Portland State University Portland State University

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Student Research Symposium Student Research Symposium 2018

May 2nd, 11:00 AM - 1:00 PM

Biochemical Reservoir Computing Biochemical Reservoir Computing

Hoang Nguyen Portland State University

Christof Teuscher Portland State University

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Nguyen, Hoang and Teuscher, Christof, "Biochemical Reservoir Computing" (2018). Student Research Symposium. 8. https://pdxscholar.library.pdx.edu/studentsymposium/2018/Poster/8

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Hoang Nguyen – hoang24@pdx.edu

Adviser: Dr. Christof Teuscher

Biochemical Reservoir Computing

Maseeh College of Engineering and Computer Science

Portland State University

BACKGROUND AND

MOTIVATION

METHODS

CONCLUSION

REFERENCES [1] A. Goudarzi, M. R. Lakin, D. Stefanovic, “DNA Reservoir Computing: A

Novel Molecular Computing Approach,” 2013.

[2] D. Angeli, “A Tutorial on Chemical Reaction Network Dynamics,” European

Journal of Control, vol. 3, no. 4, pp. 398–406, 2009.

[3] R. Rojas, “Neural Networks: A Systematic Introduction,” Springer, 1996

𝑑[𝑃1]

𝑑𝑡 = ℎ𝛽 𝑆1 𝐺1 − 𝑃3 −

𝑒

𝑉[𝑃1],

𝑑[𝑆1]

𝑑𝑡 = 𝑆1

𝑚 − ℎ𝛽 𝑆1 𝐺1 − 𝑃3 −𝑒

𝑉[𝑆1],

𝑑[𝑃2]

𝑑𝑡 = ℎ𝛽 𝑆2 𝐺2 − 𝑃1 −

𝑒

𝑉[𝑃2],

𝑑[𝑆2]

𝑑𝑡 = 𝑆2

𝑚 − ℎ𝛽 𝑆2 𝐺2 − 𝑃1 −𝑒

𝑉𝑆2 ,

𝑑[𝑃3]

𝑑𝑡 = ℎ𝛽 𝑆3 𝐺3 − 𝑃2 −

𝑒

𝑉[𝑃3],

𝑑[𝑆3]

𝑑𝑡 = 𝑆3

𝑚 − ℎ𝛽 𝑆3 𝐺3 − 𝑃2 −𝑒

𝑉𝑆3 ,

Reservoir computing is an emerging machine learning paradigm. Compared to traditional

feedforward neural networks, the reservoir can be unstructured and recurrent and only the

output layer is trained. Reservoirs can be built with various types of physical components,

yet, biochemical building blocks have not been widely used. This project focuses on

designing and testing a reservoir computer (RC) based on chemical reaction network

(CRN). We simulated high-level CRNs in MATLAB and their complex chemical

dynamics were observed over time. A CRN constructed by a network of coupled

deoxyribozyme oscillators was chosen for the final RC model. This project thus has the

potential to influence biomedical research and genetic disorder treatments.

RESULTS

The CRN dynamics inside the reservoir were mathematically model by a set of ordinary

differential equations (ODEs) shown in (1)

Key parameters:

[𝑃𝑖]: 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑝𝑟𝑜𝑑𝑢𝑐𝑡 𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑒𝑠

[𝑆𝑖]: 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑠𝑢𝑏𝑠𝑡𝑟𝑎𝑡𝑒 𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑒𝑠

[𝐺𝑖]: 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑔𝑎𝑡𝑒 𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑒𝑠

𝑆𝑖𝑚: Influx rate of the substrate molecules

1 0 1 0 0 1

0 1 1 1 0 1

Hamming

Distance

In the readout layer of the reservoir computer, we implemented a single perceptron that read

random information from the reservoir and learn the correct Hamming distance between 2

input bitstreams. In our experiments, we feed the influx rates and the concentration at a

random time of each substrate molecule to the reservoir. For simplicity purpose, the basic

perceptron algorithm with sigmoid function was employed.

ACKNOWLEDGEMENT This material is based upon work supported by the National Science Foundation

under grant no. 1518833. The original RC model of this work was described in

“DNA Reservoir Computing: A Novel Molecular Computing Approach” by

Goudarzi et al. The authors acknowledge the support of the teuscher.:lab, the

Maseeh College of Engineering and Computer Science, and the University of

New Mexico.

Figure 2: Amplifying oscillator Figure 3: Attenuating oscillator

Figure 4: Single-input reservoir computer

Figure 5: Two-input reservoir computer

Random perturbations were introduced at different times to produce random oscillations of the product

concentrations. In this RC model, substrate(s) were perturbed in every τ seconds to introduce reservoir

inputs. Figure 4 illustrates single perturbations and figure 5 illustrates double perturbations.

In the lab, the system of ODEs (1) were solved and simulated with MATLAB ode23t

solver using Runge – Kutta method.

In order for the reservoir to start oscillate, the chemistry was unperturbed for 500 seconds, following

by a change in the influx rate of at least one substrate. With a single perturbation, this reservoir showed

dynamics of an amplifying and attenuating oscillator as shown in figure 2 and 3.

OBJECTIVE Design and build a reservoir computer (RC) model based on a

system of chemical reaction networks (CRNs) that has

computational and learning capabilities.

ANALYSIS

Here we show that a reservoir computer constructed by a system of coupled

deoxyribozyme oscillators is capable of performing computational and learning

tasks. From the experiments, the results show that such an RC can successfully

learn linearly separable patterns, with an average learning error of 0.0031. Further

research will be conducted to minimize the learning error and increase the

learning success rate. In addition, DNA strands will be feed into the RC and will

be interpreted as the binary bitstreams. This model can also be further designed to

detect pathogens and genetic mutations.

The computational abilities of this coupled deoxyribozyme RC model were tested

by learning the Hamming distance. 1000 different sets of 6-bit inputs were

applied to the reservoirs consecutively in 1000 experiments. Table 1 below

illustrates the average error of each bit on a sample simulation, together with their

targets and actual outputs.

Bit index # Target Actual output Average error

1 0 5.2396e-04 0.0028

2 1 0.9994 0.0025

3 0 2.1464e-10 0.0036

4 0 2.7559e-05 0.0029

5 1 0.9995 0.0034

6 0 6.4227e-04 0.0031

Table 1: Results of a sample Hamming distance learning performed by the

coupled deoxyribozyme oscillators

(1)

Figure 6: DNA strands with genetic information Source: https://en.wikipedia.org/wiki/DNA

Figure 1: An abstract reservoir computer with perceptron implemented