
between the best solutions. Mechanisms responsible for the two characteristics are analyzed in terms of
network energy, photoreaction ratio, and dynamics/statistics of Euglena movements. The spontaneous
fluctuation in input/output signals and reduction in photoreaction ratio were found to be key factors in
producing characteristic (1), while the photo-insensitive Euglena cells or the accidental evacuation of cells
from non-illuminated areas causes characteristic (2). Furthermore, we show that the photophobic reactions of Euglena involves various survival strategies such as adaptation to blue-light or awakening from
dormancy, which can extend the performance of Euglena-based neurocomputing toward deadlock avoidance or program-less adaptation. Finally, two approaches for achieving a high-speed Euglena-inspired
Si-based computation are described.
© 2012 Elsevier B.V. All rights reserved.
1. Introduction
Motile microbes display various strategies for survival in harsh
environmental conditions such as scarcity of food, low moisture, or
harmful light exposure. They generally move towards more favorable conditions [1–9]. They also adapt to imposed stimuli [10–14],
take risks to obtain food [15,16], go into dormancy [17], memorize
stimuli history [18–20], or change their movements by interacting
with others [21]. Such nature-developed behavior can be useful
in the realization of flexible natural computation [22–24]; we can
incorporate motile microbes in a computing system to determine
the computing process through the reactions of the microbes to
intentionally imposed time-variant stimuli. Such microbe/physical
systems would show autonomous evolution in computing processes, according to the artificial interaction between the microbe
and the outer physical system via reaction/stimuli feedback.
∗ Corresponding author at: RIKEN Advanced Science Institute, 2-1 Hirosawa,
Wako, Saitama 351-0198, Japan. Tel.: +81 48 462 1111x4444; fax: +81 48 462 4695.
E-mail address: [email protected] (K. Ozasa).
1568-4946/$ – see front matter © 2012 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.asoc.2012.09.008
Aono et al. reported amoeba-based neurocomputing [25–27],
in which the food-searching capability and photophobic reaction
of the slime mold (plasmodium of the true slime mold Physarum
polycephalum) were used to drive neurocomputation to solve
combinatorial optimization problems [27]. Compared with conventional Si-based computing, this amoeba-based neurocomputing
was quite slow, but showed multi-solution search capability realized by the cooperative and exploratory behavior of the slime mold
[26] and not by a man-made program. However, since a single cell
of slime mold was used, the nature-developed survival strategies
involved were limited to those of single bodies. To incorporate the
social survival strategies of a group of cells to maintain its own
species, e.g., personality diversity among the cells, it is necessary to
implement microbe-based neurocomputing with a group of individual microbe cells. Because microbe cells are at the micron scale,
a microfluidic device is required to confine the group of target
microbe cells and to measure their reactions under a microscope.
For the implementation of microbe-based neurocomputing, the
taxis of target microbes is the key issue, since stimuli to the microbe
should induce observable reactions by the microbe. Euglena gracilis
[28–30], a common flagellated microbe swimming in pure water,
shows photophobic reactions against “harmfully-strong” blue light
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K. Ozasa et al. / Applied Soft Computing 13 (2013) 527–538
Fig. 1. (a, top) Illustration of the confinement of Euglena cells in a micro-aquarium, and schematic diagram of the 2D optical feedback system. (b, bottom left) Design of the
16-branch micro-aquarium. The scale bar represents 1 mm. (c, bottom right) Photograph of the micro-aquarium sealed in a glass-bottom dish. The Euglena dish was placed
on the stage of an optical microscope, and illuminated by red observation light during the experiments. Blue light was irradiated on the 16 branches individually according
to illumination signals calculated with the Hopfield–Tank algorithm. The scale bar represents 10 mm. (For interpretation of the references to color in this figure legend, the
reader is referred to the web version of the article.)
higher than 10 mW/cm2 [1,2,31]. Euglena cells change their swimming direction to escape from the light; however, they occasionally
fail to escape and are captured in the light. Most of the captured
cells turn continuously around their position, like a spinning top,
and drift aimlessly with the hope of escaping into the dark.
We previously reported the simulation of Euglena-based neurocomputing and proved that it can solve the same traveling salesman
problem (TSP) that Aono et al. solved with their amoeba-based
neurocomputing [32,33]. The photophobic reactions of Euglena
cells that we assumed in the Monte Carlo simulation were simple: the swimming speeds of the cells were reduced to one tenth
of the original speeds when the cells were photo-exposed [32,33].
Therefore, the performance of the simulation originated primarily from statistical fluctuations in the spatial distribution of the
cells, and not from nature-developed survival strategies against
photo-exposure. The performance of real-cell Euglena-based neurocomputing must therefore be elucidated experimentally, with
the expectation of more complicated photoreactions of Euglena. The
performance analysis of real-cell Euglena-based neurocomputing
would contribute to the development of a high-speed Euglenainspired Si-based computation.
In this study, we investigate the performance of neurocomputing with real Euglena cells confined in micro-aquariums and
discuss the detailed behaviors/mechanisms of the solution search
and the transition between the solutions. Dynamical/statistical
behaviors of state variables in Euglena-based neurocomputing are
analyzed in terms of network energy, photoreaction ratio, and celllevel Euglena movements. The similarities and differences between
Euglena-based neurocomputing and a Boltzmann machine using
simulated annealing are elucidated. Furthermore, various survival strategies of Euglena are considered for incorporation in the
microbe/physical feedback system. We also discuss the scale-up
issues of Euglena-based neurocomputing and briefly describe two
approaches for achieving a high-speed Euglena-inspired Si-based
computation.
2. Experiments
2.1. Optical feedback to Euglena in micro-aquariums
Euglena cells (100–400 cells) were confined in a polydimethylsiloxane micro-aquarium [Fig. 1(a)], with 16 equivalent
branches (184 ␮m in width, 700 ␮m in length, and 0.012 mm3 in
volume) around a center circle, 1.1-mm in diameter [Fig. 1(b)]. The
depth and total volume of the micro-aquarium were approximately
100 ␮m and 0.30 mm3 , respectively. The micro-aquarium was then
capped with a cover glass and placed in a glass-bottom dish to prevent water evaporation. The dish was placed on the stage of an
optical microscope (BX51, Olympus).
K. Ozasa et al. / Applied Soft Computing 13 (2013) 527–538
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individual branches, and is a positive integer typically between 0
and 2500.
The input signals are converted to positive real numbers
between 0.0 and 1.0 by a sigmoid function (x) with adjustable
parameters b and c.
(x) =
1
1 + exp(−b(x − c))
(1)
Parameters b and c compensate for variations in the number
of Euglena cells and photoreactivity of the cells, and are adjusted
automatically during the neurocomputation as described in detail
in Section 2.3.
