Dynamic positional information: Patterning mechanism versus precision in gradient-driven systems

There is much talk about information in biology. In developmental biology, this takes the form of "positional information," especially in the context of morphogen-based pattern formation. Unfortunately, the concept of "information" is rarely defined in any precise manner. Here, we provide two alternative interpretations of "positional information," and examine the complementary meanings and uses of each concept. Positional information defined as Shannon information helps us understand decoding and error propagation in patterning systems. General relativistic positional information, in contrast, provides a metric to assess the output of pattern-forming mechanisms. Both interpretations provide powerful conceptual tools that do not compete, but are best used in combination to gain a proper mechanistic understanding of robust patterning.

Lighting up the central dogma for predictive developmental biology

Although the last 30years have witnessed the mapping of the wiring diagrams of the gene regulatory networks that dictate cell fate and animal body plans, specific understanding building on such network diagrams that shows how DNA regulatory regions control gene expression lags far behind. These networks have yet to yield the predictive power necessary to, for example, calculate how the concentration dynamics of input transcription factors and DNA regulatory sequence prescribes output patterns of gene expression that, in turn, determine body plans themselves. Here, we argue that reaching a predictive understanding of developmental decision-making calls for an interplay between theory and experiment aimed at revealing how the regulation of the processes of the central dogma dictate network connections and how network topology guides cells toward their ultimate developmental fate. To make this possible, it is crucial to break free from the snapshot-based understanding of embryonic development facilitated by fixed-tissue approaches and embrace new technologies that capture the dynamics of developmental decision-making at the single cell level, in living embryos.

On Markov blankets and hierarchical self-organisation

Biological self-organisation can be regarded as a process of spontaneous pattern formation; namely, the emergence of structures that distinguish themselves from their environment. This process can occur at nested spatial scales: from the microscopic (e.g., the emergence of cells) to the macroscopic (e.g. the emergence of organisms). In this paper, we pursue the idea that Markov blankets - that separate the internal states of a structure from external states - can self-assemble at successively higher levels of organisation. Using simulations, based on the principle of variational free energy minimisation, we show that hierarchical self-organisation emerges when the microscopic elements of an ensemble have prior (e.g., genetic) beliefs that they participate in a macroscopic Markov blanket: i.e., they can only influence - or be influenced by - a subset of other elements. Furthermore, the emergent structures look very much like those found in nature (e.g., cells or organelles), when influences are mediated by short range signalling. These simulations are offered as a proof of concept that hierarchical self-organisation of Markov blankets (into Markov blankets) can explain the self-evidencing, autopoietic behaviour of biological systems.

Dynamic synergetic configurations of resting-state networks in ADHD

Attention deficit hyperactivity disorder (ADHD) is characterized by high distractibility and impaired executive functions. Notably, there is mounting evidence suggesting that ADHD could be regarded as a default mode network (DMN) disorder. In particular, failure in regulating the dynamics of activity and interactions of the DMN and cognitive control networks have been hypothesized as the main source of task interference causing attentional problems. On the other hand, previous studies indicated pronounced fluctuations in the strength of functional connections over time, particularly for the inter-network connections between the DMN and fronto-parietal control networks. Hence, characterization of connectivity disturbances in ADHD requires a thorough assessment of time-varying functional connectivity (FC). In this study, we proposed a dynamical systems perspective to assess how the DMN over time recruits different configurations of network segregation and integration. Specifically, we were interested in configurations for which both intra- and inter-network connections are retained, as opposed to commonly used methods which assess network segregation as a single measure. From resting-state fMRI data, we extracted three different stable configurations of FC patterns for the DMN, namely synergies. We provided evidence supporting our hypothesis that ADHD differs compared to controls, both in terms of recruitment rate and topology of specific synergies between resting-state networks. In addition, we found a relationship between synergetic cooperation patterns of the DMN with cognitive control networks and a behavioral measure which is sensitive to ADHD-related symptoms, namely the Stroop color-word task.

Network-based Observability and Controllability Analysis of Dynamical Systems: the NOCAD toolbox

The network science-based determination of driver nodes and sensor placement has become increasingly popular in the field of dynamical systems over the last decade. In this paper, the applicability of the methodology in the field of life sciences is introduced through the analysis of the neural network of Caenorhabditis elegans. Simultaneously, an Octave and MATLAB-compatible NOCAD toolbox is proposed that provides a set of methods to automatically generate the relevant structural controllability and observability associated measures for linear or linearised systems and compare the different sensor placement methods.

Dynamic and stochastic systems as a framework for metaphysics and the philosophy of science

Scientists often think of the world (or some part of it) as a dynamical system, a stochastic process, or a generalization of such a system. Prominent examples of systems are (i) the system of planets orbiting the sun or any other classical mechanical system, (ii) a hydrogen atom or any other quantum-mechanical system, and (iii) the earth's atmosphere or any other statistical mechanical system. We introduce a general and unified framework for describing such systems and show how it can be used to examine some familiar philosophical questions, including the following: how can we define nomological possibility, necessity, determinism, and indeterminism; what are symmetries and laws; what regularities must a system display to make scientific inference possible; how might principles of parsimony such as Occam's Razor help when we make such inferences; what is the role of space and time in a system; and might they be emergent features? Our framework is intended to serve as a toolbox for the formal analysis of systems that is applicable in several areas of philosophy.

Multiscale movement coordination dynamics in collaborative team problem solving

During collaborative problem solving (CPS), coordination occurs at different spatial and temporal scales. This multiscale coordination should play a functional role in facilitating effective collaboration. To evaluate this, we conducted a study of computer-based CPS with 42 dyadic teams. We used cross-wavelet coherence to examine movement coordination, extracted from videos, at several scales, and tested whether the observed coordination was greater than expected due to chance and due to task demands. We found that coordination at scales less than 2s was greater than chance and at most scales (except 16s, 1m, and 2m), was greater than expected due to task demands. Lastly, we observed that coherence at .25s and 1s scales was predictive of performance. However, when including relative phase, our results suggest that higher in-phase movement coordination at the 1s scale was the strongest predictor of CPS performance. Further, we used growth curve modeling to examine how movement coordination changes across the duration of the task and whether this is moderated by CPS performance. We found that coordination over the duration of the CPS task is quadratic (a U shape) and that better performing teams have higher coordination with a shallower curve. We discuss these findings and their relevance to understanding how low-level movement coordination facilitates CPS.

Adaptive frequency-based modeling of whole-brain oscillations: Predicting regional vulnerability and hazardousness rates

Whole-brain computational modeling based on structural connectivity has shown great promise in successfully simulating fMRI BOLD signals with temporal coactivation patterns that are highly similar to empirical functional connectivity patterns during resting state. Importantly, previous studies have shown that spontaneous fluctuations in coactivation patterns of distributed brain regions have an inherent dynamic nature with regard to the frequency spectrum of intrinsic brain oscillations. In this modeling study, we introduced frequency dynamics into a system of coupled oscillators, where each oscillator represents the local mean-field model of a brain region. We first showed that the collective behavior of interacting oscillators reproduces previously shown features of brain dynamics. Second, we examined the effect of simulated lesions in gray matter by applying an in silico perturbation protocol to the brain model. We present a new approach to map the effects of vulnerability in brain networks and introduce a measure of regional hazardousness based on mapping of the degree of divergence in a feature space.

