Biocomputation: materials, algorithms, devices and fabrication

Resume : Artificial neural networks inspired by biological systems can dramatically improve the ability of computers to perform a variety of tasks such as navigation. In recent years, novel efficient nanoscale optoelectronic components as well as concepts for sub-wavelength light manipulation have been developed, but these have not yet been explored for such neural circuits. We propose a network solution in which the weighted connectivity between neural nodes is achieved by emitting and receiving overlapping light signals inside a shared quasi 2D waveguide. This decreases the circuit footprint by orders of magnitude compared to existing optical solutions. The reception, evaluation and emission of the optical signals are performed by a new neural node based on known, highly efficient III-V nanowire optoelectronics. This minimizes power consumption of the network. To demonstrate the concept, we build a computational model based on an anatomically correct, functioning model of the central-complex navigation circuit of the insect brain. We simulate in detail both the optical and electronic parts of the most interconnected and central part of this network, using experimentally derived parameters. The results from our simulation are used as input in the full central complex model and we successfully demonstrate homing navigation. Our approach points to a general way of drastically reducing the footprint and improving power efficiency of optoelectronic neural networks, leveraging the superior speed and energy efficiency of light as a carrier of information.

Resume : Many technologically and societally important mathematical problems are intractable for conventional, serial computers. Therefore, a significant need exists for parallel-computing approaches that are capable of solving such problems within reasonable time frames. We introduce a parallel-computation system in which a given combinatorial problem is encoded into a graphical, modular network that is embedded in a nanofabricated planar device. The problem is then solved by a large number of independent biological agents, namely molecular-motor-propelled protein filaments, exploring the network in a highly parallel fashion. Notably, this approach uses orders of magnitude less energy than conventional computers, thus addressing issues related to power-consumption and heat-dissipation. We demonstrate the feasibility and scalability of this approach by fabricating and operating devices that solve several NP-complete problems: a small Subset Sum and a larger Exact Cover. Finally, we address challenges and prospects of further upscaling, which will be critical in order to solve problems of practical importance. Funding: H2020 Bio4Comp, GA No: 732482, FP7 ABACUS, GA No: 613044

Resume : In this talk, I'll discuss an exact cover problem arising from airline scheduling and how to solve it on a quantum computer. The problem consists of a set of flights that should be flown and set of possible routes, each containing one or more of the flights. These possible routes are straightforward to produce by letting an airplane move through the graph of airports. The exact cover problem consists of finding a combination of these possible routes that together contains all individual flights once and only once. We can identify each possible route with a binary decision variable, which is 1 if the route is in the solution and 0 otherwise. Thus, we can map a problem containing N possible routes to finding an N-bit string that fulfills the constraints. Furthermore, we can create a cost function for these bit strings, which has a minimum for allowed solutions. We have then analyzed how a quantum computer can be used to find this minimum, using the Quantum Approximate Optimization Algorithm (QAOA) for instances with 8, 15 and 25 decision variables [1]. These instances were derived from real world problems. We have also solved a toy exact cover problem with two decision variables using QAOA on a superconducting quantum computer [2]. [1] "Applying the Quantum Approximate Optimization Algorithm to the Tail Assignment Problem", P. Vikstål, M. Grönkvist, M. Svensson, M. Andersson, G. Johansson, G. Ferrini, arXiv:1912.10499; [2] "Quantum approximate optimization of the exact-cover problem on a superconducting quantum processor", A. Bengtsson, et al., arXiv:1912.10495

Resume : The three satisfiability (3-SAT) problem is an NP-complete problem for which the current fastest algorithm requires exponential time with sequentially operating electronic computers. The requirement for brute force searching all the possible solutions is well suited to take advantage of the parallelism provided by Network-based Biocomputation (NBC). The key to solving any problem with NBC is to find an efficient way to encode the mathematic problems in 2D networks. Here we present a novel encoding method for solving 3-SAT problems by converting the decision problem into a unary summation problem. A 3-SAT problem with m variables in CNF includes n clauses, each of which contains at most 3 variables. By assigning 1 and 0 to the corresponding satisfied clauses, the problem is reduced to find if there are sets of variables to make the sums of n formed base-2 numbers have nonzero digits in every digit. By converting the binary information to unary spatial information, the search for possible solutions is then encoded in the summation network. Four types of junction structures are designed to guide the motions of agents to achieve selective (OR) summation. The solution to the problem is based on whether biological agents could leave from a certain exit (correct sum). This work will not only demonstrate the potential of NBC but also explores the possibility of encoding and solving other NP-complete problems. Funding: H2020 Bio4Comp, GA No: 732482