The converted input signals (xj (t)) are weighted with a fixed
weight matrix wij , summed, and thresholded at a cutting level of (= 0.5) by a step function f(x), according to the Hopfield–Tank model
[34,35] with time step t.
⎛
Fig. 2. Schematic illustration of a neuron in Euglena-based neurocomputing. Unlike
neurons in conventional neurocomputing, a neuron in Euglena-based neurocomputing has a sigmoid function to covert the input signals {xj (t)} to real values [0.0. . .1.0].
The neuron contains illumination in the corresponding branch in the Euglena dish
after the weighted summation and thresholding. Since all branches are connected
to the center circle of the micro-aquarium, the neuron has a little influence on/from
other neurons. The movements of Euglena cells in the corresponding branch are
observed and evaluated as the output signal {xi (t + t)}. The output from each neuron is connected to the other neurons in the network to give the inputs for the next
time step.
yi (t) = f
⎝
N
2.2. Neurocomputing algorithm
The schematic concept of neurons of Euglena-based neurocomputing is illustrated in Fig. 2, where the two major differences
from the neurons in conventional neurocomputing are sigmoid
functions at the input signal and light illumination onto the
Euglena dish after the summation and thresholding. Sixteen neurons were used for the four-city TSP in this study, similar to
our previous investigation through Monte Carlo simulation of
Euglena-based neurocomputing [32,33]. The output from each
neuron is connected to all other neurons in the network thus
providing inputs for the next time step. The input/output signals of the 16 neurons {xj (t) (j = 1, 2, . . ., 16)} are obtained as
the sum of the swimming traces of Euglena cells (that is, trace
momentum, TM) for 16 individual branches of the micro-aquarium.
TM can be evaluated in real-time as the number of “on” pixels
in trace images obtained as binarized differential video images
every 2.6 s (10 image accumulation, 0.26 s interval). TM approximates the product of the swimming speed and cell number in
wij (xj (t)) − ⎠
(2)
j
f (x) = 1,
0,
when x > 0,
otherwise
(3)
wij = distance/40 (between route choices i and j),
0.5 (between invalid choices i and j),
0
The images of Euglena cells in the micro-aquarium were
taken through a 5× objective lens (MPLFLN5X, Olympus) with
a video camera (IUC-200CK2, Trinity) [Fig. 1(a)]. The microaquarium was illuminated from the bottom by light from a
liquid-crystal (LC) projector (LP-XU84, Sanyo) through reduction lenses [Fig. 1(c)]. An image-processing personal computer
(PC; MG/D70N, Fujitsu) was used to capture the raw images
of Euglena cells with the video camera. The PC processed the
images into input/output signals used in neurocomputing [Fig. 1(a)]
and produced 2D feedback patterns. Each 2D pattern was projected onto the micro-aquarium through the LC projector. The
image-capture resolution and the pattern-projection resolution
were both 200 pixel/mm. The typical blue-light intensity used to
induce the photoreaction of Euglena was 18.8 mW/cm2 , whereas
a red light of 19.5 mW/cm2 was irradiated onto the whole area
of the micro-aquarium to observe the movement of Euglena
cells.
⎞
(4)
(otherwise)
Each yi (t) (i = 1, 2, . . ., 16) in Eq. (2) is an illumination signal, corresponding to the firing of neuron i. When yi = 1, blue light of fixed
intensity (18.8 mW/cm2 ) is irradiated onto branch i, inducing the
photophobic reaction of Euglena cells in that branch. The output
of the neuron for the next time step {xi (t + t)} is governed by the
entering/exiting movement of Euglena cells through the photophobic reaction in branch i. Unlike in conventional discrete-time-step
neurocomputing, in which only one yi is refreshed by Eq. (2), all 16
yi are refreshed every time step in Euglena-based neurocomputing,
and each TM, i.e., xi (t), is spontaneously evolved within a certain
limit according to Euglena activities in the corresponding branch,
even if yi remains unchanged.
The four-city TSP and the eight best solutions are illustrated in
Fig. 3. Each branch in the micro-aquarium was labeled with a city
index (A, B, C, or D) and visiting order (1, 2, 3, or 4) to represent
the traveling route as a set of non-illuminated branches (yi = 0).
For instance, the illumination pattern #3 in Fig. 3 represents the
route (A2, B1, C4, D3) corresponding to a route from B to A to D
to C and back to B (total distance = 12). The eight routes shown in
Fig. 3 are the best solutions with a total distance of 12. Other valid
solutions for the given four-city TSP are the eight second best with
total distance 20 and the eight third best with total distance 24.
The connections between the 16 neurons in the present neural
network are suppressive, i.e., a higher value of a certain state variable (TM of a certain branch) contributes to turning on the light
for the other related branches to reduce their respective TM. As
shown in Fig. 4, the higher TM of branch A2 tends to illuminate
the {A1, A3, A4, B2, C2, D2} branches to reduce their respective
TM because the choice of A2 and one of those six branches at the
same time results in an invalid solution (visiting the same city
twice, or visiting two different cities at the same time). The higher
TM of branch A2 also tends to illuminate the {B1, B3, C1, C3, D1,
D3} branches with distance-dependent weights to avoid a longer
connecting route. The former has a larger effect (wij = 0.5) than
the latter (wij = 0.005–0.375, depending on the distance between
cities). The relations of suppressive connections are symmetric; a
higher TM for one of the {A1, A3, A4, B2, C2, D2} and {B1, B3, C1,
C3, D1, D3} branches tends to turn on the light for branch A2. As
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Fig. 3. Illustration of a four-city TSP to be computed in this study (top, left) and the eight best solutions for the four-city TSP with solution index #n. Values in the problem
are the distances between cities. Each branch in the micro-aquarium is labeled with a city index (A, B, C, or D) and the visiting order (1, 2, 3, or 4). The set of non-illuminated
branches represents the solution of the traveling route given as city visiting order.
shown in Fig. 4, the TM values for these 12 branches are converted
to [0.0. . .1.0], weighted, summed, and finally compared with the
threshold ( = 0.5) to determine whether the light for branch A2
turns on or off at the next time step. Branch A2 is illuminated
only when the total suppressive effect of these 12 related branches
exceeds the threshold.
2.3. Automatic parameter adjustment
To compensate for inter-experimental differences in the number of Euglena cells, parameters b and c in Eq. (2) were calculated
by empirically derived Eqs. (5)–(7) using the average TM without
blue-light (av TM0) and with blue-light (av TM1):
b() = (0.72 + 0.246) ×
22.0 av TM0
c() = (32.1 2 × 2.79 + 11.9) ×
=
av TM1
.
av TM0
,
av TM0 22.0
(5)
,
(6)
(7)
The av TM0 and av TM1 were calculated from the 10 latest TM
values without and with blue light, respectively, every 10 time
steps in the course of Euglena-based neurocomputing. Equation (7)
defines the photoreaction ratio .