The hidden repertoire of brain dynamics and dysfunction

The purpose of this paper is to describe a framework for the understanding of rules that govern how neural system dynamics are coordinated to produce behavior. The framework, structured flows on manifolds (SFM), posits that neural processes are flows depicting system interactions that occur on relatively low-dimension manifolds, which constrain possible functional configurations. Although this is a general framework, we focus on the application to brain disorders. We first explain the Epileptor, a phenomenological computational model showing fast and slow dynamics, but also a hidden repertoire whose expression is similar to refractory status epilepticus. We suggest that epilepsy represents an innate brain state whose potential may be realized only under certain circumstances. Conversely, deficits from damage or disease processes, such as stroke or dementia, may reflect both the disease process per se and the adaptation of the brain. SFM uniquely captures both scenarios. Finally, we link neuromodulation effects and switches in functional network configurations to fast and slow dynamics that coordinate the expression of SFM in the context of cognition. The tools to measure and model SFM already exist, giving researchers access to the dynamics of neural processes that support the concomitant dynamics of the cognitive and behavioral processes.

Staying Together: A Bidirectional Delay-Coupled Approach to Joint Action

To understand how individuals adapt to and anticipate each other in joint tasks, we employ a bidirectional delay-coupled dynamical system that allows for mutual adaptation and anticipation. In delay-coupled systems, anticipation is achieved when one system compares its own time-delayed behavior, which implicitly includes past information about the other system's behavior, with the other system's instantaneous behavior. Applied to joint music performance, the model allows each system to adapt its behavior to the dynamics of the other. Model predictions of asynchrony between two simultaneously produced musical voices were compared with duet pianists' behavior; each partner performed one voice while auditory feedback perturbations occurred at unpredictable times during live performance. As the model predicted, when auditory feedback from one musical voice was removed, the asynchrony changed: The pianist's voice that was removed anticipated (preceded) the actions of their partner. When the auditory feedback returned and both musicians could hear each other, they rapidly returned to baseline levels of asynchrony. To understand how the pianists anticipated each other, their performances were fitted by the model to examine change in model parameters (coupling strength, time-delay). When auditory feedback for one or both voices was removed, the fits showed the expected decrease in coupling strength and time-delay between the systems. When feedback about the voice(s) returned, the coupling strength and time-delay returned to baseline. These findings support the idea that when people perform actions together, they do so as a coupled bidirectional anticipatory system.

Amalgamating evidence of dynamics

Many approaches to evidence amalgamation focus on relatively static information or evidence: the data to be amalgamated involve different variables, contexts, or experiments, but not measurements over extended periods of time. However, much of scientific inquiry focuses on dynamical systems; the system's behavior over time is critical. Moreover, novel problems of evidence amalgamation arise in these contexts. First, data can be collected at different measurement timescales, where potentially none of them correspond to the underlying system's causal timescale. Second, missing variables have a significantly different impact on time series measurements than they do in the traditional static setting; in particular, they make causal and structural inference much more difficult. In this paper, we argue that amalgamation should proceed by integrating causal knowledge, rather than at the level of "raw" evidence. We defend this claim by first outlining both of these problems, and then showing that they can be solved only if we operate on causal structures. We therefore must use causal discovery methods that are reliable given these problems. Such methods do exist, but their successful application requires careful consideration of the problems that we highlight.

Sample-level sound synthesis with recurrent neural networks and conceptors

Conceptors are a recent development in the field of reservoir computing; they can be used to influence the dynamics of recurrent neural networks (RNNs), enabling generation of arbitrary patterns based on training data. Conceptors allow interpolation and extrapolation between patterns, and also provide a system of boolean logic for combining patterns together. Generation and manipulation of arbitrary patterns using conceptors has significant potential as a sound synthesis method for applications in computer music but has yet to be explored. Conceptors are untested with the generation of multi-timbre audio patterns, and little testing has been done on scalability to longer patterns required for audio. A novel method of sound synthesis based on conceptors is introduced. Conceptular Synthesis is based on granular synthesis; sets of conceptors are trained to recall varying patterns from a single RNN, then a runtime mechanism switches between them, generating short patterns which are recombined into a longer sound. The quality of sound resynthesis using this technique is experimentally evaluated. Conceptor models are shown to resynthesise audio with a comparable quality to a close equivalent technique using echo state networks with stored patterns and output feedback. Conceptor models are also shown to excel in their malleability and potential for creative sound manipulation, in comparison to echo state network models which tend to fail when the same manipulations are applied. Examples are given demonstrating creative sonic possibilities, by exploiting conceptor pattern morphing, boolean conceptor logic and manipulation of RNN dynamics. Limitations of conceptor models are revealed with regards to reproduction quality, and pragmatic limitations are also shown, where rises in computation and memory requirements preclude the use of these models for training with longer sound samples. The techniques presented here represent an initial exploration of the sound synthesis potential of conceptors, demonstrating possible creative applications in sound design; future possibilities and research questions are outlined.

Combinatorial perturbation analysis reveals divergent regulations of mesenchymal genes during epithelial-to-mesenchymal transition

Epithelial-to-mesenchymal transition (EMT), a fundamental transdifferentiation process in development, produces diverse phenotypes in different physiological or pathological conditions. Many genes involved in EMT have been identified to date, but mechanisms contributing to the phenotypic diversity and those governing the coupling between the dynamics of epithelial (E) genes and that of the mesenchymal (M) genes are unclear. In this study, we employed combinatorial perturbations to mammary epithelial cells to induce a series of EMT phenotypes by manipulating two essential EMT-inducing elements, namely TGF-β and ZEB1. By measuring transcriptional changes in more than 700 E-genes and M-genes, we discovered that the M-genes exhibit a significant diversity in their dependency to these regulatory elements and identified three groups of M-genes that are controlled by different regulatory circuits. Notably, functional differences were detected among the M-gene clusters in motility regulation and in survival of breast cancer patients. We computationally predicted and experimentally confirmed that the reciprocity and reversibility of EMT are jointly regulated by ZEB1. Our integrative analysis reveals the key roles of ZEB1 in coordinating the dynamics of a large number of genes during EMT, and it provides new insights into the mechanisms for the diversity of EMT phenotypes.

