Nonlinear detrended fluctuation analysis of sitting center-of-pressure data as an early measure of motor development pathology in infants.

Upright sitting is one of the first motor skills an infant learns, and thus sitting postural control provides an early window into the infant's motor development. Early identification of infants with motor developmental delay, such as infants with cerebral palsy, allows for early therapeutic intervention by physical therapists. Early intervention is thought to produce better outcomes, due to greater neural plasticity in younger infants. Postural sway, as measured by a force plate, can be used to objectively and quantitatively characterize infant motor control during sitting. Pathology, such as cerebral palsy, may alter the fractal properties of motor function. Often physiologic time series data, including infant sitting postural sway data, is mathematically non-stationary. Detrended Fluctuation Analysis (DFA) is useful to characterize the fractal nature of time series data because it is does not assume stationarity of the data. In this study we found that suitable selection of the order of the detrending function improves the performance of the DFA algorithm, with a higher order polynomial detrending better able to distinguish infant sitting posture time series data from Brown noise (random walk), and first order detrending better able to distinguish infants with motor delay (cerebral palsy) from infants with typical development.

Sensitivity analysis of biological Boolean networks using information fusion based on nonadditive set functions.

BACKGROUND: An algebraic method for information fusion based on nonadditive set functions is used to assess the joint contribution of Boolean network attributes to the sensitivity of the network to individual node mutations. The node attributes or characteristics under consideration are: in-degree, out-degree, minimum and average path lengths, bias, average sensitivity of Boolean functions, and canalizing degrees. The impact of node mutations is assessed using as target measure the average Hamming distance between a non-mutated/wild-type network and a mutated network. RESULTS: We find that for a biochemical signal transduction network consisting of several main signaling pathways whose nodes represent signaling molecules (mainly proteins), the algebraic method provides a robust classification of attribute contributions. This method indicates that for the biochemical network, the most significant impact is generated mainly by the combined effects of two attributes: out-degree, and average sensitivity of nodes. CONCLUSIONS: The results support the idea that both topological and dynamical properties of the nodes need to be under consideration. The algebraic method is robust against the choice of initial conditions and partition of data sets in training and testing sets for estimation of the nonadditive set functions of the information fusion procedure.

A comprehensive, multi-scale dynamical model of ErbB receptor signal transduction in human mammary epithelial cells.

The non-receptor tyrosine kinase Src and receptor tyrosine kinase epidermal growth factor receptor (EGFR/ErbB1) have been established as collaborators in cellular signaling and their combined dysregulation plays key roles in human cancers, including breast cancer. In part due to the complexity of the biochemical network associated with the regulation of these proteins as well as their cellular functions, the role of Src in EGFR regulation remains unclear. Herein we present a new comprehensive, multi-scale dynamical model of ErbB receptor signal transduction in human mammary epithelial cells. This model, constructed manually from published biochemical literature, consists of 245 nodes representing proteins and their post-translational modifications sites, and over 1,000 biochemical interactions. Using computer simulations of the model, we find it is able to reproduce a number of cellular phenomena. Furthermore, the model predicts that overexpression of Src results in increased endocytosis of EGFR in the absence/low amount of the epidermal growth factor (EGF). Our subsequent laboratory experiments also suggest increased internalization of EGFR upon Src overexpression under EGF-deprived conditions, further supporting this model-generated hypothesis.

Mean-field Boolean network model of a signal transduction network.

In this paper we provide a mean-field Boolean network model for a signal transduction network of a generic fibroblast cell. The network consists of several main signaling pathways, including the receptor tyrosine kinase, the G-protein coupled receptor, and the Integrin signaling pathway. The network consists of 130 nodes, each representing a signaling molecule (mainly proteins). Nodes are governed by Boolean dynamics including canalizing functions as well as totalistic Boolean functions that depend only on the overall fraction of active nodes. We categorize the Boolean functions into several different classes. Using a mean-field approach we generate a mathematical formula for the probability of a node becoming active at any time step. The model is shown to be a good match for the actual network. This is done by iterating both the actual network and the model and comparing the results numerically. Using the Boolean model it is shown that the system is stable under a variety of parameter combinations. It is also shown that this model is suitable for assessing the dynamics of the network under protein mutations. Analytical results support the numerical observations that in the long-run at most half of the nodes of the network are active.

Bio-logic builder: a non-technical tool for building dynamical, qualitative models.

Computational modeling of biological processes is a promising tool in biomedical research. While a large part of its potential lies in the ability to integrate it with laboratory research, modeling currently generally requires a high degree of training in mathematics and/or computer science. To help address this issue, we have developed a web-based tool, Bio-Logic Builder, that enables laboratory scientists to define mathematical representations (based on a discrete formalism) of biological regulatory mechanisms in a modular and non-technical fashion. As part of the user interface, generalized "bio-logic" modules have been defined to provide users with the building blocks for many biological processes. To build/modify computational models, experimentalists provide purely qualitative information about a particular regulatory mechanisms as is generally found in the laboratory. The Bio-Logic Builder subsequently converts the provided information into a mathematical representation described with Boolean expressions/rules. We used this tool to build a number of dynamical models, including a 130-protein large-scale model of signal transduction with over 800 interactions, influenza A replication cycle with 127 species and 200+ interactions, and mammalian and budding yeast cell cycles. We also show that any and all qualitative regulatory mechanisms can be built using this tool.

Nonlinear analysis of ambulatory activity patterns in community-dwelling older adults.

BACKGROUND: The natural ambulatory activity patterns of older adults are not well understood. User-worn monitors illuminate patterns of ambulatory activity and generate data suitable for analysis using measures derived from nonlinear dynamics. METHODS: Ambulatory activity data were collected continuously from 157 community-dwelling older adults for 2 weeks. Participants were separated post hoc into groups based on the mean number of steps per day: highly active (steps > or = 10,000), moderately active (5,000 < or = steps < 10,000 steps), and inactive (steps <5,000 steps). Detrended fluctuation analysis (DFA), entropy rate (ER), and approximate entropy (ApEn) were used to examine the complexity of daily time series composed of 1-minute step count values. Coefficient of variation was used to examine time series variability. Between-group differences for each parameter were evaluated using analysis of variance. RESULTS: All groups displayed patterns of fluctuating step count values containing complex temporal structure. DFA, ER, and ApEn parameter values increased monotonically and significantly with increasing activity level (p < .001). The variability of step count fluctuations did not differ among groups. CONCLUSIONS: Highly active participants had more complex patterns of ambulatory activity than less active participants. The results supported the idea that, in addition to the volume of activity produced by an individual, patterns of ambulatory activity contain unique information that shows promise for offering insights into walking behavior associated with healthy aging.