The above empirical equations were obtained from the parameter dependence of neurocomputing performance investigated by
the Monte Carlo simulation [32,33] assuming that the input/output
variables {xj (t) (j = 1, 2, . . ., 16)} have a fixed Gaussian probability
distribution (average 22.0, standard deviation 5.0) and a photoreaction ratio between 0.1 and 0.6. Figure 5(a) and (b) shows the
parameter dependence with = 0.1 and 0.3, respectively, where
the neurocomputing performance was evaluated by the number
of time steps in the simulation occupied by the eight best solutions, i.e., (sum of time steps for the best eight solutions)/(total time
steps). As the photoreaction ratio increases, the range of optimum
parameters shrinks and shifts toward higher values for b and c. Taking into account the shrinking/shifting trend in the optimum range
and smooth connection among the various values between 0.1
and 0.5, the optimum sets of parameters were selected as marked
in Fig. 5(a) and (b). Equations (5) and (6) were obtained from the
relationship between b or c and , as summarized in Fig. 5(c).
Although Eqs. (5)–(7) were empirically obtained for a numerical
simulation of the four-city TSP, the automatic parameter adjustment by Eqs. (5)–(7) can be used for other types of combinatorial
optimization problems, since the adjustment leads to a higher separation of {xj (t)} into smaller values for illuminated neurons and
larger values for non-illuminated neurons. As described in Section 3.3, the photophobic reaction ratio tends to converge to a
small value, less than 0.1–0.3, in the course of Euglena-based neurocomputing. This means that the range of optimum parameters
has the margin shown in Fig. 5(a) and (b), indicating insensitivity
of computing performance to parameter selection for b and c.
K. Ozasa et al. / Applied Soft Computing 13 (2013) 527–538
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Fig. 4. Illustration of suppressive connection between branch A2 (example) and the
other branches. Invalid selections related to A2 are highly suppressed by a high
weight of 0.5, whereas non-related selections are ignored by a zero weight. Route
selections from/to A2 are evaluated with weights proportional to the corresponding
distances.
The total calculation flow of the neurocomputing process
including the observation and illumination of the Euglena dish is
summarized in Fig. 6. The observed raw image of the Euglena dish
was processed to evaluate 16 TM values, i.e., input signals {xj (t)
(j = 1, 2, . . ., 16)}. From the {xj (t)}, parameters b and c were obtained
using Eqs. (5)–(7) every 10 calculation cycles. After converting
{xj (t)} into {(xj (t))} by Eq. (1), the illumination signals {yi (t) (j = 1,
2, . . ., 16)} were calculated using the Hopfield–Tank model given
in Eq. (2). According to {yi (y)}, 16 branches were illuminated/nonilluminated by blue light to induce the photophobic reaction of
Euglena cells in each branch, which in turn produced the output
{xj (t + t)} of the 16 neurons. One cycle of the calculation took 2.6 s.
3. Results
3.1. Dynamics in a single trial case
At the beginning of Euglena-based neurocomputing, Euglena
cells were randomly distributed in the micro-aquarium with no
branches illuminated. Initially, a natural deviation in cell density
caused an imbalance among the 16 TM values, leading to feedback
illumination according to Eqs. (1)–(3). The TM of each illuminated branch decreased as a result of the photophobic reaction of
Euglena cells in that branch. This decrease in TM induced further
changes in the TM values of other branches through the feedback
algorithm/illumination. Spontaneous fluctuation in TM values also
affected the temporal evolution of illumination patterns.
One typical example of the temporal transition of feedback illumination obtained with approximately 200 Euglena cells is shown
Fig. 5. (a, top) Parameter map of neurocomputing performance obtained using a
Monte Carlo simulation, where TM without blue light is a random number with a
Gaussian probability distribution with an average of 22.0 and a standard deviation
of 5.0. Photoreaction ratio is 0.1. The performance was evaluated by the number
of time steps in the simulation occupied by the best solutions i.e., (sum of time steps
for the best solutions)/(total time steps). The red dot indicates the selected set of
parameters b and c. (b, middle) Parameter map with photoreaction ratio = 0.3. (c,
bottom) Selected parameter set (b, c) for = 0.1, 0.2, 0.3, 0.4, and 0.5. The curve shows
the dependence of b() and c() obtained through fitting (inset). As the photoreaction ratio increases, the range of optimum parameters shrinks with a shift toward
higher values for b and c. The optimum sets of parameters b and c were selected to
produce a smooth connection among various between 0.1 and 0.5, by considering the shrinking/shifting trend of the optimum range in the parameter maps. (For
interpretation of the references to color in this figure legend, the reader is referred
to the web version of the article.)
in Fig. 7, where the feedback illumination patterns are categorized
into the best (identified by solution index #n in Fig. 3), second best,
third best, and invalid solutions. In the initial stage between 0 and
2684 time steps, frequent transitions between various illumination
patterns were observed. Several best solutions appeared, but could
not be sustained for longer periods owing to a larger fluctuation in
the TM values. The best solutions occupied 18% of the 2684 time
steps.
After the initial stage, transitions between the best solutions
were observed, and the best solutions achieved were found to be
more stable than those that appeared before 2684 time steps. For
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K. Ozasa et al. / Applied Soft Computing 13 (2013) 527–538
The experimental results shown in Fig. 7 indicate that the optical
feedback system with real Euglena cells converged into one of the
best solutions and eventually transitioned to another best solution.
The results are the experimental elucidation of the two fundamental characteristics of Euglena-based neurocomputing: (1) attaining
one of the best solutions of the problem, and (2) searching for a
number of solutions via dynamic transition between the solutions
(multi-solution search).
3.2. Multi trial statistics
Fig. 6. Diagram of calculation flow of Euglena-based neurocomputing. The movements of Euglena cells in the 16 branches are evaluated to produce input signals
{xj (t)}, which are typically integer values in the range [0. . .2500]. The input signals
are converted to real values by a sigmoid function, with parameters b and c calculated
from the statistics of {xj (t)}. According to the Hopfield–Tank model, the converted
input signals are summed after being multiplied by weight values and thresholded
to produce illumination signals {yi (t)}, corresponding to the firing of the neurons
(yi = 1). The 16 branches are individually illuminated/non-illuminated by blue light
according to the corresponding illuminated signal yi = 0 (non-illuminate) or 1 (illuminate). (For interpretation of the references to color in this figure legend, the reader
is referred to the web version of the article.)
instance, the best solution #1 was sustained for the period between
2685 and 11,720 time steps, occupying 89% of the 9036 time steps.