The effect of running speed on joint coupling coordination and its variability in recreational runners

The purpose of this study was to examine the effect of speed on coordination and its variability in running gait using vector coding analysis. Lower extremity kinematic data were collected for thirteen recreational runners while running at three different speeds in random order: preferred speed, 15% faster and 15% lower than preferred speed. A dynamical systems approach, using vector coding and circular statistics, were used to quantify coordination and its variability for selected hip-knee and knee-ankle joint couplings. The influence of running speed was calculated from the continuous data sets of the running cycle, allowing for the identification of time percentages where differences existed. Results indicate that increases in running speed produced moderate alterations in the frequency of movement patterns which were not enough to alter classification of coordination. No effects of speed on coordination variability were observed. This study has demonstrated that coordination and coordination variability is generally stable in the range of ±15% around of preferred speed in recreational runners.

A process account of the uncontrolled manifold structure of joint space variance in pointing movements

In many situations, the human movement system has more degrees of freedom than needed to achieve a given movement task. Martin et al. (Neural Comput 21(5):1371-1414, 2009) accounted for signatures of such redundancy like self-motion and motor equivalence in a process model in which a neural oscillator generated timed end-effector virtual trajectories that a neural dynamics transformed into joint virtual trajectories while decoupling task-relevant and task-irrelevant combinations of joint angles. Neural control of muscle activation and the biomechanical dynamics of the arm were taken into account. The model did not address the main signature of redundancy, however, the UCM structure of variance: Many experimental studies have shown that across repetitions, variance of joint configuration trajectories is structured. Combinations of joint angles that affect task variables (lying in the uncontrolled manifold, UCM) are much more variable than combinations of joint angles that do not. This finding has been robust across movement systems, age, and tasks and is often preserved in clinical populations as well. Here, we provide an account for the UCM structure of variance by adding four types of noise sources to the model of Martin et al. (Neural Comput 21(5):1371-1414, 2009). Comparing the model to human pointing movements and systematically examining the role of each noise source and mechanism, we identify three causes of the UCM effect, all of which, we argue, contribute: (1) the decoupling of motor commands across the task-relevant and task-irrelevant subspaces together with "neural" noise at the level of these motor commands; (2) "muscle noise" combined with imperfect control of the limb; (3) back-coupling of sensed joint configurations into the motor commands which then yield to the sensed joint configuration within the UCM.

Dynamic mode decomposition in vector-valued reproducing kernel Hilbert spaces for extracting dynamical structure among observables

Understanding nonlinear dynamical systems (NLDSs) is challenging in a variety of engineering and scientific fields. Dynamic mode decomposition (DMD), which is a numerical algorithm for the spectral analysis of Koopman operators, has been attracting attention as a way of obtaining global modal descriptions of NLDSs without requiring explicit prior knowledge. However, since existing DMD algorithms are in principle formulated based on the concatenation of scalar observables, it is not directly applicable to data with dependent structures among observables, which take, for example, the form of a sequence of graphs. In this paper, we formulate Koopman spectral analysis for NLDSs with structures among observables and propose an estimation algorithm for this problem. This method can extract and visualize the underlying low-dimensional global dynamics of NLDSs with structures among observables from data, which can be useful in understanding the underlying dynamics of such NLDSs. To this end, we first formulate the problem of estimating spectra of the Koopman operator defined in vector-valued reproducing kernel Hilbert spaces, and then develop an estimation procedure for this problem by reformulating tensor-based DMD. As a special case of our method, we propose the method named as Graph DMD, which is a numerical algorithm for Koopman spectral analysis of graph dynamical systems, using a sequence of adjacency matrices. We investigate the empirical performance of our method by using synthetic and real-world data.

Identification of an early cell fate regulator by detecting dynamics in transcriptional heterogeneity and co-regulation during astrocyte differentiation

There are an increasing number of reports that characterize the temporal behavior of gene expression at the single-cell level during cell differentiation. Despite accumulation of data describing the heterogeneity of biological responses, the dynamics of gene expression heterogeneity and its regulation during the differentiation process have not been studied systematically. To understand transcriptional heterogeneity during astrocyte differentiation, we analyzed single-cell transcriptional data from cells representing the different stages of astrocyte differentiation. When we compared the transcriptional variability of co-expressed genes between the undifferentiated and differentiated states, we found that there was significant increase in transcriptional variability in the undifferentiated state. The genes showing large changes in both "variability" and "correlation" between neural stem cells (NSCs) and astrocytes were found to be functionally involved in astrocyte differentiation. We determined that these genes are potentially regulated by Ascl1, a previously known oscillatory gene in NSCs. Pharmacological blockade of Ntsr2, which is transcriptionally co-regulated with Ascl1, showed that Ntsr2 may play an important role in the differentiation from NSCs to astrocytes. This study shows the importance of characterizing transcriptional heterogeneity and rearrangement of the co-regulation network between different cell states. It also highlights the potential for identifying novel regulators of cell differentiation that will further increase our understanding of the molecular mechanisms underlying the differentiation process.

Evaluating sociotechnical dynamics in a simulated remotely-piloted aircraft system: a layered dynamics approach

As coordination mechanisms change and technology failures occur, a sociotechnical system must reorganise itself across human and technological layers to maintain effectiveness. We present a study examining reorganisation across communication, controls and vehicle layers of a remotely-piloted aircraft system (RPAS) using a layered dynamics approach. Team members (pilot; navigator; photographer) performed 5 simulated RPAS missions using different operator configurations, including all-human and human-autonomy teams. Reorganization (operationally defined using entropy) time series measured the changing system reorganisation profiles under different operator configurations and following autonomy failures. Correlations between these reorganisation profiles and team effectiveness scores describe the manner in which the system had to be coordinated to maintain effectiveness under these changing conditions. Four unplanned autonomy failures were analysed to visualise system reorganisation following a technology failure. With its objective and real-time modelling and measurement capabilities, layered dynamics complements existing systems thinking tools for understanding sociotechnical complexity and enhancing system effectiveness. Practitioner summary: A layered dynamics approach for understanding how a sociotechnical system dynamically reorganises itself is presented. The layered dynamics of RPAS were analysed under different operator configurations and following autonomy failures. Layered dynamics complements existing system-thinking tools for modelling sociotechnical system complexity and effectiveness. Abbreviation: RPAS: remotely-piloted aircraft system; HIS: human-systems integration; EAST: event analysis of systemic teamwork; H1: hypothesis 1; H2: hypothesis 2; H3: hypothesis 3; CERTT-STE: cognitive engineering research on team tasks--synthetic task environment; AVO: air vehicle operator; PLO: payload operator; DEMPC: data exploitation, mission planning, and communications; ACT-R: adaptive control of thought-rational; sec: seconds; ANOVA: analysis of variance.