Resume : Time is an essential element in any scientific theory. We use clocks to measure time. Different systems have their natural time scale; therefore, we use different clocks to measure different aspects of the system. A biological system may have several critical scales of time. Many biological networks are characterized by a high complexity, which makes it hard to build and analyze the underlying network models. For a biological network with several steady-states, a critical event is a moment where the system has decided to progress towards a particular steady state with a high probability. Here we apply a method for finding critical events in drama to biological networks. We study the interaction between two clocks to pinpoint critical events in the evolution of the biological system. To study the effectiveness of our method, we study the approximate majority algorithm and show our method succeeds in computing a critical event in chemical reaction networks.

Resume : To find scalable ways to solve NP-complete problems, that is the big challenge. One of these problems, Satisfiability (SAT), asks, given a Boolean formula P containing binary variables, whether there exists a combination of variable assignments, for which P is true. Actually, the SAT problem can be split into two questions, Q1: “Can P be true?” and Q2: “If so, for which variable assignments?”. The intention of this paper is to show a compact, scalable network design (Folded Binary Chain) which, in principle, enables any SAT problem to be solved by simultaneously operating biological agents in a brute force approach. The agents can e.g., be motor-driven cytoskeletal filaments or autonomously moving bacteria. It is essential that the clauses in the Boolean formula P can be represented by tags given to the agents running in the network. P is true if at least one agent can be detected, which has collected all the clause tags (Q1). By additionally applying tags that represent the variable assignments visited by the individual agents, Q2 can also be solved. It will be shown that the stochastic variable assignment employed here allows for massively parallel operation, both inside one network and by running multiple networks simultaneously. The scalability (in mass, space and time) of our design is discussed in comparison with other designs for solving NP-complete problems, and with classical sequentially operating one CPU electronics. [ Funding: H2020 Bio4Comp, GA No: 732482 ]

Resume : The estimated efficiency of two forms of non-conventional computation, namely, molecular operation-based DNA computing, and agent-based network computing are compared, using the classical Subset Sum Problem as benchmark NP-complete problem. The comparison includes operational parameters, such as the number of computing operations, sample size, readout, and time taken to explore all possible solutions. Both approaches enable massively parallel, energy efficient operations, and exponentially increasing computing power. Both computation paradigms, when tested against scaling, present specific benefits and drawbacks. The agent-based computation exploits advantageously the logic embedded into the design of physical microfluidics networks, leading to a substantial reduction of solutions to be explored, and possibly a more efficient parallel readout. In contrast, DNA computation is performed in exquisitely short time, but it also requires unreasonably large amounts of molecular reagents, which impacts on the readout time due to the very large number of libraries to be sequenced. A numerical comparison of the two computational paradigms is presented, by solving several instances of increasingly large Subset Sum Problems. The study helps in building the comparative roadmap for network computing with agents versus alternative other non-conventional computing paradigms.

Resume : Living systems use biological molecular motors to achieve sorting, actuation, and assembly of materials on cytoskeletal tracks inside cells. Although they have promising potential to be used as microscopic actuators and robots in artificial systems, there are severe limitations in both biological motors and cytoskeletal tracks in terms of customizability and controllability. Here we describe a modular-engineering approach of two building blocks, a biological motor dynein and DNA-binding proteins. The resultant hybrid motors recognized specific base sequences that were periodically incorporated along the long axis of synthetic DNA nanotubes and moved unidirectionally along the specific DNA nanotubes at an average velocity of 14–30 nm/s. The direction of movement was entirely dependent on the direction of the recognition sequence. Furthermore, we developed mutually orthogonal motor proteins each recognizing a different DNA sequence, enabling an autonomous cargo sorter and integrator on DNA nanotube tracks. Our strategy opens the way to systematic research on the mechanisms of biomolecular motors and to nanotechnological applications, including microscopic robots that undergo sequential procedure, computation, and synthesis of chemical compounds according to the programmed code incorporated into DNA tracks.