Invalid solutions observed in the period between 2685 and 11,720
time steps were mostly one-branch missing or two-branch missing patterns of #1. For the period between 11,720 and 12,219 time
steps, invalid solutions were observed with transitions to the second and third best solutions. Two other best solutions #4 and #7
were subsequently achieved after 12,219 time steps. Solution #4
occupied 80% of the 12,219–16,028 time steps, while #7 occupied
74% of the 16,898–20,000 time steps. The total occupation ratio of
the three best solutions in this trial was 66%, with 40% for #1, 15%
for #4, and 11% for #7, as shown in the inset in Fig. 7.
Fig. 8 shows the average frequency of solutions obtained in 33
trials of Euglena-based neurocomputing. The eight best solutions
occupied 77% of the time steps on average, whereas the second
and third best solutions occupied only 0.7% and 0.07%, respectively.
Best solutions of odd-number indices (Fig. 3) appeared with higher
frequencies than those of even-number indices. This discrepancy
might be partly due to the polarization of blue light [31] and partly
due to a slight unevenness in blue-light intensity among illuminated branches because of the isotropic characteristics of the LC
projector and optics. As shown in the two examples of solution frequency for single trials in the inset, two best solutions achieved in
one single trial often had two common non-illuminated branches.
For instance, solutions #5 and #6 have A3 and C1 in common, and
solutions #3 and #7 have B1 and D3 in common.
The total frequency of the eight best solutions was in the range
0.41–1.00 for each single trial, as shown in Fig. 9. Since the second
and third best solutions were negligible, the remaining frequency
consisted of invalid solutions. The number of eight best solutions
achieved in a single trial (occupying more than 5% of the time
steps) varied between one and three. When three of the eight best
solutions were achieved in a single trial, the total frequency was
0.45–0.77 (0.60 on average), which was relatively small compared
with the one-solution (0.62–1.00, 0.87 on average) or two-solution
(0.41–0.97, 0.71 on average) cases, suggesting that the frequent
transitions tended to increase the frequency of invalid solutions.
The number of cells estimated from the total number of TM values for 20,000 time steps in each trial is also plotted in Fig. 9. When
the number of Euglena cells in the micro-aquarium increased, the
number of eight best solutions achieved in a single trial decreased.
The number of best solutions was one where the number of cells
Fig. 7. Temporal transition of feedback illumination (solution index in Fig. 2) during Euglena-based neurocomputing. Invalid solutions are unified into one (NG), and the
eight second best and third best (worst) solutions are unified into two groups (2nd and 3rd). One time step corresponds to approximately 2.6 s. (inset) Occupation ratio of
solutions in 20,000 time steps. Solutions #1, #4, and #7 were achieved sequentially with higher occupation ratios, although invalid solutions appeared occasionally.
K. Ozasa et al. / Applied Soft Computing 13 (2013) 527–538
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Fig. 8. Average frequency of solutions obtained in 33 trials of Euglena-based neurocomputing. (inset) Two typical examples of single trials. The eight best solutions occupied
77% of the time steps on average, whereas the second and third best solutions occupied only 0.7% and 0.07%, respectively. Best solutions of odd-number indices appeared
with higher frequencies than those of even-number indices, probably due to the polarization of blue light and partly due to a slight unevenness in blue-light intensity among
illuminated branches because of the isotropic characteristics of the LC projector and optics. (For interpretation of the references to color in this figure legend, the reader is
referred to the web version of the article.)
was greater than 300. Trial cases in which three best solutions were
obtained were those with cell numbers less than 200, except for one
case. This trend reveals that one of the best solutions achieved with
larger Euglena cell numbers is more stabilized with larger cell numbers. Larger cell numbers result in a higher TM and less fluctuation
in the TM, which contribute to the stabilization of the best solution
once achieved.
3.3. Network energy and photoreaction ratio
From the definition of network energy in conventional neurocomputing [34,35], we defined two types of network energy for
Euglena-based neurocomputing, taking into account that the illumination signal yi = 1 induces the photophobic reaction of Euglena
cells and reduces the input/output signals xj .
E1 =
1
wij (xi )(xj ) − (xi )
2
(8)
1
wij yi yj − yi
2
(9)
i,j
E2 =
i,j
Fig. 9. Frequency and number of best solutions obtained for 33 trials, and cell number estimated from total number of TM values for 20,000 time steps in each trial.
When three of the eight best solutions were achieved in a single trial, the total frequency was 0.45–0.77 (0.60 on average), which was relatively small compared with
the one-solution (0.62–1.00, 0.87 on average) or two-solution (0.41–0.97, 0.71 on
average) cases, suggesting that the frequent transitions tended to increase the frequency of invalid solutions. When the number of Euglena cells in the micro-aquarium
increased, the number of eight best solutions achieved in a single trial decreased,
revealing that one of the best solutions achieved with larger Euglena cell numbers
is more stabilized with larger cell numbers.
i
i
Network energy E1 is based on (xi ) and takes continuous values, whereas E2 is based on yi and takes discrete values. If we
assume that (xi ) is 0 (1) for every illuminated (non-illuminated)
branch, E1 is equal to E2 . The network energy E2 is −1.7 for the
eight best solutions, and −1.5, −1.4, and −1.35 for the second
best, third best, and one-branch-missing from the best solutions,
respectively.
The temporal evolutions of E1 and E2 are plotted in Fig. 10
for the single trial presented in Fig. 7. Network energy E1 shows
mostly a constant fluctuation between −1.35 and −0.75 throughout the trial, whereas the initial network energy at time step
1 was −0.30. The sustained fluctuation in network energy E1
was due to the spontaneous change in TM values according to
the movement of Euglena cells, and suggests that the stochastic
behavior of TM is essential in Euglena-based neurocomputing. Network energy E2 showed a large fluctuation prior to 2000 time
steps, but converged mostly to −1.7 thereafter. Relatively larger
spikes in E2 were observed at 11,740–12,220, 16,030–16,910,
and 19,200–19,500 time steps, where transitions between the
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K. Ozasa et al. / Applied Soft Computing 13 (2013) 527–538
Fig. 10. Temporal changes in network energy E1 and E2 in the same experiment
as shown in Fig. 7. The sustained fluctuation in network energy E1 was due to the
spontaneous change in TM values according to the movement of Euglena cells, and
suggests that the stochastic behavior of TM is essential in Euglena-based neurocomputing. The convergence of E2 shows that Euglena-based neurocomputing basically
directs to minimum network energy, whereas the occasional spikes in E2 reveal that
excitation to unstable transitional states occurs eventually owing to the spontaneous
fluctuation of state variables in Euglena-based neurocomputing.
best solutions were observed. The convergence of E2 shows that
Euglena-based neurocomputing basically directs to minimum network energy, whereas the occasional spikes in E2 reveal that
excitation to unstable transitional states occurs eventually owing
to the spontaneous fluctuation of state variables in Euglena-based
neurocomputing.