Walking with avatars: Gait-related visual information for following a virtual leader

Dynamic situations, such as interactive sports or walking on a busy street, impose high demands on a person's ability to interact with (others in) its environment (i.e., 'interact-ability'). The current study examined how distance regulation, a fundamental component of these interactions, is mediated by different sources of visual information. Participants were presented with a back and forwards moving virtual leader, which they had to follow by walking back and forwards themselves. We presented the leader in several appearances that differed in the presence of segmental (i.e., relative movements of body segments), cadence-related (i.e., sway and bounce), and global (i.e., optical expansion-compression) information. Results indicated that removing segmental motion information from the virtual leader significantly deteriorated both temporal synchronization and spatial accuracy of the follower to the leader, especially when the movement path of the leader was less regular/predictable. However, no difference was found between cadence-related and global motion information appearances. We argue that regulating distance with others effectively requires a versatile attunement to segmental and global motion information depending on the specific task demands. The results further support the notion that detection of especially segmental information allows for more timely 'anticipatory' tuning to another person's locomotor movements and intentions.

Slowdown of BCM plasticity with many synapses

During neural development sensory stimulation induces long-term changes in the receptive field of the neurons that encode the stimuli. The Bienenstock-Cooper-Munro (BCM) model was introduced to model and analyze this process computationally, and it remains one of the major models of unsupervised plasticity to this day. Here we show that for some stimulus types, the convergence of the synaptic weights under the BCM rule slows down exponentially as the number of synapses per neuron increases. We present a mathematical analysis of the slowdown that shows also how the slowdown can be avoided.

Using RuleBuilder to Graphically Define and Visualize BioNetGen-Language Patterns and Reaction Rules

RuleBuilder is a tool for drawing graphs that can be represented by the BioNetGen language (BNGL), which is used to formulate mathematical, rule-based models of biochemical systems. BNGL provides an intuitive plain text, or string, representation of such systems, which is based on a graphical formalism. Reactions are defined in terms of graph-rewriting rules that specify the necessary intrinsic properties of the reactants, a transformation, and a rate law. Rules also contain contextual constraints that restrict application of the rule. In some cases, the specification of contextual constraints can be verbose, making a rule difficult to read. RuleBuilder is designed to ease the task of reading and writing individual reaction rules or other BNGL patterns required for model formulation. The software assists in the reading of existing models by converting BNGL strings of interest into a graph-based representation composed of nodes and edges. RuleBuilder also enables the user to construct de novo a visual representation of BNGL strings using drawing tools available in its interface. As objects are added to the drawing canvas, the corresponding BNGL string is generated on the fly, and objects are similarly drawn on the fly as BNGL strings are entered into the application. RuleBuilder thus facilitates construction and interpretation of rule-based models.

Optimal modularity and memory capacity of neural reservoirs

The neural network is a powerful computing framework that has been exploited by biological evolution and by humans for solving diverse problems. Although the computational capabilities of neural networks are determined by their structure, the current understanding of the relationships between a neural network's architecture and function is still primitive. Here we reveal that a neural network's modular architecture plays a vital role in determining the neural dynamics and memory performance of the network of threshold neurons. In particular, we demonstrate that there exists an optimal modularity for memory performance, where a balance between local cohesion and global connectivity is established, allowing optimally modular networks to remember longer. Our results suggest that insights from dynamical analysis of neural networks and information-spreading processes can be leveraged to better design neural networks and may shed light on the brain's modular organization.

An anisotropic interaction model for simulating fingerprints

Evidence suggests that both the interaction of so-called Merkel cells and the epidermal stress distribution play an important role in the formation of fingerprint patterns during pregnancy. To model the formation of fingerprint patterns in a biologically meaningful way these patterns have to become stationary. For the creation of synthetic fingerprints it is also very desirable that rescaling the model parameters leads to rescaled distances between the stationary fingerprint ridges. Based on these observations, as well as the model introduced by Kücken and Champod we propose a new model for the formation of fingerprint patterns during pregnancy. In this anisotropic interaction model the interaction forces not only depend on the distance vector between the cells and the model parameters, but additionally on an underlying tensor field, representing a stress field. This dependence on the tensor field leads to complex, anisotropic patterns. We study the resulting stationary patterns both analytically and numerically. In particular, we show that fingerprint patterns can be modeled as stationary solutions by choosing the underlying tensor field appropriately.

A simple mechanochemical model for calcium signalling in embryonic epithelial cells

Calcium signalling is one of the most important mechanisms of information propagation in the body. In embryogenesis the interplay between calcium signalling and mechanical forces is critical to the healthy development of an embryo but poorly understood. Several types of embryonic cells exhibit calcium-induced contractions and many experiments indicate that calcium signals and contractions are coupled via a two-way mechanochemical feedback mechanism. We present a new analysis of experimental data that supports the existence of this coupling during apical constriction. We then propose a simple mechanochemical model, building on early models that couple calcium dynamics to the cell mechanics and we replace the hypothetical bistable calcium release with modern, experimentally validated calcium dynamics. We assume that the cell is a linear, viscoelastic material and we model the calcium-induced contraction stress with a Hill function, i.e. saturating at high calcium levels. We also express, for the first time, the "stretch-activation" calcium flux in the early mechanochemical models as a bottom-up contribution from stretch-sensitive calcium channels on the cell membrane. We reduce the model to three ordinary differential equations and analyse its bifurcation structure semi-analytically as two bifurcation parameters vary-the [Formula: see text] concentration, and the "strength" of stretch activation, [Formula: see text]. The calcium system ([Formula: see text], no mechanics) exhibits relaxation oscillations for a certain range of [Formula: see text] values. As [Formula: see text] is increased the range of [Formula: see text] values decreases and oscillations eventually vanish at a sufficiently high value of [Formula: see text]. This result agrees with experimental evidence in embryonic cells which also links the loss of calcium oscillations to embryo abnormalities. Furthermore, as [Formula: see text] is increased the oscillation amplitude decreases but the frequency increases. Finally, we also identify the parameter range for oscillations as the mechanical responsiveness factor of the cytosol increases. This work addresses a very important and not well studied question regarding the coupling between chemical and mechanical signalling in embryogenesis.

Coordination and variability during anticipated and unanticipated sidestepping

BACKGROUND

Numerous investigations have attempted to link the incidence and risk of non-contact anterior cruciate ligament injuries to specific intrinsic and extrinsic mechanisms. However, these are often measured in isolation.

RESEARCH QUESTION

This study utilizes a dynamical systems approach to investigate differences in coordination and coordination variability between segments and joints in anticipated and unanticipated sidestepping, a task linked to a high risk of non-contact anterior cruciate ligament injuries.

METHODS

Full body, three-dimensional kinematics and knee kinetic data were collected on 22 male collegiate soccer players during anticipated and unanticipated sidestepping tasks. A modified vector coding technique was used to quantify coordination and coordination variability of the trunk and pelvis segments and the hip and knee joints.

RESULTS

Sagittal and frontal plane trunk-pelvis coordination were more in-phase during unanticipated sidestepping. Sagittal plane hip-knee and hip (rotation)-knee (flexion/extension) coordination were more in-phase with the knee dominating the movement during unanticipated sidestepping (P < 0.05). Coordination variability was greater in unanticipated sidestepping for trunk (flexion)-pelvis (tilt), trunk (lateral flexion)-pelvis (obliquity), hip (flexion/extension)-knee (flexion/extension) and hip (rotation)-knee (flexion/extension) (P < 0.05). In unanticipated sidestepping where there is limited time to pre-plan the movement, multiple kinematic solutions and high coordinative variability is required to achieve the task.

