Towards a theoretical foundation for morphological computation with compliant bodies

The control of compliant robots is, due to their often nonlinear and complex dynamics, inherently difficult. The vision of morphological computation proposes to view these aspects not only as problems, but rather also as parts of the solution. Non-rigid body parts are not seen anymore as imperfect realizations of rigid body parts, but rather as potential computational resources. The applicability of this vision has already been demonstrated for a variety of complex robot control problems. Nevertheless, a theoretical basis for understanding the capabilities and limitations of morphological computation has been missing so far. We present a model for morphological computation with compliant bodies, where a precise mathematical characterization of the potential computational contribution of a complex physical body is feasible. The theory suggests that complexity and nonlinearity, typically unwanted properties of robots, are desired features in order to provide computational power. We demonstrate that simple generic models of physical bodies, based on mass-spring systems, can be used to implement complex nonlinear operators. By adding a simple readout (which is static and linear) to the morphology such devices are able to emulate complex mappings of input to output streams in continuous time. Hence, by outsourcing parts of the computation to the physical body, the difficult problem of learning to control a complex body, could be reduced to a simple and perspicuous learning task, which can not get stuck in local minima of an error function.     

Automated Design of Complex Dynamic Systems

Several fields of study are concerned with uniting the concept of computation with that of the design of physical systems. For example, a recent trend in robotics is to design robots in such a way that they require a minimal control effort. Another example is found in the domain of photonics, where recent efforts try to benefit directly from the complex nonlinear dynamics to achieve more efficient signal processing. The underlying goal of these and similar research efforts is to internalize a large part of the necessary computations within the physical system itself by exploiting its inherent non-linear dynamics. This, however, often requires the optimization of large numbers of system parameters, related to both the system''s structure as well as its material properties. In addition, many of these parameters are subject to fabrication variability or to variations through time. In this paper we apply a machine learning algorithm to optimize physical dynamic systems. We show that such algorithms, which are normally applied on abstract computational entities, can be extended to the field of differential equations and used to optimize an associated set of parameters which determine their behavior. We show that machine learning training methodologies are highly useful in designing robust systems, and we provide a set of both simple and complex examples using models of physical dynamical systems. Interestingly, the derived optimization method is intimately related to direct collocation a method known in the field of optimal control. Our work suggests that the application domains of both machine learning and optimal control have a largely unexplored overlapping area which envelopes a novel design methodology of smart and highly complex physical systems.     

Towards computing with proteins

Can proteins be used as computational devices to address difficult computational problems? In recent years there has been much interest in biological computing, that is, building a general purpose computer from biological molecules. Most of the current efforts are based on DNA because of its ability to self‐hybridize. The exquisite selectivity and specificity of complex protein‐based networks motivated us to suggest that similar principles can be used to devise biological systems that will be able to directly implement any logical circuit as a parallel asynchronous computation. Such devices, powered by ATP molecules, would be able to perform, for medical applications, digital computation with natural interface to biological input conditions. We discuss how to design protein molecules that would serve as the basic computational element by functioning as a NAND logical gate, utilizing DNA tags for recognition, and phosphorylation and exonuclease reactions for information processing. A solution of these elements could carry out effective computation. Finally, the model and its robustness to errors were tested in a computer simulation. Proteins 2006. © 2006 Wiley‐Liss, Inc.     

Dynamic sensitivity and nonlinear interactions influence the system-level evolutionary patterns of phototransduction proteins

Determining the influence of complex, molecular-system dynamics on the evolution of proteins is hindered by the significant challenge of quantifying the control exerted by the proteins on system output. We have employed a combination of systems biology and molecular evolution analyses in a first attempt to unravel this relationship. We employed a comprehensive mathematical model of mammalian phototransduction to predict the degree of influence that each protein in the system exerts on the high-level dynamic behaviour. We found that the genes encoding the most dynamically sensitive proteins exhibit relatively relaxed evolutionary constraint. We also investigated the evolutionary and epistatic influences of the many nonlinear interactions between proteins in the system and found several pairs to have coevolved, including those whose interactions are purely dynamical with respect to system output. This evidence points to a key role played by nonlinear system dynamics in influencing patterns of molecular evolution.     

Multifractality in the Peripheral Cardiovascular System from Pointwise Hölder Exponents of Laser Doppler Flowmetry Signals

We study the dynamics of skin laser Doppler flowmetry signals giving a peripheral view of the cardiovascular system. The analysis of Hölder exponents reveals that the experimental signals are weakly multifractal for young healthy subjects at rest. We implement the same analysis on data generated by a standard theoretical model of the cardiovascular system based on nonlinear coupled oscillators with linear couplings and fluctuations. We show that the theoretical model, although it captures basic features of the dynamics, is not complex enough to reflect the multifractal irregularities of microvascular mechanisms.     