Resume : When using myosin propelled actin filaments in biocomputation, the filaments explore nanostructured networks in solving combinatorial problems. In such applications, it is of interest to temporarily switch on/off motile function in parts of the network to enable programming of the network. Here, we lay the grounds for such developments by immobilization of engineered, light-switchable Myosin XI with maintained actin propelling function in dedicated nanoscale channels with simultaneous inhibition of function on surrounding areas. After excluding the feasibility of immobilization strategies using silanized tracks surrounded by resist polymers, previously employed for Myosin II based biocomputation, we tested alternative approaches. First, we investigated nanostructured gold surfaces with SiO2 surroundings. In such devices, myosin propelled actin motility was observed on both the Au and the SiO2 areas. Importantly, however, after PEG silane derivatization we observed selective motility only on the Au areas with complete inhibition of actin filament binding to surrounding SiO2 areas. These results lay a critical foundation for optically controlled on/off switching and programming of motility in biocomputation networks. We next aim to optimize the motility quality and to implement actual control of the actin filament movement by optical switching of the myosin motors. Funding: H2020 Bio4Comp, GA No: 732482; Carl Trygger and Helge Axson Johnson foundations.

Resume : Recently an approach to solve combinatorial problems was demonstrated by kinesin-1 driven microtubules exploring, as autonomous agents, physical networks of nanometer-sized channels [Nicolau et al., PNAS, 113(10), 2016]. The possibility to multiply the agents exponentially while traversing such networks is crucial for the scalability of these systems. We developed and tested a method for the multiplication of microtubules gliding on surface-immobilized kinesin-1 and kinesin-14 molecules, respectively. Specifically, our method comprises two simultaneously proceeding processes: (1) elongation of microtubules by self-assembly of tubulin dimers and (2) cutting of microtubules by the severing enzyme spastin. The main challenge in doing so is to optimize both processes such that the average length of the filaments stays roughly constant over time while the number of filaments increases exponentially. Additionally, nucleation of new filaments ought to be avoided in order to prevent errors in the calculations performed by the microtubules. Thus, we first studied each of the two processes separately under various conditions before combining the optimized protocols to actually multiply microtubules. Finally, we aim to multiply microtubules in a physical network with channel structures. Funding: H2020 Bio4Comp, GA No: 732482

Resume : In network based biocomputers, myosin propelled actin filaments solve mathematical problems by exploring nanofabricated networks encoding the problem. Filament dilution during progression through the network is a challenge to upscaling but would be resolved by actin filament multiplication. This process should ideally preserve constant filament length and a filament polarity that allows motor driven transportation only in appropriate directions as defined by network geometry. For the latter reason, newly nucleated filaments would be problematic due to random orientation. Here, we hypothesized that effective filament multiplication is achievable by splitting due to motor induced forces during motility at low ionic strength (with weak bonds between actin subunits) followed by actin polymerization at high [KCl] and [MgCl2]. The motor induced splitting was effective, increasing the number of actin filaments up to 4-fold in 30 s. Further, >80 % of the actin filaments, immobilized on either heavy meromyosin (HMM) or N-ethylmaleimide (NEM) treated, non-propulsive HMM, approximately doubled in length 2 min after adding G-actin monomers (~1 µM). With use of NEM-HMM, an appreciable number of newly nucleated filaments (> 44 % of all) was observed, whereas, importantly, only few such filaments (< 5 %) were seen with HMM and simultaneous motility. Overall, our results are promising for filament multiplication in upscaled network-based biocomputers. Funding: H2020 Bio4Comp, GA No: 732482

Resume : Deep learning is a class of machine learning techniques that uses multi-layered artificial neural networks for automated analysis of signals or data. The name comes from the general structure of deep neural networks, which consist of several layers of artificial neurons, each performing a nonlinear operation, stacked over each other. Beyond its main stream applications such as the recognition and labeling of specific features in images, deep learning holds numerous opportunities for revolutionizing image formation, reconstruction and sensing fields. In fact, deep learning is mysteriously powerful and has been surprising optics researchers in what it can achieve for advancing optical microscopy, and introducing new image reconstruction and transformation methods. From physics-inspired optical designs and devices, we are moving toward data-driven designs that will holistically change both optical hardware and software of next generation microscopy and sensing, blending the two in new ways. Today, we sample an image and then act on it using a computer. Powered by deep learning, next generation optical microscopes and sensors will understand a scene or an object and accordingly decide on how and what to sample based on a given task – this will require a perfect marriage of deep learning with new optical microscopy hardware that is designed based on data. For such a thinking microscope, unsupervised learning would be the key to scale up its impact on various areas of science and engineering, where access to labeled image data might not be immediately available or very costly, difficult to acquire. In this presentation, I will provide an overview of some of our recent work on the use of deep neural networks in advancing computational microscopy and sensing systems, also covering their biomedical applications.

