Using chemical reaction network theory to discard a kinetic mechanism hypothesis

Feinberg's chemical reaction network theory (CRNT) connects the structure of a biochemical reaction network to qualitative properties of the corresponding system of ordinary differential equations. No information about parameter values is needed. As such, it seems to be well suited for application in systems biology, where parameter uncertainty is predominant. However, its application in this area is rare. To demonstrate the potential benefits from its application, different reaction networks representing a single layer of the well-studied mitogen-activated protein kinase (MAPK) cascade are analysed. Recent results from Markevich et al. (2004) show that, unexpectedly, multilayered protein kinase cascades can exhibit multistationarity, even on a single cascade level. Using CRNT, we show that their assumption of a distributive mechanism for double phosphorylation and dephosphorylation is crucial for multistationarity on the single cascade level.     

A theory for ecological survey methods to map individual distributions

Spatially explicit approaches are widely recommended for ecosystem management. The quality of the data, such as presence/absence or habitat maps, affects the management actions recommended and is, therefore, key to management success. However, available data are often biased and incomplete. Previous studies have advanced ways to resolve data bias and missing data, but questions remain about how we design ecological surveys to develop a dataset through field surveys. Ecological surveys may have multiple spatial scales, including the spatial extent of the target ecosystem (observation window), the resolution for mapping individual distributions (mapping unit), and the survey area within each mapping unit (sampling unit). We developed an ecological survey method for mapping individual distributions by applying spatially explicit stochastic models. We used spatial point processes to describe individual spatial placements using either random or clustering processes. We then designed ecological surveys with different spatial scales and individual detectability. We found that the choice of mapping unit affected the presence mapped fraction, and the fraction of the total individuals covered by the presence mapped patches. Tradeoffs were found between these quantities and the map resolution, associated with equivalent asymptotic behaviors for both metrics at sufficiently small and large mapping unit scales. Our approach enabled consideration of the effect of multiple spatial scales in surveys, and estimation of the survey outcomes such as the presence mapped fraction and the number of individuals situated in the presence detected units. The developed theory may facilitate management decision-making and inform the design of monitoring and data gathering.     

Using information theory to search for co-evolving residues in proteins

MOTIVATION: Some functionally important protein residues are easily detected since they correspond to conserved columns in a multiple sequence alignment (MSA). However important residues may also mutate, with compensatory mutations occurring elsewhere in the protein, which serve to preserve or restore functionality. It is difficult to distinguish these co-evolving sites from other non-conserved sites. RESULTS: We used Mutual Information (MI) to identify co-evolving positions. Using in silico evolved MSAs, we examined the effects of the number of sequences, the size of amino acid alphabet and the mutation rate on two sources of background MI: finite sample size effects and phylogenetic influence. We then assessed the performance of various normalizations of MI in enhancing detection of co-evolving positions and found that normalization by the pair entropy was optimal. Real protein alignments were analyzed and co-evolving isolated pairs were often found to be in contact with each other. AVAILABILITY: All data and program files can be found at http://www.biochem.uwo.ca/cgi-bin/CDD/index.cgi     

Application of network theory to potential mycorrhizal networks

The concept of a common mycorrhizal network implies that the arrangement of plants and mycorrhizal fungi in a community shares properties with other networks. A network is a system of nodes connected by links. Here we apply network theory to mycorrhizas to determine whether the architecture of a potential common mycorrhizal network is random or scale-free. We analyzed mycorrhizal data from an oak woodland from two perspectives: the phytocentric view using trees as nodes and fungi as links and the mycocentric view using fungi as nodes and trees as links. From the phytocentric perspective, the distribution of potential mycorrhizal links, as measured by the number of ectomycorrhizal morphotypes on trees of Quercus garryana, was random with a short tail, implying that all the individuals of this species are more or less equal in linking to fungi in a potential network. From the mycocentric perspective, however, the distribution of plant links to fungi was scale-free, suggesting that certain fungus species may act as hubs with frequent connections to the network. Parallels exist between social networks and mycorrhizas that suggest future lines of study on mycorrhizal networks.     

Stoichiometric network theory for nonequilibrium biochemical systems.

We introduce the basic concepts and develop a theory for nonequilibrium steady-state biochemical systems applicable to analyzing large-scale complex isothermal reaction networks. In terms of the stoichiometric matrix, we demonstrate both Kirchhoff's flux law sigma(l)J(l)=0 over a biochemical species, and potential law sigma(l) mu(l)=0 over a reaction loop. They reflect mass and energy conservation, respectively. For each reaction, its steady-state flux J can be decomposed into forward and backward one-way fluxes J = J+ - J-, with chemical potential difference deltamu = RT ln(J-/J+). The product -Jdeltamu gives the isothermal heat dissipation rate, which is necessarily non-negative according to the second law of thermodynamics. The stoichiometric network theory (SNT) embodies all of the relevant fundamental physics. Knowing J and deltamu of a biochemical reaction, a conductance can be computed which directly reflects the level of gene expression for the particular enzyme. For sufficiently small flux a linear relationship between J and deltamu can be established as the linear flux-force relation in irreversible thermodynamics, analogous to Ohm's law in electrical circuits.     