Preventing extinction and outbreaks in chaotic populations

Interactions in ecological communities are inherently nonlinear and can lead to complex population dynamics including irregular fluctuations induced by chaos. Chaotic population dynamics can exhibit violent oscillations with extremely small or large population abundances that might cause extinction and recurrent outbreaks, respectively. We present a simple method that can guide management efforts to prevent crashes, peaks, or any other undesirable state. At the same time, the irregularity of the dynamics can be preserved when chaos is desirable for the population. The control scheme is easy to implement because it relies on time series information only. The method is illustrated by two examples: control of crashes in the Ricker map and control of outbreaks in a stage-structured model of the flour beetle Tribolium. It turns out to be effective even with few available data and in the presence of noise, as is typical for ecological settings.     

Simulating the evolution of signal transduction pathways

We use a generic model of a network of proteins that can activate or deactivate each other to explore the emergence and evolution of signal transduction networks and to gain a basic understanding of their general properties. Starting with a set of non-interacting proteins, we evolve a signal transduction network by random mutation and selection to fulfill a complex biological task. In order to validate this approach we base selection on a fitness function that captures the essential features of chemotactic behavior as seen in bacteria. We find that a system of as few as three proteins can evolve into a network mediating chemotaxis-like behavior by acting as a "derivative sensor". Furthermore, we find that the dynamics and topology of such networks show many similarities to the natural chemotaxis pathway, that the response magnitude can increase with increasing network size and that network behavior shows robustness towards variations in some of the internal parameters. We conclude that simulating the evolution of signal transduction networks to mediate a certain behavior may be a promising approach for understanding the general properties of the natural pathway for that behavior.     

Reconstructing embryonic development

Novel approaches to bio-imaging and automated computational image processing allow the design of truly quantitative studies in developmental biology. Cell behavior, cell fate decisions, cell interactions during tissue morphogenesis, and gene expression dynamics can be analyzed in vivo for entire complex organisms and throughout embryonic development. We review state-of-the-art technology for live imaging, focusing on fluorescence light microscopy techniques for system-level investigations of animal development, and discuss computational approaches to image segmentation, cell tracking, automated data annotation, and biophysical modeling. We argue that the substantial increase in data complexity and size requires sophisticated new strategies to data analysis to exploit the enormous potential of these new resources.     

Nonlinear fractal dynamics of human colonic pressure activity based upon the box-counting method

The computational fractal dimension of human colonic pressure activity acquired by a telemetric capsule robot under normal physiological conditions was studied using the box-counting method. The fractal dimension is a numeric value that quantifies to measure how rough the signal is from nonlinear dynamics, rather than its amplitude or other linear statistical features. The colonic pressure activities from the healthy subject during three typical periods were analysed. The results showed that the activity might be fractal with a non-integer fractal dimension after it being integrated over time using the cumsum method, which was never revealed before. Moreover, the activity (after it being integrated) acquired soon after wakening up was the roughest (also the most complex one) with the largest fractal dimension, closely followed by that acquired during sleep with that acquired long time after awakening up (in the daytime) ranking third with the smallest fractal dimension. Fractal estimation might provide a new method to learn the nonlinear dynamics of human gastrointestinal pressure recordings.     

Nonlinear transient computation as a potential "kernel trick" in cortical processing

Evidence has been found for the presence of chaotic dynamics at all levels of the mammalian brain. This has led to some searching questions about the potential role that nonlinear dynamics may have in neural information processing. We propose that chaos equips the brain with the equivalent of a kernel trick for solving hard nonlinear problems. The approach presented, which is described as nonlinear transient computation, uses the dynamics of a well known chaotic attractor. The paper provides experimental results to show that this approach can be used to solve some challenging pattern recognition tasks. The paper also offers evidence to suggest that the efficacy of nonlinear transient computation for nonlinear pattern classification is dependent only on the generic properties of chaotic attractors and is not sensitive to the particular dynamics of specific sub-regions of chaotic phase space. If, as this work suggests, nonlinear transient computation is independent of the particulars of any given chaotic attractor, then it could be offered as a possible explanation of how the chaotic dynamics that have been observed in brain structures contribute to neural information processing tasks.     