Resume : The present numerical work explores the two-sided lid-driven cubical cavity induced by a cylindrical shape at the center. This problem is studied by a finite volume method using multigrid acceleration. The cavity has left and right parallel lid-driven walls and all the other walls completing the domain are motionless. Different radii size (R=0.075, 0.1,0.125 & 0.15) and positions of the inner cylinder [P1(0.3,0.3), P2(0.7, 0.3), P3(0.7, 0.7) & P4(0.3, 0.7)] are employed by using different Reynolds numbers that range three orders of magnitude 100, 400 and 1000. The obtained results show that positions P3 and P4 of the inner cylinder promote cell distortion and when the radius equates to R=0.15, that may lead to the birth of tertiary cells at Re=400 and persist for Re=1000. Thereafter, the study has been extended to the unsteady state by further increasing Reynolds number till reaching high values 1200 and 1500. Results indicate that positions P3 and P4 accelerate the transition from the steady state to the unsteady state since their favorable locations near the sided driven walls of the cavity. Moreover, it has been proved that using the largest radius size of the inner cylinder which is equates to 0.15 promote the transition to the unsteadiness faster than using the other radii. Typical plots of velocity contours, kinetic energy and spanwise velocity are presented to analyze the effect of pertinent parameters such as the radius size and position of the cylinder on fluid behavior in both steady and unsteady states. Therefore, a systematic description of various effects illuminates the optimum geometrical parameters to achieve effective flow behavior in those systems. Keywords: Computational analysis, cylindrical shape, lid-driven cubical cavity, two-parallel wall motions, cylinder radius, cylinder position.

Resume : Spider silk is well known for its extraordinary mechanical properties such as high strength and toughness, but its crystalline sequence is consisted of counterintuitive sequence. While the poly-alanine is expected to be a stronger material than poly-glycine-alanine, the crystalline sequence of the spider silk is composed of a mixture of the poly-alanine and poly-glycine alanine. We investigate the reason behind this characteristic sequence by molecular dynamics simulations. In this study the three models used such as, the wildtype sequence, silk with crystalline region replaced by poly-alanine, silk with crystalline region replaced by poly-glycine-alanine (WT, AA, GA, descending order). By comparing these three, we study how the sequence of the wildtype silk result in different properties from poly-alanine or poly-glycine-alanine.

Resume : New approaches in the fields of bioengineering (i.e biocomputing) and biomedicine (i.e. implants) increase the interest of nanotechnologically fabricated and encapsulated devices. The usage of biocompatible materials is essential to realize bio-functionalized surfaces as well as to supply these devices with e.g. biomolecules using microfluidic systems. Parylene is a thermoplastic polymer, containing a variety of excellent properties like chemical inertness, biocompatibility and biostability as well as a good thermal stability and high impermeability for gases and moisture. They allow a biocompatible bonding of nanotechnologically fabricated structures as well as the fabrication of microfluidic systems on silicon and glass wafers. Here, a low temperature bonding process using Parylene as an adhesive for 6” wafers was developed to enable advanced bio-microsystems for applications such as biocomputational networks. Due to its properties, Parylene holds the microfluidic channels as well as realizes a biocompatible sealing of the nano-network devices. The wafer bonding by the patterned Parylene was performed successfully using a 6” glass wafer and a SiO2 coated silicon device-wafer. In order to reduce the diffusion of gold during the bonding process, time and temperature were adapted experimentally to a minimum. The success of the bonding process is analyzed by IR imaging, tensile and shear tests as well as SEM analyses of cross-sections. Funding: H2020 Bio4Comp, GA No: 732482