Figure 11 shows the temporal evolution of the photoreaction
ratio and the moving average (averaging 30 data) of network
energy E2 . The photoreaction ratio showed a number of large
spikes in the initial stage of the experiment, but settled down
mostly below 0.2 after 2850 time steps, at which time the best
solution #1 became dominant (Fig. 7). Ratio increased to 0.2–0.3
after 11,580 time steps, where the best solutions #4 and #7
were obtained. When a certain illumination pattern was sustained dominantly, Euglena cells gradually evacuated from the
illuminated branches and entered the non-illuminated branches.
This cell redistribution caused a decrease (increase) in TM values for illuminated (non-illuminated) branches, leading to a lower
Fig. 11. Temporal change in the photoreaction ratio and moving average of the
network energy E2 in the same experiment as shown in Fig. 7. The photoreaction
ratio and moving average E2 correspond remarkably well, indicating that a lower
E2 leads to longer sustainment of a certain illumination pattern, resulting in a lower
photoreaction ratio .
Fig. 12. Temporal evolution of four selected TM values for the early stage of the
experiment in Fig. 7. The four TM values are for branches A1, B2, C3, and D4, corresponding to the best solution #1. Illumination status On/Off (yi = 1/0) for each branch
is given by binary lines. After achieving best solution #1 after 2700 time steps, the
four main TM values increased to A1 (1330), B2 (1220), C3 (1280), and D4 (1250),
corresponding to the high stability of solution #1 for the period between 2700 and
11,700 time steps.
photoreaction ratio . When dropped lower than 0.05, transition between solutions was not observed effectively. When
remained in the range 0.1–0.3, transitions between the best
solutions were observed two or three times during 20,000 time
steps.
The photoreaction ratio and moving average E2 correspond
remarkably well in Fig. 11. The correspondence indicates that a
lower E2 leads to longer sustainment of a certain illumination pattern, resulting in a lower photoreaction ratio . The correspondence
also implies that the photoreaction ratio is an essential index
of Euglena-based neurocomputing that represents a kind of thermal energy (temperature) of the neural network system with real
Euglena cells.
3.4. Output signal evolution
Fig. 12 shows the temporal evolution of TM (output signals xi
in this study) for four selected branches, corresponding to the best
solution #1, in the early stage of the single trial presented in Fig. 7.
Initially, before 800 time steps, the TM of each of the four branches
remained below 1000 (A1, B2, C3, D4 = 230, 390, 290, 160, respectively, on average), since the branches were illuminated for most of
the time steps. Among the other branches (not shown here), A3, B4,
and C1 each had a relatively large TM (A3, B4, C1 = 950, 820, 810,
respectively, on average) in this period. The best solution #6 was
achieved in this period (Fig. 7) but was not sustained stably owing
to the smaller TM of D2 (380 on average).
The four main TM values for the period between 1100 and
2050 time steps were A4 (740), B2 (920), C1 (700), and C3 (460),
i.e., an invalid solution. The main four values changed to A3
(740), B4 (740), C1 (680), and D2 (810), and were sustained for
the period between 2050 and 2450 time steps, corresponding to
best solution #6, and then A3 (740), B2 (890), C1 (740), and D4
(960) for the period between 2450 and 2700 time steps, yielding
another best solution #5. After achieving best solution #1 after
2700 time steps, the four main TM values increased to A1 (1330),
B2 (1220), C3 (1280), and D4 (1250), corresponding to the high
stability of solution #1 for the period of 2700 and 11,700 time
steps.
The blue-light illumination leads to a reduction in TM by two different means: a reduction in swimming speed of Euglena cells and
K. Ozasa et al. / Applied Soft Computing 13 (2013) 527–538
535
4. Discussion
4.1. Attraction to best solutions
Fig. 13. Frequency distribution of trace momentum observed in the experiment
in Fig. 7, decomposed into illuminated and non-illuminated branches. (Inset) Frequency distribution of (xji ) for all branches. TM peaks for illuminated branches
correspond to the number of Euglena cells swimming in one illuminated branch;
the first peak at 124 for TM corresponds to one single cell per branch and the second
peak at 230 to two cells per branch. The widths of these peaks are due to the variation
in swimming speed of the cells in illuminated branches. From the peak positions, we
can deduce that most illuminated (non-illuminated) branches contained 0–4 (8–12)
Euglena cells.
a decrease in the number of cells in the illuminated branch. The
reduction in swimming speed occurs within several seconds and
causes the TM to decrease to approximately 80% with 18.8 mW/cm2
illumination. The decrease in the number of cells takes longer
(approximately 10 s or more), because the cells in the illuminated
branches exit with a slower migration speed under illumination.
The few remaining cells in the illuminated branches after a longer
illumination of 1 min or more were mostly photo-insensitive cells,
which were robust to 18.8 mW/cm2 illumination and entered the
illuminated branches without hesitation. When the illumination is
switched on and off repeatedly and rapidly, the TM values for the
illuminated branches may have had larger instant values than those
for the non-illuminated branches, because many cells remained in
the illuminated branches for a short time after the illumination was
turned on.
Figure 13 shows the frequency distribution of the TM values for all branches during the single trial presented in Fig. 7.
The TM values for non-illuminated branches have a broad single
peak with an average (standard deviation) of 1235 (390), whereas
those for illuminated branches showed a multi-peak distribution
with an average (standard deviation) of 239 (215). TM peaks for
illuminated branches correspond to the number of Euglena cells
swimming in one illuminated branch; the first peak at 124 for TM
corresponds to one single cell per branch and the second peak at
230 to two cells per branch. The widths of these peaks are due
to the variation in swimming speed of the cells in illuminated
branches. From the peak positions in Fig. 13, we can deduce that
most illuminated (non-illuminated) branches contained 0–4 (8–12)
Euglena cells.
The TM values at every time step were converted to values
between 0 and 1 using Eq. (1) with time-step-variant parameters
b and c. Parameters b and c, determined by Eqs. (5)–(7), were in
the range 0.0037–0.012 (0.0077 on average) and 620–810 (715 on
average), respectively. The frequency distribution of (xi ) is shown
in the inset in Fig. 13. The broad frequency distribution of TM values
was mostly binarized by Eq. (1), having been separated by parameter c. The position of the lower peak of (xi ) was not zero, but
close to 0.02, corresponding to 1–2 Euglena cells in an illuminated
branch.
