Implications of the Turing completeness of reaction-diffusion models, informed by GPGPU simulations on an XBox 360: cardiac arrhythmias, re-entry and the Halting problem

An RNA-Based Theory of Natural Universal Computation

Life is confronted with computation problems in a variety of domains including animal behavior, single-cell behavior, and embryonic development. Yet we currently do not know of a naturally existing biological system that is capable of universal computation, i.e., Turing-equivalent in scope. Generic finite-dimensional dynamical systems (which encompass most models of neural networks, intracellular signaling cascades, and gene regulatory networks) fall short of universal computation, but are assumed to be capable of explaining cognition and development. I present a class of models that bridge two concepts from distant fields: combinatory logic (or, equivalently, lambda calculus) and RNA molecular biology. A set of basic RNA editing rules can make it possible to compute any computable function with identical algorithmic complexity to that of Turing machines. The models do not assume extraordinarily complex molecular machinery or any processes that radically differ from what we already know to occur in cells. Distinct independent enzymes can mediate each of the rules and RNA molecules solve the problem of parenthesis matching through their secondary structure. In the most plausible of these models all of the editing rules can be implemented with merely cleavage and ligation operations at fixed positions relative to predefined motifs. This demonstrates that universal computation is well within the reach of molecular biology. It is therefore reasonable to assume that life has evolved - or possibly began with - a universal computer that yet remains to be discovered. The variety of seemingly unrelated computational problems across many scales can potentially be solved using the same RNA-based computation system. Experimental validation of this theory may immensely impact our understanding of memory, cognition, development, disease, evolution, and the early stages of life.

Large-scale Interactive Numerical Experiments of Chaos, Solitons and Fractals in Real Time via GPU in a Web Browser

The study of complex systems has emerged as an important field with many discoveries still to be made. Computer simulation and visualization provide important tools for studying complex dynamics including chaos, solitons, and fractals, but available computing power has been a limiting factor. In this work, we describe a novel and highly efficient computing and visualization paradigm using a Web Graphics Library (WebGL 2.0) methodology along with our newly developed library (Abubu.js). Our approach harnesses the power of widely available and highly parallel graphics cards while maintaining ease of use by simplifying programming through hiding implementation details, running in a web browser without the need for compilation, and avoiding the use of plugins. At the same time, it allows for interactivity, such as changing parameter values on the fly, and its computing is so fast that zooming in on a region of a fractal like the Mandelbrot set can incur no delay despite having to recalculate values for the entire plane. We demonstrate our approach using a wide range of complex systems that display dynamics from fractals to standing and propagating waves in 1, 2 and 3 dimensions. We also include some models with instabilities that can lead to chaotic dynamics. For all the examples shown here we provide links to the codes for anyone to use, modify and further develop with other models. Overall, the enhanced visualization and computation capabilities provided by WebGL together with Abubu.js have great potential to facilitate new discoveries about complex systems.

Top-down models in biology: explanation and control of complex living systems above the molecular level

It is widely assumed in developmental biology and bioengineering that optimal understanding and control of complex living systems follows from models of molecular events. The success of reductionism has overshadowed attempts at top-down models and control policies in biological systems. However, other fields, including physics, engineering and neuroscience, have successfully used the explanations and models at higher levels of organization, including least-action principles in physics and control-theoretic models in computational neuroscience. Exploiting the dynamic regulation of pattern formation in embryogenesis and regeneration requires new approaches to understand how cells cooperate towards large-scale anatomical goal states. Here, we argue that top-down models of pattern homeostasis serve as proof of principle for extending the current paradigm beyond emergence and molecule-level rules. We define top-down control in a biological context, discuss the examples of how cognitive neuroscience and physics exploit these strategies, and illustrate areas in which they may offer significant advantages as complements to the mainstream paradigm. By targeting system controls at multiple levels of organization and demystifying goal-directed (cybernetic) processes, top-down strategies represent a roadmap for using the deep insights of other fields for transformative advances in regenerative medicine and systems bioengineering.