Resume : Parallel computation is needed to efficiently solve complex combinatorial problems. To tackle such problems, network-based biocomputation has been demonstrated – a parallel computation approach, where a mathematical problem is encoded into a nanofabricated network, which is explored by molecular-motor powered microtubules thus solving the problem. However, this approach is currently limited by the size of the network which increases drastically with the increase of the size of a given problem. The main reason for the large size of the current network design is the fact, that all information is stored in the position of the microtubules within the network. To allow more compact encodings, we developed a mechanism of encoding information directly into fluorescently labeled microtubules by photo-bleaching them with barcode-like patterns. Read-out of the stored information is then performed with a special image analysis algorithm. With this method, we were able to successfully store and read out 8 bits of information per 10 µm for stationary microtubules and 4 bits of information for moving microtubules. When combined with small nanofabricated networks, this method can be used to solve the Boolean satisfiability problem.

Resume : Network Based Biocomputation (NBC) offers a new paradigm for solving complex computational problems by utilizing biological agents that operate in parallel to explore manufactured planar devices. The devices should be designed in a way that ensures their correctness and robust operation, and for this purpose software tools can offer significant advantages by allowing to explore the designs and identify various limitations and errors before physical manufacturing and experimentation in the lab. We have developed a formal verification-based software tool that can assist in the design of NBC Circuits. The tool enables verifying that a given design is correct and does not contain any logical errors. The tool also allows to evaluate different designs prior to manufacturing. Similar verification tools are now a common practice in the hardware industry, where any error in the design of a device that can be identified at an early stage can lead to significant savings in costs (money, development time, reputation). The current version of the software tool allows to verify the correctness of NBC designs for the Subset Sum Problem (SSP), Exact Cover (ExCov) and Satisfiability (SAT). Our approach is based on defining a formal semantics for NBC circuits and using temporal logic for specifying and proving properties of the design. Different encodings, formulae and parameters have been explored to scale up the verification to handle large devices. Funding: H2020 Bio4Comp, GA No: 732482

Resume : Network-based biocomputation (NBC) requires (bio-)chemical tagging or labelling of agents moving inside microfluidic channels in order to enhance the accessible classes of mathematical problems. Water-compatibility and excellent PL properties of the architectural elements are a necessity. We report on water-based photoluminescent inorganic-organic (i.e., hybrid) nanosytems comprising semiconductor quantum dots (QDs) and functionalizing molecules, in particular, colloidal Ag-In-S/ZnS QDs capped with glutathione (GSH), porphyrins and/or other molecular chromophores. Due to their excellent broad-band photoluminescence (PL) emission quantum yield of 50 % and above [1] and various opportunities for further (bio)chemical functionalization, these QD-GSH hybrids can be considered excellent candidates for labelling and tagging purposes of NBC agents. We report on attempts to tune the PL properties of the obtained QD hybrids in water upon their functionalization with molecules such as porphyrin and methyl viologen, down to the level of individual molecules. As another potential architectural NBC element, we refer to nanomembrane-like tubular porphyrin j-aggregates representing templates for hybrid molecular wires. Funding: H2020 Bio4Comp, GA No: 732482. Reference: [1] O. Stroyuk et al.: “Inherently broadband photoluminescence in Ag–In–S/ZnS quantum dots observed in ensemble and single-particle studies.” J. Phys. Chem. C 2019, 123, 2632–2641.

Resume : Network-based biocomputation (NBC) is a parallel computing paradigm in which combinatorial problems are (i) encoded into nanofabricated graphical networks and (ii) solved by exploring the networks in a parallel fashion using a large number of independent, biological agents, such as molecular motors. Exploration of these paths by the agents then finds all possible solutions to the combinatorial problem. A key aim in the upscaling of biocomputation devices is to be able to use the same device to solve multiple, different instances of a problem. To achieve reversible switching, we use the thermally responsive polymer PNIPAM anchored to PGMA to locally block and unblock pathways within premade networks. Thus, it is possible to switch the functionality of agents guiding networks. This would essentially establish programmable devices. PGMA is a negative tone resist that can be locally patterned using electron beam lithography. The key to the selective binding is to achieve PGMA deposition inside the deep SiO2 channels(~450nm). A proof-of-concept network has been designed to demonstrate the switching paths/guiding for molecular agents. This work will not only be a necessary element for programmable use biocomputation networks but also explores the possibility of precise patterning inside existing nanostructures. Funding: H2020 Bio4Comp, GA No: 732482