Protein significance analysis in selected reaction monitoring (SRM) measurements

Selected reaction monitoring (SRM) is a targeted mass spectrometry technique that provides sensitive and accurate protein detection and quantification in complex biological mixtures. Statistical and computational tools are essential for the design and analysis of SRM experiments, particularly in studies with large sample throughput. Currently, most such tools focus on the selection of optimized transitions and on processing signals from SRM assays. Little attention is devoted to protein significance analysis, which combines the quantitative measurements for a protein across isotopic labels, peptides, charge states, transitions, samples, and conditions, and detects proteins that change in abundance between conditions while controlling the false discovery rate. We propose a statistical modeling framework for protein significance analysis. It is based on linear mixed-effects models and is applicable to most experimental designs for both isotope label-based and label-free SRM workflows. We illustrate the utility of the framework in two studies: one with a group comparison experimental design and the other with a time course experimental design. We further verify the accuracy of the framework in two controlled data sets, one from the NCI-CPTAC reproducibility investigation and the other from an in-house spike-in study. The proposed framework is sensitive and specific, produces accurate results in broad experimental circumstances, and helps to optimally design future SRM experiments. The statistical framework is implemented in an open-source R-based software package SRMstats, and can be used by researchers with a limited statistics background as a stand-alone tool or in integration with the existing computational pipelines.     

Neural mechanisms of human texture processing: texture boundary detection and visual search

Texture of various appearances, geometric distortions, spatial frequency content and densities is utilized by the human visual system to segregate items from background and to enable recognition of complex geometric forms. For automatic, or pre-attentive, segmentation of a visual scene, sophisticated analysis and comparison of surface properties over wide areas of the visual field are required. We investigated the neural substrate underlying human texture processing, particularly the computational mechanisms of texture boundary detection. We present a neural network model which uses as building blocks model cortical areas that are bi-directionally linked to implement cycles of feedforward and feedback interaction for signal detection, hypothesis generation and testing within the infero-temporal pathway of form processing. In the spirit of Jake Beck's early investigations our model particularly builds upon two key hypotheses, namely that (i) texture segregation is based on boundary detection, rather than clustering homogeneous items, and (ii) texture boundaries are detected mainly on the basis of larger scenic contexts mediated by higher cortical areas, such as area V4. The latter constraint provides a basis for element grouping in accordance to the Gestalt laws of similarity and good continuation. It is shown through simulations that the model integrates a variety of psychophysical findings on texture processing and provides a link to the underlying physiology. The functional role of feedback processing is demonstrated by context dependent modulation of V1 cell activation, leading to sharply localized detection of texture boundaries. It furthermore explains why pre-attentive processing in visual search tasks can be directly linked to texture boundary processing as revealed by recent EEG studies on visual search.     

Bayesian-Estimated Hierarchical HMMs Enable Robust Analysis of Single-Molecule Kinetic Heterogeneity

Single-molecule kinetic experiments allow the reaction trajectories of individual biomolecules to be directly observed, eliminating the effects of population averaging and providing a powerful approach for elucidating the kinetic mechanisms of biomolecular processes. A major challenge to the analysis and interpretation of these experiments, however, is the kinetic heterogeneity that almost universally complicates the recorded single-molecule signal versus time trajectories (i.e., signal trajectories). Such heterogeneity manifests as changes and/or differences in the transition rates that are observed within individual signal trajectories or across a population of signal trajectories. Because characterizing kinetic heterogeneity can provide critical mechanistic information, we have developed a computational method that effectively and comprehensively enables such analysis. To this end, we have developed a computational algorithm and software program, hFRET, that uses the variational approximation for Bayesian inference to estimate the parameters of a hierarchical hidden Markov model, thereby enabling robust identification and characterization of kinetic heterogeneity. Using simulated signal trajectories, we demonstrate the ability of hFRET to accurately and precisely characterize kinetic heterogeneity. In addition, we use hFRET to analyze experimentally recorded signal trajectories reporting on the conformational dynamics of ribosomal pre-translocation (PRE) complexes. The results of our analyses demonstrate that PRE complexes exhibit kinetic heterogeneity, reveal the physical origins of this heterogeneity, and allow us to expand the current model of PRE complex dynamics. The methods described here can be applied to signal trajectories generated using any type of signal and can be easily extended to the analysis of signal trajectories exhibiting more complex kinetic behaviors. Moreover, variations of our approach can be easily developed to integrate kinetic data obtained from different experimental constructs and/or from molecular dynamics simulations of a biomolecule of interest.     

A highly sensitive near‐infrared fluorescent detection method to analyze signalling pathways by reverse‐phase protein array

The comprehensive and quantitative analysis of the protein phosphorylation patterns in different cellular context is of considerable and general interest. The ability to quantify phosphorylation of discrete signalling proteins in large collections of biological samples would greatly favour the development of systems biology in the field of cell signalling. Reverse‐phase protein array (RPPA) potentially represents a very attractive approach to map signal transduction networks with high throughput. In the present report, we describe an improved detection method for RPPA combining near‐infrared with one or two rounds of tyramide‐based signal amplification. The LOQ was lowered from 6.84 attomoles with a direct detection protocol to 0.21 attomole with two amplification steps. We validated this method in the context of intracellular signal transduction triggered by follicle‐stimulating hormone in HEK293 cells. We consistently detected phosphorylated proteins in the sub‐attomole range from less than 1 ng of total cell extracts. Importantly, the method correlated with Western blot analysis of the same samples while displaying excellent intra‐ and inter‐slide reproducibility. We conclude that RPPA combined with amplified near‐infrared detection can be used to capture the subtle regulations intrinsic to signalling network dynamics at an unprecedented throughput, from minute amounts of biological samples.     