Gap junctional signaling in pattern regulation: Physiological network connectivity instructs growth and form

Gap junctions (GJs) are aqueous channels that allow cells to communicate via physiological signals directly. The role of gap junctional connectivity in determining single-cell functions has long been recognized. However, GJs have another important role: the regulation of large-scale anatomical pattern. GJs are not only versatile computational elements that allow cells to control which small molecule signals they receive and emit, but also establish connectivity patterns within large groups of cells. By dynamically regulating the topology of bioelectric networks in vivo, GJs underlie the ability of many tissues to implement complex morphogenesis. Here, a review of recent data on patterning roles of GJs in growth of the zebrafish fin, the establishment of left-right patterning, the developmental dysregulation known as cancer, and the control of large-scale head-tail polarity, and head shape in planarian regeneration has been reported. A perspective in which GJs are not only molecular features functioning in single cells, but also enable global neural-like dynamics in non-neural somatic tissues has been proposed. This view suggests a rich program of future work which capitalizes on the rapid advances in the biophysics of GJs to exploit GJ-mediated global dynamics for applications in birth defects, regenerative medicine, and morphogenetic bioengineering. © 2016 Wiley Periodicals, Inc. Develop Neurobiol 77: 643-673, 2017.

On Having No Head: Cognition throughout Biological Systems

The central nervous system (CNS) underlies memory, perception, decision-making, and behavior in numerous organisms. However, neural networks have no monopoly on the signaling functions that implement these remarkable algorithms. It is often forgotten that neurons optimized cellular signaling modes that existed long before the CNS appeared during evolution, and were used by somatic cellular networks to orchestrate physiology, embryonic development, and behavior. Many of the key dynamics that enable information processing can, in fact, be implemented by different biological hardware. This is widely exploited by organisms throughout the tree of life. Here, we review data on memory, learning, and other aspects of cognition in a range of models, including single celled organisms, plants, and tissues in animal bodies. We discuss current knowledge of the molecular mechanisms at work in these systems, and suggest several hypotheses for future investigation. The study of cognitive processes implemented in aneural contexts is a fascinating, highly interdisciplinary topic that has many implications for evolution, cell biology, regenerative medicine, computer science, and synthetic bioengineering.

Fast acceleration of 2D wave propagation simulations using modern computational accelerators

Recent developments in modern computational accelerators like Graphics Processing Units (GPUs) and coprocessors provide great opportunities for making scientific applications run faster than ever before. However, efficient parallelization of scientific code using new programming tools like CUDA requires a high level of expertise that is not available to many scientists. This, plus the fact that parallelized code is usually not portable to different architectures, creates major challenges for exploiting the full capabilities of modern computational accelerators. In this work, we sought to overcome these challenges by studying how to achieve both automated parallelization using OpenACC and enhanced portability using OpenCL. We applied our parallelization schemes using GPUs as well as Intel Many Integrated Core (MIC) coprocessor to reduce the run time of wave propagation simulations. We used a well-established 2D cardiac action potential model as a specific case-study. To the best of our knowledge, we are the first to study auto-parallelization of 2D cardiac wave propagation simulations using OpenACC. Our results identify several approaches that provide substantial speedups. The OpenACC-generated GPU code achieved more than speedup above the sequential implementation and required the addition of only a few OpenACC pragmas to the code. An OpenCL implementation provided speedups on GPUs of at least faster than the sequential implementation and faster than a parallelized OpenMP implementation. An implementation of OpenMP on Intel MIC coprocessor provided speedups of with only a few code changes to the sequential implementation. We highlight that OpenACC provides an automatic, efficient, and portable approach to achieve parallelization of 2D cardiac wave simulations on GPUs. Our approach of using OpenACC, OpenCL, and OpenMP to parallelize this particular model on modern computational accelerators should be applicable to other computational models of wave propagation in multi-dimensional media.