Resume : Over the years several methods were used to separate cells within a microfluidic device such as cavities, with vortex microfluidics method, or cell trapping mechanisms using size filters. However, one of the methods that is widely used to separate cancer cells from blood cells is the dielectrophoresis. In this work we employ the numerical code COMSOL Multiphysics for a dielectrophoretic separation of CTCs (circulating tumor cells) from RBCs (red blood cells) in a 3D microchannel. The microfluidic device is composed of one inlet and three outlets. The non-uniform alternative electric field is generated using interdigitated electrodes and it separates the cells within the device to the corresponding outlet. The electric field frequency was set to 100kHz. For this paper, one single CTC line is selected MDA-MB-231, breast cancer cells. The CTCs and the RBCs are considered in an ideal way in the simulation as spheres, but with the afferent characteristics. This work can be extended to testing multiple CTC lines at various flow velocities and electric field frequencies. keywords: numerical simulation, dielectrophoresis, microchannel Acknowledgments: This work was supported by the grant of PN-III-P1-1.2-PCCDI-2017-0214 (Project No. 3PCCDI/2018). The author would like to express his gratitude towards the support of Prof. Corneliu Balan and University Politehnica of Bucharest for the fellowship.

Resume : Computational problems of a combinatorial nature require exponential time to explore the solution space, making traditional serial computation intractable, and parallel computation a necessity. Network-based Biocomputation (NBC) was recently demonstrated to solve the subset sum problem (SSP) [Nicolau et al, PNAS 113(10) 2016], by encoding it into a graphical network of channels in a nanofabricated device, which was then explored by molecular motors to find all possible solutions. This poster will describe our approach to using NBC for solving another problem, namely Exact Cover (ExCov). For an ExCov problem with a collection X of subsets for a set Y, an exact cover is a subcollection X* such that each element in Y is contained in exactly one subset in X*. We can encode this problem into a SSP network by first translating each subset into a binary number by assigning 1 to the elements existing in the sets and 0 for others which are then converted to decimal numbers. The exact cover of the problem has 1 in all the bit locations and thus sum corresponding to this is the required solution. Thus in the network, we only need to look at the exit corresponding to the solution and if the channel guided filaments exit at this network exit, then the set of sets contains an exact cover. This work demonstrates that a given NBC approach can be used for more than one combinatorial problem, because NP-complete problems can be converted into one another. Funding: H2020 Bio4Comp, GA No: 732482

Resume : Computational methods and tools are essential for studying biological computation in engineered biological devices and in living cells. We describe methods and tools for simulation and formal verification of engineered and natural biological systems. We demonstrate the methods as applied to the Caenorhabditis elegans germ line, which is an exceptional model system for stem cell research. The dynamics of the underlying genetic network and potential regulatory interactions are important for understanding proliferation vs. differentiation mechanisms, and tissue maintenance. We model the stem cell fate versus meiotic development decision circuit in young adult germ line based on published gene expression data and known genetic interactions. We apply formal verification methods and the Reasoning Engine for Interaction Networks tool (RE:IN) to the analysis of C. elegans germ line and derive predictive networks for control of cell division and differentiation. RE:IN allows to simultaneously specify many possible scenarios and experimental observations, and to synthesize gene networks consistent with all experiments. In silico analysis of knock-down and overexpression experiments within our model recapitulate published phenotypes of mutant animals and can be applied to make new predictions on cellular decision making. We discuss the scalability challenges in applying formal verification algorithms for gene regulatory network synthesis and for verifying Network Based Biocomputation devices. Funding: H2020 Bio4Comp, GA No: 732482, Israeli Science Foundation 190/19