SIGNIFICANCE

Our results suggest that coordination becomes more in-phase and the variability of this coordination increases as a function of task complexity and reduced planning time as that which occurs in unanticipated sporting task scenarios. Consequently, injury prevention programs must incorporate perceptual components in order to optimise planning time and coordinate appropriate postural adjustments to reduce external knee joint loading and subsequent injury risk in sport.

Computational Analysis of Altering Cell Fate

The notion of reprogramming cell fate is a direct challenge to the traditional view in developmental biology that a cell's phenotypic identity is sealed after undergoing differentiation. Direct experimental evidence, beginning with the somatic cell nuclear transfer experiments of the twentieth century and culminating in the more recent breakthroughs in transdifferentiation and induced pluripotent stem cell (iPSC) reprogramming, have rewritten the rules for what is possible with cell fate transformation. Research is ongoing in the manipulation of cell fate for basic research in disease modeling, drug discovery, and clinical therapeutics. In many of these cell fate reprogramming experiments, there is often little known about the genetic and molecular changes accompanying the reprogramming process. However, gene regulatory networks (GRNs) can in some cases be implicated in the switching of phenotypes, providing a starting point for understanding the dynamic changes that accompany a given cell fate reprogramming process. In this chapter, we present a framework for computationally analyzing cell fate changes by mathematically modeling these GRNs. We provide a user guide with several tutorials of a set of techniques from dynamical systems theory that can be used to probe the intrinsic properties of GRNs as well as study their responses to external perturbations.

A data driven diagnosis tool for thyroid hormones

Thyroid hormones play a significant role in human health. Understanding their dynamics is crucial to diagnoses and maintaining the well-being of the thyroid. In this work we propose a data driven algorithm to detect a fixed point and a limit cycle in real data for thyroid hormones. This algorithm finds the maximum frequency point (fixed point) and extracts a smooth ellipse (limit cycle) from the data. These features characterize various data sets and provide interesting insights to differentiate healthy from malfunctioning thyroid data. This scheme which is backed by a solid dynamical analysis determines the size, orientation and location of a detected limit cycle and provides information about the behavior of the thyroid in its various normal and abnormal conditions. This algorithm does not require tuning any ad-hoc parameters. This approach could lead to an effective way of implementing a personal treatment strategy, and a control system to improve the performance of the thyroid.

Stability of equilibria in quantitative genetic models based on modified-gradient systems

Motivated by questions in biology, we investigate the stability of equilibria of the dynamical system [Formula: see text] which arise as critical points of f, under the assumption that [Formula: see text] is positive semi-definite. It is shown that the condition [Formula: see text], where [Formula: see text] is the smallest eigenvalue of [Formula: see text], plays a key role in guaranteeing uniform asymptotic stability and in providing information on the basis of attraction of those equilibria.

Modeling the impact of biolarvicides on malaria transmission

Biolarvicides are in use in several parts of the world for malaria vector control. We propose a five compartment dynamical systems model to study malaria transmission when biolarvicides are administered, to study the impact of this environmentally safe method on malaria spread. A comprehensive analysis of the model is presented. Model analysis shows that the basic reproductive rate R is larger in the absence of biolarvicides as compared to their presence. Theoretical analysis is corroborated by data from field studies. We show that there exist intermediate parameter regimes that separate disease-free and endemic states, which can in turn be modulated by biolarvicide use. Using Latin hypercube sampling we study the sensitivity of the model to parameter value changes. Calibration of our model to mosquito population and biolarvicide data for indoor and outdoors scenarios, yield parameter values hitherto not available or measurable. We validate our model with malaria incidence data from a region in India and provide predictions for malaria incidence in the presence and absence of biolarvicide. This model provides a prognostic tool to field work involving biolarvicide use in control of malaria.

Viral replication modes in single-peak fitness landscapes: A dynamical systems analysis

Positive-sense, single-stranded RNA viruses are important pathogens infecting almost all types of organisms. Experimental evidence from distributions of mutations and from viral RNA amplification suggest that these pathogens may follow different RNA replication modes, ranging from the stamping machine replication (SMR) to the geometric replication (GR) mode. Although previous theoretical work has focused on the evolutionary dynamics of RNA viruses amplifying their genomes with different strategies, little is known in terms of the bifurcations and transitions involving the so-called error threshold (mutation-induced dominance of mutants) and lethal mutagenesis (extinction of all sequences due to mutation accumulation and demographic stochasticity). Here we analyze a dynamical system describing the intracellular amplification of viral RNA genomes evolving on a single-peak fitness landscape focusing on three cases considering neutral, deleterious, and lethal mutants. We analytically derive the critical mutation rates causing lethal mutagenesis and error threshold, governed by transcritical bifurcations that depend on parameters α (parameter introducing the mode of replication), replicative fitness of mutants (k₁), and on the spontaneous degradation rates of the sequences (ϵ). Our results relate the error catastrophe with lethal mutagenesis in a model with continuous populations of viral genomes. The former case involves dominance of the mutant sequences, while the latter, a deterministic extinction of the viral RNAs during replication due to increased mutation. For the lethal case the critical mutation rate involving lethal mutagenesis is μ_c=1-ɛ/α. Here, the SMR involves lower critical mutation rates, being the system more robust to lethal mutagenesis replicating closer to the GR mode. This result is also found for the neutral and deleterious cases, but for these later cases lethal mutagenesis can shift to the error threshold once the replication mode surpasses a threshold given by α=ϵ/k₁.

Geometric classification of brain network dynamics via conic derivative discriminants

BACKGROUND

Over the past decade, pattern decoding techniques have granted neuroscientists improved anatomical specificity in mapping neural representations associated with function and cognition. Dynamical patterns are of particular interest, as evidenced by the proliferation and success of frequency domain methods that reveal structured spatiotemporal rhythmic brain activity. One drawback of such approaches, however, is the need to estimate spectral power, which limits the temporal resolution of classification.

NEW METHOD

We propose an alternative method that enables classification of dynamical patterns with high temporal fidelity. The key feature of the method is a conversion of time-series data into temporal derivatives. By doing so, dynamically-coded information may be revealed in terms of geometric patterns in the phase space of the derivative signal.

RESULTS

We derive a geometric classifier for this problem which simplifies into a straightforward calculation in terms of covariances. We demonstrate the relative advantages and disadvantages of the technique with simulated data and benchmark its performance with an EEG dataset of covert spatial attention. We reveal the timecourse of covert spatial attention and, by mapping the classifier weights anatomically, its retinotopic organization.