The analysis of TM-dynamics (Fig. 12) and TM-statistics (Fig. 13)
reveals that Euglena-based neurocomputing is similar to a Boltzmann machine [36] from the viewpoint of the stochastic behavior
of the input/output signals, the frequent switching of illumination
signal yi , and the fluctuation in network energy. Attaining one of
the best solutions in Euglena-based neurocomputing is based on
the same principle as a Boltzmann machine, which can achieve
the global minimum beyond local minima traps in the network
energy. However, the origin of stochastic behavior of illumination
switching is completely different in a Boltzmann machine than in
Euglena-based neurocomputing. In a Boltzmann machine using the
simulated annealing technique [37], the probability p(ui ) to produce yi = 1 is calculated as
p(yi = 1|ui ≡
j
T∝
wij (xj ) − ) =
1
1 + exp(−ui /T )
1
log(t + 1)
(10)
(11)
The state variables ui in the Boltzmann machine do not fluctuate spontaneously, and the output yi is determined stochastically.
The stochastic determination of yi contributes to the global minimum search. On the other hand, the input/output signals xi in
Euglena-based neurocomputing fluctuate spontaneously owing to
the entering/exiting behaviors of Euglena cells in the branches. This
fluctuation results in the stochastic behavior of the illumination signals yi , leading to the best solution-search ability of Euglena-based
neurocomputing. Parameter T is decreased monotonically with
time to zero in the Boltzmann machine, allowing to the machine
to converge to the global minimum. In Euglena-based neurocomputing, the average of each TM increases (decreases) gradually as
non-illumination (illumination) continues, resulting in a decrease
in the photoreaction ratio . The gradual decrease in the ratio has
a similar effect as the simulated annealing (decrease in T), although
the temporal change the ratio is not monotonic decreasing and
does not converge to zero. The non-zero level of the photoreaction
ratio causes the multi-solution-search ability of Euglena-based
neurocomputing.
4.2. Transition between solutions
The transition between the best solutions in Euglena-based neurocomputing is caused by two individual mechanisms; swapping
non-illuminated branches and accidental decline in TM in multiple
non-illuminated branches. The former can be seen at around 2700
time steps and the latter at around 12,000 time steps in Fig. 7.
In the transition from best solution #5 to #1 observed between
2660 and 2700 time steps, non-illuminated branches of A3 and
C1 were swapped to A1 and C3, preserving the non-illuminated
branches of B2 and D4. As presented in Fig. 14, the intermediate state observed at 2680 time steps shows many traces of
Euglena cells swimming in the illuminated branches of A1, A2, A3,
C1, C2, and C3. The increase in TM for the illuminated branches
of A1, A2, C2, and C3 turned on illumination for A3 and C1.
The traces in A3 and C1 branches in Fig. 14 represent residual
cells originally swimming in these branches before illumination
at 2660 time steps, whereas those in A1, A2, C2, and C3 are
the photo-insensitive cells newly entered into these illuminated
branches at 2680 time steps. At 2700 time steps, one of the nearest best solutions #1 was achieved by chance. This observation
reveals that the transition between the best solutions by swapping
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K. Ozasa et al. / Applied Soft Computing 13 (2013) 527–538
Fig. 14. Transition of trace images from solution #5 to #1 observed for the period between 2660 and 2700 time steps and from #1 to #4 observed around 12,000 time steps
in the experiment of Fig. 7. Transition from #5 to #1 was caused by swapping mechanism originates from photo-insensitive cells entering illuminated branches. Transition
from #1 to #4 was caused by accidental decline in TM in multiple non-illuminated branches, which induces unstable transition between the invalid, second best, and third
best solutions, resetting the history of the previous best solution #1. After unstable transition, a new best solution #4 having no common non-illuminated branches with #1
was achieved.
mechanism originates from photo-insensitive cells entering illuminated branches.
For the transition from best solution #1 to #4 observed at around
12,000 time steps, the TM of both branches A1 and D4 accidentally declined from a level of 1200–1500 to 800–900 at 11720 time
steps even though the two branches were non-illuminated. The
accidental decrease in TM resulted from the occurrence that several cells in the non-illuminated branch exited it by chance. When
only one of the four TM values of the best solution accidentally
decreases for a few time steps, the decreased TM is recovered naturally and the solution remains as before. However, when two TM
values decreased simultaneously, the chance of other TM values
taking over from these two is high. As a result, an invalid solution
appeared at 11,740 time steps as shown in Fig. 14, and transition
between the invalid, second best, and third best solutions occurred
between 11,740 and 12,220 time steps. This unstable transition
reset the history of the previous best solution #1, and a new best
solution #4 was achieved at 12,220 time steps, having no common
non-illuminated branches with #1.
4.3. Euglena survival strategies and neurocomputing
The essential merits of applying Euglena-based TM as
input/output signals in neurocomputing are summarized below.
(i) All TM values fluctuate spontaneously, resulting in a global
searching capability similar to that of a Boltzmann machine.
(ii) TM values gradually decrease (increase) according to continuous illumination (non-illumination), leading to the simulated
annealing effect.
(iii) The existence of photo-insensitive Euglena cells, which is one
of the survival strategies of Euglena to escape from a harsh
environment, causes transition between the best solutions.
(iv) The gradual changes in TM values according to
illumination/non-illumination create a short-term memory,
which stabilizes the best solution once achieved.
Changes in TM for (i)–(iv) are caused mainly by the localization of Euglena cells according to illumination/non-illumination,
i.e., the cells tend to enter non-illuminated branches and escape
from illuminated branches. The localization results from a simple photophobic reaction to change swimming direction on
encountering illumination. Further complicated photophobic reactions were observed in reference experiments as shown in Fig. 15,
in which the whole micro-aquarium was periodically illuminated
with blue light of 42.9 mW/cm2 . The temporal evolution of TM
in Fig. 15 reveals that the photophobic reaction of Euglena contains various elemental reactions with different time constants.
For instance, a gradual increase in TM for the illumination “on”
period in Fig. 15 suggests the adaptation of Euglena cells to blue
light. Moreover, the steep dip in TM on turning illumination off
suggests that the flagellate movements of spinning Euglena cells are
suspended suddenly to revert to continuous straightforward swimming. These time-scale-variations in the photoreaction of Euglena
cells can be incorporated in Euglena-based neurocomputing by
tuning the experimental conditions such as the time-step duration
or blue-light intensity.
Other survival strategies of Euglena cells also give rise to interesting behaviors in the temporal evolution of the microbe/physical
feedback system, as listed below.