GPGPU accelerated cardiac arrhythmia simulations

Computational modeling of cardiac electrophysiology is a powerful tool for studying arrhythmia mechanisms. In particular, cardiac models are useful for gaining insights into experimental studies, and in the foreseeable future they will be used by clinicians to improve therapy for the patients suffering from complex arrhythmias. Such models are highly intricate, both in their geometric structure and in the equations that represent myocyte electrophysiology. For these models to be useful in a clinical setting, cost-effective solutions for solving the models in real time must be developed. In this work, we hypothesized that low-cost GPGPU-based hardware systems can be used to accelerate arrhythmia simulations. We ported a two dimensional monodomain cardiac model and executed it on various GPGPU platforms. Electrical activity was simulated during point stimulation and rotor activity. Our GPGPU implementations provided significant speedups over the CPU implementation: 18X for point stimulation and 12X for rotor activity. We found that the number of threads that could be launched concurrently was a critical factor in optimizing the GPGPU implementations.

Smoldyn on graphics processing units: massively parallel Brownian dynamics simulations

Space is a very important aspect in the simulation of biochemical systems; recently, the need for simulation algorithms able to cope with space is becoming more and more compelling. Complex and detailed models of biochemical systems need to deal with the movement of single molecules and particles, taking into consideration localized fluctuations, transportation phenomena, and diffusion. A common drawback of spatial models lies in their complexity: models can become very large, and their simulation could be time consuming, especially if we want to capture the systems behavior in a reliable way using stochastic methods in conjunction with a high spatial resolution. In order to deliver the promise done by systems biology to be able to understand a system as whole, we need to scale up the size of models we are able to simulate, moving from sequential to parallel simulation algorithms. In this paper, we analyze Smoldyn, a widely diffused algorithm for stochastic simulation of chemical reactions with spatial resolution and single molecule detail, and we propose an alternative, innovative implementation that exploits the parallelism of Graphics Processing Units (GPUs). The implementation executes the most computational demanding steps (computation of diffusion, unimolecular, and bimolecular reaction, as well as the most common cases of molecule-surface interaction) on the GPU, computing them in parallel on each molecule of the system. The implementation offers good speed-ups and real time, high quality graphics output

Logical and arithmetic circuits in Belousov-Zhabotinsky encapsulated disks

Excitation waves on a subexcitable Belousov-Zhabotinsky (BZ) substrate can be manipulated by chemical variations in the substrate and by interactions with other waves. Symbolic assignment and interpretation of wave dynamics can be used to perform logical and arithmetic computations. We present chemical analogs of elementary logic and arithmetic circuits created entirely from interconnected arrangements of individual BZ encapsulated cell-like disk. Interdisk wave migration is confined in carefully positioned connecting pores. This connection limits wave expansion and unifies the input-output characteristic of the disks. Circuit designs derived from numeric simulations are optically encoded onto a homogeneous photosensitive BZ substrate.

Integrative multicellular biological modeling: a case study of 3D epidermal development using GPU algorithms

BACKGROUND

Simulation of sophisticated biological models requires considerable computational power. These models typically integrate together numerous biological phenomena such as spatially-explicit heterogeneous cells, cell-cell interactions, cell-environment interactions and intracellular gene networks. The recent advent of programming for graphical processing units (GPU) opens up the possibility of developing more integrative, detailed and predictive biological models while at the same time decreasing the computational cost to simulate those models.

RESULTS

We construct a 3D model of epidermal development and provide a set of GPU algorithms that executes significantly faster than sequential central processing unit (CPU) code. We provide a parallel implementation of the subcellular element method for individual cells residing in a lattice-free spatial environment. Each cell in our epidermal model includes an internal gene network, which integrates cellular interaction of Notch signaling together with environmental interaction of basement membrane adhesion, to specify cellular state and behaviors such as growth and division. We take a pedagogical approach to describing how modeling methods are efficiently implemented on the GPU including memory layout of data structures and functional decomposition. We discuss various programmatic issues and provide a set of design guidelines for GPU programming that are instructive to avoid common pitfalls as well as to extract performance from the GPU architecture.

CONCLUSIONS

We demonstrate that GPU algorithms represent a significant technological advance for the simulation of complex biological models. We further demonstrate with our epidermal model that the integration of multiple complex modeling methods for heterogeneous multicellular biological processes is both feasible and computationally tractable using this new technology. We hope that the provided algorithms and source code will be a starting point for modelers to develop their own GPU implementations, and encourage others to implement their modeling methods on the GPU and to make that code available to the wider community.