Resume : Sudoku is a number placement puzzle where one assigns a number to each cell. We first consider the 9 × 9 puzzle. The aim is to assign a number from 1 to 9 to each cell so that each row, column, and 3 x 3 block contains exactly one instance of each number. We study how Sudoku puzzles can be solved by a Network Based Biocomputation (NBC) approach. This is done by a reduction to the satisfiability (SAT) problem. In SAT we are given a propositional logic formula over Boolean variables and need to decide if the formula is satisfiable, meaning that it has at least one assignment that evaluates to True. The problem is represented using propositional variables, which can be assigned truth values 1 (true) or 0 (false). In an n×n Sudoku puzzle each cell can contain a number from 1 to n. Thus, each cell is associated with n propositional variables. Sudoku rules are represented as a set of clauses to guarantee that each row, column and block contains exactly one instance of each number from 1 to n. We show how the resulting SAT instance can be solved using an NBC approach where filaments explore a network in parallel, and by reductions to the subset sum problem (SSP). We also explore Sudoku puzzles where there is more than one way to solve the puzzle, considering questions of obtaining several different solutions in NBC and the ability to uniformly sample from the set of correct solutions.

Resume : In this study, we used quantum chemistry calculations in order to determine some kinetic parameters of the isomerization reaction of the substituted icosadeca-ene. The studied molecules are: (C20H20, C20H10F10, C20H10Cl8, C20H10Br8 and C20H10I8) Cis and Trans. One of the adopted ways to access these parameters (activation energy, rate constant, etc ...) is looking for the transition state that is based on the exploration of intermediaries during the passage of Cis-Trans isomerization process. The study of a ten molecules series gives the following results: * The trans conformer is more stable than the Cis. * The activation energy changes very greatly depending on the size and nature of the substituent according to the reaction profile. * The constants of the isomerization reaction rates are in the following order: kC20H22 >> k C20H10F10 >> k C20H10Cl10 >>k C20H10Br10 >> k C20H10I10. * The geometrical parameters vary considerably according to intermediate products The calculation methods are DFT (TD-B3LYP) and Ab-initio methods at STO-3G*. Keywords: substituted icosadeca-ene, kinetics; isomerisation, HF (AM1+PM6), DFT

Resume : In space-encoded, network-based biocomputation (Nicolau et al., PNAS 113(10) 2016), biological agents solve combinatorial problems by exploring a 2D physical network. It is crucial to minimize errors, for example due to agents taking a wrong turn within the network. 3D “bridges” could eliminate such wrong turns at channel crossings. We present an approach to manufacturing 3D-junctions by two-photon polymerization (2PP), a 3D-printing technology on the micron-scale. The process is carried out in a layer-to-layer fashion by scanning a focused femtosecond laser across a photopolymerizable resin. The solidification of this inorganic-organic hybrid polymer (ORMOCER®) is confined to the focal volume, enabling the manufacturing of arbitrary 3D microstructures according to CAD data. The motility of biomolecular agents in nanofluidic channels not only depends on the biological system itself but also on the hydrophilicity of the substrate material. We focused on two different 3D-junction designs: (1) In the “monorail” design filament motility is only supported along ORMOCER® tracks but suppressed in the surrounding. (2) In the “channel” design filaments are guided by the ORMOCER®. We will discuss 3D-junction fabrication according to both designs on several substrates (silicon, gold, glass) and present first motility results on these ORMOCER® structures highlighting the potential for network based biocomputation. [Funding: H2020 Bio4Comp, GA No: 732482]

Resume : Triplex oligonucleotide nanostructures are formed between a duplex helical structure and a single-stranded oligonucleotide, where Hoogsteen base-pairing between a homopurine sequence in the duplex structure and the third oligonucleotide stabilizes the triplex structure.[1] DNA triplex nanostructures were previously demonstrated to form in vitro at the engineered promoter region of a phage transcription unit and to inhibit transcription of the downstream genes.[2] In the present study, RNA oligonucleotides are used to inhibit transcription from a designed bacterial promoter, by formation of DNA-RNA hybrid triplex nanostructures. By using the RNA strands as inputs, logic gates were fabricated, where the readout is provided by a fluorescent RNA aptamer. The use of RNA-regulated transcription units and fluorescent RNA aptamers as readouts allows the fabrication of biocomputation units characterized by a reduced set of components. In the simplest case, only DNA templates and E.coli RNA polymerase are required. This approach is expected to represent an alternative to current methods for producing logic gates based on biochemical components. [1] Y. Hu, A. Cecconello, A. Idili, F. Ricci, I. Willner, Angew Chem Int Ed Engl 2017, 56, 15210-15233. [2] J. U. Skoog, L. J. Maher, Nucleic Acids Res 1993, 21, 4055-4058.