(v) The threshold for photophobic reaction differs among the cells
(personality).
(vi) Blue illumination enhances Euglena swimming in some cells
by them being awakened from dormancy or through increased
speed of flagellate movement (strengthening).
K. Ozasa et al. / Applied Soft Computing 13 (2013) 527–538
(vii) Some Euglena cells acquire photo-resistance during the illumination (adaptation).
(viii) Some Euglena cells may be used in frequent encounters with
illumination and be able to escape from it effectively (learning).
(ix) Chemicals emitted from Euglena cells may lead to interaction
among the cells (chemical communication).
(x) Selective cell-division may take place during the experiments
to increase the number of photo-resistive Euglena cells (group
adaptation).
Characteristics (v) and (vii) have been elucidated in our other
experiments and will be described in a separate report. Characteristics (viii)–(x) need to be investigated in future experiments. The
above list shows that various survival strategies of motile microbes
have high potential in neurocomputing and/or spontaneous functionalization of a microbe-based feedback system.
4.4. Scalability of Euglena-based neurocomputing
The same scheme for Euglena-based neurocomputing in this
study can be applied to other combinatorial optimization problems
as well as the N-city TSP with larger numbers of N. As elucidated in
our previous study using Monte Carlo simulation based on a simple photophobic reaction model of Euglena [32,33], some solutions
of the top 30% (10%) were obtained with an occupation ratio of
48% (24%) in 20,000 time steps for a randomly located eight-city
TSP. In general, a few solutions of the top 10–30% can be obtained
within a similar number of time steps (20,000) for a larger scale of
combinatorial optimization problems.
When the scale of the combinatorial optimization problem is
increased, however, the number of branches in the micro-aquarium
must also be increased, causing a problem with the scale of the
micro-aquarium. If the size of the micro-aquarium remains constant, the width of branches becomes too small for Euglena to
swim, whereas if the width of the branches remains constant, the
size of the micro-aquarium becomes too large to observe with
a microscope. This issue is partly resolved by employing multiple isolated micro-aquariums and correlating them through blue
light illumination. This expands the scalability of Euglena-based
neurocomputing, and leads to the concept of a network of microaquariums correlated artificially through optical feedback.
537
4.5. Euglena-inspired Si-based neurocomputing
The most dominant obstacle in Euglena-based neurocomputing
is its calculation speed. The total computation time for 20,000
time steps was 14.4 h. The usage of Euglena-based neurocomputing with real living cells is thus limited for auxiliary functions
to complement Si-based computing. For instance, the movement
of Euglena cells can be used as noise oscillators in Si-based computing to avoid deadlock in computing or nonsense solutions,
since a group of Euglena cells try to escape from imposed harsh
illumination with various survival strategies, as discussed in the
previous section.
One promising approach to overcome the calculation speed
issue is to simulate the movements of Euglena cells in Si-based
computers (approach A). As previously investigated [32,32], the
movements of individual Euglena cells can be simulated by means of
Monte-Carlo simulation to perform neurocomputing of combinatorial optimization problems. We can incorporate various survival
strategies of Euglena into the simulation of approach A, such as
personality, interaction among cells, or adaptation to blue light
illumination.
The other approach is to simulate the input/output signal of neurons in Euglena-based neurocomputing as illumination-dependent
noise oscillators (approach B). Instead of simulating movements of
individual cells, the temporal changes in the TM values are calculated as noise oscillators whose amplitude depends on the history
of virtual blue light illumination. The amplitude of noise oscillators is gradually reduced with illumination time as observed in
Euglena-based neurocomputing in this study. The calculation speed
of approach B is much faster than that of approach A, since the
movements of many cells are reduced to a small number of noise
oscillators. On the other hand, it may be difficult to incorporate
some of the survival strategies such as interaction among cells, in
this approach.
The two approaches A and B are referred to as Euglena-inspired
Si-based neurocomputing, exhibiting the same characteristics
of Euglena-based neurocomputing as real living cells. Although
the details and wide variation in survival strategies of Euglena
may not be incorporated completely in Euglena-inspired Si-based
neurocomputing, high speed neurocomputing based on Euglena
behavior can be achieved without geometrical limitations on
micro-aquariums. The performances of approaches A and B will
be reported in the near future in a separate report.
5. Conclusion
Fig. 15. Temporal evolution of trace momentum according to whole-area illumination On/Off with an intensity of 42.9 mW/cm2 . The photophobic reaction of Euglena
contains various elemental reactions with different time constants under a higher
illumination intensity, suggesting the possibility of incorporating them in Euglenabased neurocomputing by tuning the experimental conditions, such as the time-step
duration or blue-light intensity. (For interpretation of the references to color in this
figure legend, the reader is referred to the web version of the article.)
We examined the performance of Euglena-based neurocomputing with real cells confined in micro-aquariums and elucidated: (1)
attaining one of the best solutions of the problem, and (2) searching for a number of solutions via dynamic transition between the
solutions (multi-solution search). We analyzed the detailed behaviors/mechanisms of the solution search and transition between the
solutions in terms of the network energy, photoreaction ratio, and
dynamics/statistics of Euglena movements, and concluded that similar effects to a Boltzmann machine using the simulated annealing
technique can be realized in Euglena-based neurocomputing, owing
to the spontaneous fluctuation in TM values as well as the reduction in the photoreaction ratio . Essential differences between the
Boltzmann machine and Euglena-based neurocomputing are that
in the latter, all TM values are spontaneously changed at every
time step and that the photoreaction ratio does not decrease
monotonically nor converge to zero. The spontaneous fluctuation
in TM values originates from stochastic movements of Euglena
cells, whereas the reduction in photoreaction ratio originates from
the photophobic movements of Euglena cells to escape from an
538
K. Ozasa et al. / Applied Soft Computing 13 (2013) 527–538
illuminated area. The existence of photo-insensitive cells, which
is one survival strategy of Euglena, plays an important role in the
transition between solutions. We also showed that the photophobic reaction of Euglena contains various elemental reactions
with different time constants, which may lead to more complicated behavior of the TM when shorter time steps or higher
illumination intensities are employed. Two approaches for achieving a high-speed Euglena-inspired Si-based computation were
described: Monte-Carlo simulation of individual cells and numerical simulation of the output signal of neurons in Euglena-based
neurocomputing as illumination-dependent noise oscillators. This
study revealed a high potential for Euglena-based neurocomputing to develop soft natural computation, in which Euglena survival
strategies play an important role in avoiding deadlock in computation or nonsense solutions.