COMPARISON WITH EXISTING METHOD

We especially highlight the ability of the method to provide strong group-level classification performance compared to existing benchmarks, while providing information that is complementary with classical spectral-based techniques. The robustness and sensitivity of the method to noise is also examined relative to spectral-based techniques.

CONCLUSION

The proposed classification technique enables decoding of dynamic patterns with high temporal resolution, performs favorably to benchmark methods, and facilitates anatomical inference.

Are Homeostatic States Stable? Dynamical Stability in Morphoelasticity

Biological growth is often driven by mechanical cues, such as changes in external pressure or tensile loading. Moreover, it is well known that many living tissues actively maintain a preferred level of mechanical internal stress, called the mechanical homeostasis. The tissue-level feedback mechanism by which changes in the local mechanical stresses affect growth is called a growth law within the theory of morphoelasticity, a theory for understanding the coupling between mechanics and geometry in growing and evolving biological materials. This coupling between growth and mechanics occurs naturally in macroscopic tubular structures, which are common in biology (e.g., arteries, plant stems, airways). We study a continuous tubular system with spatially heterogeneous residual stress via a novel discretization approach which allows us to obtain precise results about the stability of equilibrium states of the homeostasis-driven growing dynamical system. This method allows us to show explicitly that the stability of the homeostatic state depends nontrivially on the anisotropy of the growth response. The key role of anisotropy may provide a foundation for experimental testing of homeostasis-driven growth laws.

Descriptive Modeling of the Dynamical Systems and Determination of Feedback Homeostasis at Different Levels of Life Organization

The state-of-art research in the field of life's organization confronts the need to investigate a number of interacting components, their properties and conditions of sustainable behaviour within a natural system. In biology, ecology and life sciences, the performance of such stable system is usually related to homeostasis, a property of the system to actively regulate its state within a certain allowable limits. In our previous work, we proposed a deterministic model for systems' homeostasis. The model was based on dynamical system's theory and pairwise relationships of competition, amensalism and antagonism taken from theoretical biology and ecology. However, the present paper proposes a different dimension to our previous results based on the same model. In this paper, we introduce the influence of inter-component relationships in a system, wherein the impact is characterized by direction (neutral, positive, or negative) as well as its (absolute) value, or strength. This makes the model stochastic which, in our opinion, is more consistent with real-world elements affected by various random factors. The case study includes two examples from areas of hydrobiology and medicine. The models acquired for these cases enabled us to propose a convincing explanation for corresponding phenomena identified by different types of natural systems.

The origin and early evolution of life in chemical composition space

Life can be viewed as a localized chemical system that sits in the basin of attraction of a metastable dynamical attractor state that remains out of equilibrium with the environment. To explore the implications of this conception, I introduce an abstract coordinate system, chemical composition (CC Space), which summarizes the degree to which chemical systems are out of equilibrium with the bulk environment. A system's chemical disequilibrium (CD) is defined to be proportional to the Euclidean distance between the composition of a small region of physical space, a pixel, and the origin of CC space. Such a model implies that new living states arise through chance changes in local chemical concentration ("mutations") that cause chemical systems to move in CC space and enter the basin of attraction of a life state. The attractor of a life state comprises an autocatalytic set of chemicals whose essential ("keystone") species are produced at a higher rate than they are lost to the environment by diffusion, such that spatial growth of the life state is expected. This framework suggests that new life states are most likely to form at the interface between different physical phases, where the rate of diffusion of keystone species is tied to the low-diffusion regime, whereas food and waste products are subject to the more diffusive regime. Once life nucleates, for example on a mineral surface, it will tend to grow and generate variants as a result of additional mutations that find alternative life states. By jumping from life state to life state, systems can eventually occupy areas of CC space that are too far out of equilibrium with the environment to ever arise in a single mutational step. Furthermore, I propose that variation in the capacity of different surface associated life states to persist and compete may systematically favor states that have higher chemical disequilibrium. The model also suggests a simple and predictable path from surface-associated life to cell-like individuation. This dynamical systems theoretical framework provides an integrated view of the origin and early evolution of life and supports novel empirical approaches.

Effects of treadmill running velocity on lower extremity coordination variability in healthy runners

With a growing interest in coordination variability and its role in endurance running, it is important to identify the effect of running velocity. The purpose of the current study was to investigate the effect of treadmill running velocity on the coordination and variability of coordination of lower extremity couplings of healthy runners during stance. Fourteen apparently healthy runners ran on a split-belt force instrumented treadmill at five different velocities. Continuous relative phase (CRP) was used to quantify coordination and variability (vCRP) between lower extremity couplings of the right limb (thigh-shank, thigh-foot, shank-foot) during three phases of stance (loading, mid stance, and propulsion). Multiple one-way repeated measure ANOVAs were conducted to identify differences among velocity conditions at each phase and discrete events (initial foot contact, peak knee flexion during stance, and toe-off). Thigh internal/external rotation (IR/ER)-Shank abduction/adduction (AB/AD) coupling was different during the propulsive phase (p = 0.02). Thigh flexion/extension-Shank flexion/extension showed the greatest differences in vCRP across velocity conditions with differences occurring during loading phase, mid stance, propulsive phase, and peak flexion (p < 0.05). Additionally, significant differences were seen in Thigh FL/EX-Shank FL/EX (toe-off, p = 0.01) and Thigh FL/EX-Foot inversion/eversion (IN/EV) (toe-off, p = 0.032). Interestingly, the decreases in vCRP values were accompanied by changes in center of mass vertical motion during stance, but not knee flexion angles. Increases in running velocity led to a more constrained running pattern through a reduction in degrees of freedom.

Network Translation and Steady-State Properties of Chemical Reaction Systems

Network translation has recently been used to establish steady-state properties of mass action systems by corresponding the given system to a generalized one which is either dynamically or steady-state equivalent. In this work, we further use network translation to identify network structures which give rise to the well-studied property of absolute concentration robustness in the corresponding mass action systems. In addition to establishing the capacity for absolute concentration robustness, we show that network translation can often provide a method for deriving the steady-state value of the robust species. We furthermore present a MILP algorithm for the identification of translated chemical reaction networks that improves on previous approaches, allowing for easier application of the theory.

A self-organizing short-term dynamical memory network

Working memory requires information about external stimuli to be represented in the brain even after those stimuli go away. This information is encoded in the activities of neurons, and neural activities change over timescales of tens of milliseconds. Information in working memory, however, is retained for tens of seconds, suggesting the question of how time-varying neural activities maintain stable representations. Prior work shows that, if the neural dynamics are in the 'null space' of the representation - so that changes to neural activity do not affect the downstream read-out of stimulus information - then information can be retained for periods much longer than the time-scale of individual-neuronal activities. The prior work, however, requires precisely constructed synaptic connectivity matrices, without explaining how this would arise in a biological neural network. To identify mechanisms through which biological networks can self-organize to learn memory function, we derived biologically plausible synaptic plasticity rules that dynamically modify the connectivity matrix to enable information storing. Networks implementing this plasticity rule can successfully learn to form memory representations even if only 10% of the synapses are plastic, they are robust to synaptic noise, and they can represent information about multiple stimuli.