Bursting dynamics remarkably improve the performance of neural networks on liquid computing

Burst firings are functionally important behaviors displayed by neural circuits, which plays a primary role in reliable transmission of electrical signals for neuronal communication. However, with respect to the computational capability of neural networks, most of relevant studies are based on the spiking dynamics of individual neurons, while burst firing is seldom considered. In this paper, we carry out a comprehensive study to compare the performance of spiking and bursting dynamics on the capability of liquid computing, which is an effective approach for intelligent computation of neural networks. The results show that neural networks with bursting dynamic have much better computational performance than those with spiking dynamics, especially for complex computational tasks. Further analysis demonstrate that the fast firing pattern of bursting dynamics can obviously enhance the efficiency of synaptic integration from pre-neurons both temporally and spatially. This indicates that bursting dynamic can significantly enhance the complexity of network activity, implying its high efficiency in information processing.     

Wave-Processing of Long-Scale Information by Neuronal Chains

Investigation of mechanisms of information handling in neural assemblies involved in computational and cognitive tasks is a challenging problem. Synergetic cooperation of neurons in time domain, through synchronization of firing of multiple spatially distant neurons, has been widely spread as the main paradigm. Complementary, the brain may also employ information coding and processing in spatial dimension. Then, the result of computation depends also on the spatial distribution of long-scale information. The latter bi-dimensional alternative is notably less explored in the literature. Here, we propose and theoretically illustrate a concept of spatiotemporal representation and processing of long-scale information in laminar neural structures. We argue that relevant information may be hidden in self-sustained traveling waves of neuronal activity and then their nonlinear interaction yields efficient wave-processing of spatiotemporal information. Using as a testbed a chain of FitzHugh-Nagumo neurons, we show that the wave-processing can be achieved by incorporating into the single-neuron dynamics an additional voltage-gated membrane current. This local mechanism provides a chain of such neurons with new emergent network properties. In particular, nonlinear waves as a carrier of long-scale information exhibit a variety of functionally different regimes of interaction: from complete or asymmetric annihilation to transparent crossing. Thus neuronal chains can work as computational units performing different operations over spatiotemporal information. Exploiting complexity resonance these composite units can discard stimuli of too high or too low frequencies, while selectively compress those in the natural frequency range. We also show how neuronal chains can contextually interpret raw wave information. The same stimulus can be processed differently or identically according to the context set by a periodic wave train injected at the opposite end of the chain.     

Stimulus-induced bifurcations in discrete-time neural oscillators

Based on theoretical issues and neurobiological evidence, considerable interest has recently focused on dynamic computational elements in neural systems. Such elements respond to stimuli by altering their dynamical behavior rather than by changing a scalar output. In particular, neural oscillators capable of chaotic dynamics represent a potentially very rich substrate for complex spatiotemporal information processing. However, the response properties of such systems must be studied in detail before they can be used as computational elements in neural models. In this paper, we focus on the response of a very simple discrete-time neural oscillator model to a fixed input. We show that the oscillator responds to the stimulus through a fairly complex set of bifurcations, and shows critical switching between attractors. This information can be used to construct very sophisticated dynamic computational elements with well-understood response properties. Examples of such elements are presented in the paper. We end with a brief discussion of simple architectures for networks of dynamical elements, and the relevance of our results to neurobiological models. Received: 7 August 1997 / Accepted in revised form: 22 April 1998     

Adaptive information processing in microtubule networks

Microtubule networks provide a wide range of microskeletal and micromuscular functionalities. Evidence from a number of directions suggests that they can also serve as a medium for intracellular signaling processing. The model presented here comprises an empirically motivated representation of microtubule growth dynamics, an abstract representation of signal processing, and a feedback learning mechanism that we refer to as adaptive self-stabilization. The growth model mimics the dynamic instability picture of microtubule formation and decomposition, but as modulated by the binding activity of microtubule associated proteins (or MAPs). The signal processing submodel treats each microtubule as a string of linked discrete oscillators capable of propagating signals that are introduced, manipulated, and extracted by bound MAP activity. Adaptive self-stabilization is essentially feedback acting on signal processing capabilities via the growth dynamics. The network is presented with a training set of patterns. If the input-output behavior is satisfactory MAP binding affinity increases, thereby stabilizing the network structure; otherwise the binding affinity decreases, allowing for more structural variation. The results obtained suggest that adaptive capabilities are practically inevitable in microtubule networks, a conclusion strengthened by the fact that the signal processing and growth dynamics mechanisms available in nature are undoubtedly much richer than those represented in the model.