Acknowledgments
The authors would like to thank very much Mr. Kengo Suzuki and
Ms. Sharbanee Mitra at Euglena Co., Ltd. (http://euglena.jp/engligh)
for supplying Euglena cells and suggestive information on their
nature. They also thank Dr. Masashi Aono for four-city TSP discussion. They acknowledge financial support for this study by the
Ministry of Education, Science, Sports and Culture, Grant-in-Aid
for Scientific Research (B), 21360192, 2009–2012. This research
was supported partially by the International Research & Development Program of the National Research Foundation of Korea
(NRF) funded by the Ministry of Education, Science and Technology
(MEST) of Korea (grant number: K20901000006-09E0100-00610)
and the Seoul R&BD Program (10919).
References
[1] J.J. Wolken, E. Shin, Photomotion in Euglena gracilis. I. Photokinesis. II. Phototaxis, Journal of Eukaryotic Microbiology 5 (1958) 39.
[2] B. Diehn, Phototaxis and sensory transduction in Euglena, Science 181 (1973)
1009.
[3] J. Adler, Method for measuring chemotaxis and use of the method to determine optimum conditions for chemotaxis by Escherichia coli, Journal of General
Microbiology 74 (1973) 77.
[4] J.J. Wolken, Euglena: the photoreceptor system for phototaxis, Journal of
Eukaryotic Microbiology 24 (1977) 518.
[5] J.E. Segall, M.D. Manson, H.C. Berg, Signal processing times in bacterial chemotaxis, Nature 296 (1982) 855.
[6] R. Zhao, E.J. Collins, R.B. Bourret, R.E. Silversmith, Structure and catalytic mechanism of the E. coli chemotaxis phosphatase CheZ, Nature Structural Biology 9
(2002) 570.
[7] M. Ntefidou, M. Iseki, M. Watanabe, M. Lebert, D.P. Häder, Photoactivated
adenylyl cyclase controls phototaxis in the flagellate Euglena gracilis, Plant
Physiology 133 (2003) 1517.
[8] J.S. Parkinson, Bacterial chemotaxis: a new player in response regulator
dephosphorylation, Journal of Bacteriology 185 (2003) 1492.
[9] D. Greenfield, A.L. McEvoy, H. Shroff, G.E. Crooks, N.S. Wingreen, E. Betzig, J. Liphardt, Self-organization of the Escherichia coli chemotaxis network
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
[23]
[24]
[25]
[26]
[27]
[28]
[29]
[30]
[31]
[32]
[33]
[34]
[35]
[36]
[37]
imaged with super-resolution light microscopy, PLoS Biology 7 (2009)
1000137.
W.F. Danforth, B.W. Wilson, Adaptive changes in the acetate metabolism of
Euglena, Journal of Eukaryotic Microbiology 4 (1957) 52.
J.R. Cook, Influence of light on acetate utilization in green Euglena, Plant and
Cell Physiology 6 (1965) 301.
M.J. Doughty, B. Diehn, Photosensory transduction in the flagellated alga
Euglena gracilis, Archives of Microbiology 134 (1983) 204.
J.E. Gestwicki, L.L. Kiessling, Inter-receptor communication through arrays of
bacterial chemoreceptors, Nature 415 (2002) 81.
B.S. Hughes, A.J. Cullum, A.F. Bennett, An experimental evolutionary study on
adaptation to temporally fluctuating pH in Escherichia coli, Physiological and
Biochemical Zoology 80 (2007) 406.
L. Tanya, M. Beekman, Food quality and the risk of light exposure affect patchchoice decisions in the slime mold Physarum polycephalum, Ecology 91 (2010)
22.
K. Ito, D. Sumpter, T. Nakagaki, Risk management in spatio-temporally varying
field by true slime mold, Nonlinear Theory and its Applications IEICE 1 (2010)
26.
J.J. Blum, D.E. Buetow, Biochemical changes during acetate deprivation and
repletion in Euglena, Experimental Cell Research 29 (1963) 407.
E. Kussell, R. Kishony, N.Q. Balaban, S. Leibler, Bacterial persistence: a model of
survival in changing environments, Genetics 169 (2005) 1807.
D. Dubnau, R. Losick, Bistability in bacteria, Molecular Microbiology 61 (2006)
564.
S.V. Avery, Microbial cell individuality and the underlying sources of heterogeneity, Nature Reviews Microbiology 4 (2006) 577.
R.G. Fray, Altering plant–microbe interaction through artificially manipulating
bacterial quorum sensing, Annals of Botany 89 (2002) 245.
R. Whitman (Ed.), Natural Computation, The MIT Press, Cambridge, USA, 1988.
D.H. Ballard, An Introduction to Natural Computation, The MIT Press,
Cambridge, USA, 1991.
B.J. MacLennan, Natural computation and non-Turing models of computation,
Theoretical Computer Science 317 (2004) 115.
M. Aono, M. Hara, K. Aihara, Amoeba-based neurocomputing with chaotic
dynamics, Communications of the ACM 50 (2007) 69.
M. Aono, M. Hara, Spontaneous deadlock breaking on amoeba-based neurocomputer, Biosystems 91 (2008) 83.
M. Aono, Y. Hirata, M. Hara, K. Aihara, Amoeba-based chaotic neurocomputing:
combinatorial optimization by coupled biological oscillators, New Generation
Computing 27 (2009) 129.
D.E. Buetow (Ed.), The Biology of Euglena: Biochemistry, Academic Press, New
York, USA, 1968.
D.E. Buetow (Ed.), The Biology of Euglena: Physiology, Academic Press, New
York, USA, 1968.
D.E. Buetow (Ed.), The Biology of Euglena: Subcellular biochemistry and molecular biology, Academic Press, New York, USA, 1982.
B. Diehn, Action spectra of the phototactic responses in Euglena, Biochimica et
Biophysica Acta 177 (1969) 136.
K. Ozasa, M. Aono, M. Maeda, M. Hara, Simulation of neurocomputing
based on photophobic reactions of Euglena – toward microbe-based neural network computing, Lecture Notes in Computer Science 5715 (2009)
209.
K. Ozasa, M. Aono, M. Maeda, M. Hara, Simulation of neurocomputing based on
the photophobic reactions of Euglena, Biosystems 100 (2010) 101.
J.J. Hopfield, D.W. Tank, Computing with neural circuits: a model, Science 233
(1986) 625.
P.D. Wasserman, Van Nostrand Reinhold, Neural Computing: Theory and
Practice, New York, USA, 1989.
D. Ackley, G. Hinton, T. Sejnowski, A learning algorithm for Boltzmann
machines, Cognitive Science 9 (1985) 147.
E. Aarts, J. Korst, Simulated Annealing and Boltzmann Machines, Wiley, New
York, USA, 1988.