Principal process analysis of biological models

BACKGROUND

Understanding the dynamical behaviour of biological systems is challenged by their large number of components and interactions. While efforts have been made in this direction to reduce model complexity, they often prove insufficient to grasp which and when model processes play a crucial role. Answering these questions is fundamental to unravel the functioning of living organisms.

RESULTS

We design a method for dealing with model complexity, based on the analysis of dynamical models by means of Principal Process Analysis. We apply the method to a well-known model of circadian rhythms in mammals. The knowledge of the system trajectories allows us to decompose the system dynamics into processes that are active or inactive with respect to a certain threshold value. Process activities are graphically represented by Boolean and Dynamical Process Maps. We detect model processes that are always inactive, or inactive on some time interval. Eliminating these processes reduces the complex dynamics of the original model to the much simpler dynamics of the core processes, in a succession of sub-models that are easier to analyse. We quantify by means of global relative errors the extent to which the simplified models reproduce the main features of the original system dynamics and apply global sensitivity analysis to test the influence of model parameters on the errors.

CONCLUSION

The results obtained prove the robustness of the method. The analysis of the sub-model dynamics allows us to identify the source of circadian oscillations. We find that the negative feedback loop involving proteins PER, CRY, CLOCK-BMAL1 is the main oscillator, in agreement with previous modelling and experimental studies. In conclusion, Principal Process Analysis is a simple-to-use method, which constitutes an additional and useful tool for analysing the complex dynamical behaviour of biological systems.

Optimal Therapy Scheduling Based on a Pair of Collaterally Sensitive Drugs

Despite major strides in the treatment of cancer, the development of drug resistance remains a major hurdle. One strategy which has been proposed to address this is the sequential application of drug therapies where resistance to one drug induces sensitivity to another drug, a concept called collateral sensitivity. The optimal timing of drug switching in these situations, however, remains unknown. To study this, we developed a dynamical model of sequential therapy on heterogeneous tumors comprised of resistant and sensitive cells. A pair of drugs (DrugA, DrugB) are utilized and are periodically switched during therapy. Assuming resistant cells to one drug are collaterally sensitive to the opposing drug, we classified cancer cells into two groups, [Formula: see text] and [Formula: see text], each of which is a subpopulation of cells resistant to the indicated drug and concurrently sensitive to the other, and we subsequently explored the resulting population dynamics. Specifically, based on a system of ordinary differential equations for [Formula: see text] and [Formula: see text], we determined that the optimal treatment strategy consists of two stages: an initial stage in which a chosen effective drug is utilized until a specific time point, T, and a second stage in which drugs are switched repeatedly, during which each drug is used for a relative duration (i.e., [Formula: see text]-long for DrugA and [Formula: see text]-long for DrugB with [Formula: see text] and [Formula: see text]). We prove that the optimal duration of the initial stage, in which the first drug is administered, T, is shorter than the period in which it remains effective in decreasing the total population, contrary to current clinical intuition. We further analyzed the relationship between population makeup, [Formula: see text], and the effect of each drug. We determine a critical ratio, which we term [Formula: see text], at which the two drugs are equally effective. As the first stage of the optimal strategy is applied, [Formula: see text] changes monotonically to [Formula: see text] and then, during the second stage, remains at [Formula: see text] thereafter. Beyond our analytic results, we explored an individual-based stochastic model and presented the distribution of extinction times for the classes of solutions found. Taken together, our results suggest opportunities to improve therapy scheduling in clinical oncology.

The Ball-Box Theorem for a Class of Corank 1 Non-differentiable Tangent Subbundles

We show that an analogue of the ball-box theorem holds true for a class of corank 1, non-differentiable tangent subbundles that satisfy a geometric condition. We also we give examples of such bundles and give an application to dynamical systems.

The basic reproductive ratio as a link between acquisition and change in phonotactics

Language acquisition and change are thought to be causally connected. We demonstrate a method for quantifying the strength of this connection in terms of the 'basic reproductive ratio' of linguistic constituents. It represents a standardized measure of reproductive success, which can be derived both from diachronic and from acquisition data. By analyzing phonotactic English data, we show that the results of both types of derivation correlate, so that phonotactic acquisition indeed predicts phonotactic change, and vice versa. After drawing that general conclusion, we discuss the role of utterance frequency and show that the latter exhibits destabilizing effects only on late acquired items, which belong to phonotactic periphery. We conclude that - at least in the evolution of English phonotactics - acquisition serves conservation, while innovation is more likely to occur in adult speech and affects items that are less entrenched but comparably frequent.

A second-order dynamical system with Hessian-driven damping and penalty term associated to variational inequalities

We consider the minimization of a convex objective function subject to the set of minima of another convex function, under the assumption that both functions are twice continuously differentiable. We approach this optimization problem from a continuous perspective by means of a second-order dynamical system with Hessian-driven damping and a penalty term corresponding to the constrained function. By constructing appropriate energy functionals, we prove weak convergence of the trajectories generated by this differential equation to a minimizer of the optimization problem as well as convergence for the objective function values along the trajectories. The performed investigations rely on Lyapunov analysis in combination with the continuous version of the Opial Lemma. In case the objective function is strongly convex, we can even show strong convergence of the trajectories.

Adaptive Equilibrium Regulation: Modeling Individual Dynamics on Multiple Timescales

Damped Linear Oscillators estimated by 2nd-order Latent Differential Equation have assumed a constant equilibrium and one oscillatory component. Lower-frequency oscillations may come from seasonal background processes, which non-randomly contribute to deviation from equilibrium at each occasion and confound estimation of dynamics over shorter timescales. Boker (2015) proposed a model of individual change on multiple timescales, but implementation, simulation, and applications to data have not been demonstrated. This study implemented a generalization of the proposed model; examined robustness to varied timescale ratios, measurement error, and occasions-per-person in simulated data; and tested for dynamics at multiple timescales in experience sampling affect data. Results show small standard errors and low bias to dynamic estimates at timescale ratios greater than 3:1. Below 3:1, estimate error was sensitive to noise and total occasions; rates of non-convergence increased. For affect data, model comparisons showed statistically significant dynamics at both timescales for both participants.

