Naomi Kochi

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.

Boolean modeling of biochemical networks

The use of modeling to observe and analyze the mechanisms of complex biochemical network function is be- coming an important methodological tool in the systems biology era. Number of different approaches to model these net- works have been utilized-- they range from analysis of static connection graphs to dynamical models based on kinetic in- teraction data. Dynamical models have a distinct appeal in that they make it possible to observe these networks in action, but they also pose a distinct challenge in that they require detailed information describing how the individual components of these networks interact in living cells. Because this level of detail is generally not known, dynamic modeling requires simplifying assumptions in order to make it practical. In this review Boolean modeling will be discussed, a modeling method that depends on the simplifying assumption that all elements of a network exist only in one of two states.

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.

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.

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.

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

BackgroundAn 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.ResultsWe 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.ConclusionsThe 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.

An algebraic method and a genetic algorithm to the identification of fuzzy measures based on Choquet integrals

There are different nonlinear integrals that could be used as an aggregation tool in information fusion and data mining. The Choquet integral with respect to fuzzy measures is one of them. We present some methods to identify fuzzy measures based on the Choquet integral in this paper. An iterative method introduced by Grabisch is discussed with some counterexamples. Furthermore, after removing some restrictions which are used in Grabischs model, we introduce an algebraic method and a genetic algorithm to identify fuzzy measures and present some experimental results on both artificial and real-world data sets to show their effectiveness.

Decision Making in Cells

Cellular signal transduction networks are structured in a highly complex manner that strongly suggests they have functions beyond simply passing information from the outside of the cell to the interior. Recent evidence from mathematical and systems approaches to the study of these networks indicates that these complex networks might actually process external signals in a nontrivial way, endowing the cell emergent-decision making ability. In this chapter, we will first analyze the concepts of information, information processing, and decision making from a quantitative perspective. We will then apply that analysis to the structures and functions of intracellular signal transduction networks and see that they have many features that are consistent with nontrivial decision-making systems.

Solving nonlinear programming problems based on the Choquet integral by a genetic algorithm

Nonadditive set functions represent contribution rate of individual feature attributes and combinations of feature attributes toward the target. Their nonadditivity describes the interaction among contributions. The generalized weighted Choquet integral with respect to a nonadditive set function serves as an aggregation tool, which may be used in the nonlinear objective function of optimization problems, to project n-dimensional feature space onto a real axis with a corresponding projection value. In this paper, we propose a special genetic algorithm model to identify the values of feature attributes that maximize the value of the objective function involving a generalized weighted Choquet integral. Thus, we may find the values of the feature attributes giving the greatest contribution toward the target. This is a generalization of linear programming to nonlinear cases.

THE MINIMUM NUMBER OF DATA POINTS REQUIRED TO COMPUTE APPROXIMATE ENTROPY FOR GAIT DATA

Approximate Entropy (ApEn) is a widely used nonlinear tool to analyze biological data. ApEn quantifies the predictability or regularity of the fluctuations present in a time series, with smaller values indicating greater regularity, and larger values indicate more randomness or irregularity [Pincus, 1991; Pincus et al., 1991]. ApEn is robust with relatively short and noisy data unlike many other nonlinear tools, and the range of data point requirement is rather wide. It can be from 10 to 30, where parameter m is usually set to 2. In addition, since data length N is another parameter for ApEn, ApEn must be calculated for data sets with the same N to ensure appropriate comparisons.