Statistical inference in mechanistic models: time warping for improved gradient matching

Inference in mechanistic models of non-linear differential equations is a challenging problem in current computational statistics. Due to the high computational costs of numerically solving the differential equations in every step of an iterative parameter adaptation scheme, approximate methods based on gradient matching have become popular. However, these methods critically depend on the smoothing scheme for function interpolation. The present article adapts an idea from manifold learning and demonstrates that a time warping approach aiming to homogenize intrinsic length scales can lead to a significant improvement in parameter estimation accuracy. We demonstrate the effectiveness of this scheme on noisy data from two dynamical systems with periodic limit cycle, a biopathway, and an application from soft-tissue mechanics. Our study also provides a comparative evaluation on a wide range of signal-to-noise ratios.

a two-predator one-prey model of population dynamics influenced by herd behaviour of the prey

We construct a mathematical model considering the populations of multiple predators and one prey, with herd defense by the prey modelled by modifying the law of mass action with a single parameter. This modification introduces a novel bifurcation in the case where all the predators are specialists. When some predators may be generalists, the analysis is more complicated and we consider only the case of two predators of which one or two may be generalists. In this case, novel steady states occur via saddlenode bifurcation, and in some cases the coexistence steady state exhibits Hopf bifurcation to a stable limit cycle. We show that the phenomenon of finite time extinction of prey also occurs in this context. Finally, we extend the analysis from constant herding effect to a model where predator pressure increases the strength of herding.

Modeling the Epigenetic Landscape in Plant Development

Computational mechanistic models enable a systems-level understanding of plant development by integrating available molecular experimental data and simulating their collective dynamical behavior. Boolean gene regulatory network dynamical models have been extensively used as a qualitative modeling framework for such purpose. More recently, network modeling protocols have been extended to model the epigenetic landscape associated with gene regulatory networks. In addition to understanding the concerted action of interconnected genes, epigenetic landscape models aim to uncover the patterns of cell state transition events that emerge under diverse genetic and environmental background conditions. In this chapter we present simple protocols that naturally extend gene regulatory network modeling and demonstrate their use in modeling plant developmental processes under the epigenetic landscape framework. We focus on conceptual clarity and practical implementation, providing directions to the corresponding technical literature. The protocols presented here can be applied to any well-characterized gene regulatory network in plants, animals, or human disease.

Computational analysis reveals the coupling between bistability and the sign of a feedback loop in a TGF-β1 activation model

BACKGROUND

Bistable behaviors are prevalent in cell signaling and can be modeled by ordinary differential equations (ODEs) with kinetic parameters. A bistable switch has recently been found to regulate the activation of transforming growth factor-β1 (TGF-β1) in the context of liver fibrosis, and an ordinary differential equation (ODE) model was published showing that the net activation of TGF-β1 depends on the balance between two antagonistic sub-pathways.

RESULTS

Through modeling the effects of perturbations that affect both sub-pathways, we revealed that bistability is coupled with the signs of feedback loops in the model. We extended the model to include calcium and Krüppel-like factor 2 (KLF2), both regulators of Thrombospondin-1 (TSP1) and Plasmin (PLS). Increased levels of extracellular calcium, which alters the TSP1-PLS balance, would cause high levels of TGF-β1, resembling a fibrotic state. KLF2, which suppresses production of TSP1 and plasminogen activator inhibitor-1 (PAI1), would eradicate bistability and preclude the fibrotic steady-state. Finally, the loop PLS - TGF-β1 - PAI1 had previously been reported as negative feedback, but the model suggested a stronger indirect effect of PLS down-regulating PAI1 to produce positive (double-negative) feedback in a fibrotic state. Further simulations showed that activation of KLF2 was able to restore negative feedback in the PLS - TGF-β1 - PAI1 loop.

CONCLUSIONS

Using the TGF-β1 activation model as a case study, we showed that external factors such as calcium or KLF2 can induce or eradicate bistability, accompanied by a switch in the sign of a feedback loop (PLS - TGF-β1 - PAI1) in the model. The coupling between bistability and positive/negative feedback suggests an alternative way of characterizing a dynamical system and its biological implications.

The changes in classical and nonlinear parameters after a maximal bout to elicit fatigue in competitive swimming

The aim was to assess the effect of fatigue on linear and nonlinear parameters in swimming. Twenty-four fitness-oriented swimmers performed a maximal bout of 100 m at front-crawl to elicit fatigue. Before (pre-) and immediately after (post-test) the bout, participants swam an all-out 25 m to derive the speed fluctuation (dv), approximate entropy (ApEn) and fractal dimension (FD) from the speed-time series collected by a speedo-meter. Swim speed was 10.85% slower in the post-test than in the pre-test (p < .001, η² = 0.72). There was an effect of the fatigue on the dv with a moderate effect size. The dv increased shifting the 95CI band from 0.116-0.134 to 0.140-0.161. The ApEn showed non-significant variations between the pre- and post-test having the 95CI of pre- and post-test overlapped (pre: 0.659-0.700; post: 0.641-0.682). The FD showed as well a significant variation (the 95CI moved from 1.954-1.965 to 1.933-1.951). It can be concluded that in swimming there are changes in classical and nonlinear parameters under fatigue.

Time-dependent propagators for stochastic models of gene expression: an analytical method

The inherent stochasticity of gene expression in the context of regulatory networks profoundly influences the dynamics of the involved species. Mathematically speaking, the propagators which describe the evolution of such networks in time are typically defined as solutions of the corresponding chemical master equation (CME). However, it is not possible in general to obtain exact solutions to the CME in closed form, which is due largely to its high dimensionality. In the present article, we propose an analytical method for the efficient approximation of these propagators. We illustrate our method on the basis of two categories of stochastic models for gene expression that have been discussed in the literature. The requisite procedure consists of three steps: a probability-generating function is introduced which transforms the CME into (a system of) partial differential equations (PDEs); application of the method of characteristics then yields (a system of) ordinary differential equations (ODEs) which can be solved using dynamical systems techniques, giving closed-form expressions for the generating function; finally, propagator probabilities can be reconstructed numerically from these expressions via the Cauchy integral formula. The resulting ‘library’ of propagators lends itself naturally to implementation in a Bayesian parameter inference scheme, and can be generalised systematically to related categories of stochastic models beyond the ones considered here.

Interpersonal coordination analysis of tennis players from different levels during official matches

The purpose of this study was to assess the interpersonal coordination during official male tennis matches in players of different skill levels. Players' trajectories of three levels (Juvenile, ATP-Future, ATP-250) were obtained using video-based tracking system. A vector coding technique was applied to obtain players' interpersonal coordination in four coordination patterns: "anti-phase", "in-phase", "serving player phase" and "returning player phase". These patterns allowed identification of the nature of the coupling and lead/lag relations between players. In all categories, players presented higher degree of "anti-phase" and "serving player phase" (when only the serving player is moving on the court or his opponent is moving with a time lag) coordination. Young players spent more time in "serving player phase" during lateral displacements than professional players. On the other hand, professional players spent more time in "returning player phase" (when only the returning player is moving on the court or his opponent is moving with a time lag) during antero posterior displacements, than young players. Interpersonal coordination did not change from the first to the second set of the match, showing that tennis players maintain their displacement characteristics and strategy, independently of proficiency level. The vector coding technique allowed to identify new coordination patterns in tennis, providing additional information about tennis dynamics and how players from different categories and proficiency levels behave during the matches.