Using food network unfolding to evaluate food–web complexity in terms of biodiversity: theory and applications

Food–web complexity often hinders disentangling functionally relevant aspects of food–web structure and its relationships to biodiversity. Here, we present a theoretical framework to evaluate food–web complexity in terms of biodiversity. Food network unfolding is a theoretical method to transform a complex food web into a linear food chain based on ecosystem processes. Based on this method, we can define three biodiversity indices, horizontal diversity (D_H), vertical diversity (D_V) and range diversity (D_R), which are associated with the species diversity within each trophic level, diversity of trophic levels, and diversity in resource use, respectively. These indices are related to Shannon's diversity index (H′), where H′ = D_H + D_V ? D_R. Application of the framework to three riverine macroinvertebrate communities revealed that D indices, calculated from biomass and stable isotope features, captured well the anthropogenic, seasonal, or other within‐site changes in food–web structures that could not be captured with H′ alone.     

Using successional theory to measure marine ecosystem health

Marine ecosystems are diverse and complex, providing significant challenges to the development of generalizable metrics of ecosystem health. Of particular concern is the varied form of change caused by multiple human activities, which limits the capacity to generate a single measure to encapsulate the overall condition of the ecosystem. Here we consider how successional theory can help to simplify our understanding of marine community structure, especially when viewed in context of human disturbance. During succession, the emergent properties of communities change in predictable ways. As communities mature, there is an increase in total production and biomass, the mean size of organisms, the level of internal recycling of food and nutrients, and the mean trophic level. Using a set of multi-species trophic models, we explore the changes in community structure that are likely to occur during succession. These changes include increases in biomass within trophic levels due to decreased rates of energy and food loss through trophic and production inefficiencies, and potential shifts from top-down control early in succession to bottom-up later. Because human activities disproportionately favor early-successional species, we can gain insights by considering community degradation in the context of succession being played in reverse. Indicators of health based on ecological succession thus provide a mechanistic view to measure the impact of human activities (both positive and negative) on marine ecosystems.     

Using network models to approximate spatial point-process models

Spatial effects are fundamental to ecological and epidemiological systems, yet the incorporation of space into models is potentially complex. Fixed-edge network models (i.e. networks where each edge has the same fixed strength of interaction) are widely used to study spatial processes but they make simplistic assumptions about spatial scale and structure. Furthermore, it can be difficult to parameterize such models with empirical data. By comparison, spatial point-process models are often more realistic than fixed-edge network models, but are also more difficult to analyze. Here we develop a moment closure technique that allows us to define a fixed-edge network model which predicts the prevalence and rate of epidemic spread of a continuous spatial point-process epidemic model. This approach provides a systematic method for accurate parameterization of network models using data from continuously distributed populations (such as data on dispersal kernels). Insofar as point-process models are accurate representations of real spatial biological systems, our example also supports the view that network models are realistic representations of space.     

Using a network framework to quantitatively select ecological indicators

Ecological indicators are often constructed as an integrated set to represent key information and characteristics of the ecosystem which are tightly linked to management objectives. As an effective tool, ecological indicators play an increasingly important role in ecosystem monitoring, assessment and management. Reasonable selection of an indicator is a prerequisite for effectively using it. A defined protocol with scientific rigor to select ecological indicators is imperative to solve the challenges in ecological indicator selection. This paper compares the Causal Network (CN) with the Ecological Hierarchy Network (EHN) as a framework to select ecological indicators. These frameworks are not exclusive but interdependent in constructing a network framework. Based on the network framework, a quantitative ecological indicator selection method is demonstrated through a theoretical example. In the selection process, the criteria and requirements considering the balance of science and utility are proposed and translated into quantitative constraints of a selection model. By resolving the model under a mathematical operation, the human arbitrary disturbance will be reduced and random selection minimized.     

基于聚类系数的DNA序列性质的复杂网络研究

利用一种新的基于图论理论的DNA序列(片段)分析的方法,即通过复杂网络研究生物体的拓扑结构,主要通过测量聚类系数(集团系数)构建网络的拓扑结构。依据DNA序列的前缀、后缀关联性质构造了所选取DNA序列(片段)的相关网络,发现该网络分布满足幂率特征,有较大的聚类系数。结果表明构建得到的网络同时满足小世界网络和无尺度网络的特征,证明DNA序列不全是随机的序列,而是有随机扰动的确定结构的序列。     

A network theory of mental disorders

In recent years, the network approach to psychopathology has been advanced as an alternative way of conceptualizing mental disorders. In this approach, mental disorders arise from direct interactions between symptoms. Although the network approach has led to many novel methodologies and substantive applications, it has not yet been fully articulated as a scientific theory of mental disorders. The present paper aims to develop such a theory, by postulating a limited set of theoretical principles regarding the structure and dynamics of symptom networks. At the heart of the theory lies the notion that symptoms of psychopathology are causally connected through myriads of biological, psychological and societal mechanisms. If these causal relations are sufficiently strong, symptoms can generate a level of feedback that renders them self‐sustaining. In this case, the network can get stuck in a disorder state. The network theory holds that this is a general feature of mental disorders, which can therefore be understood as alternative stable states of strongly connected symptom networks. This idea naturally leads to a comprehensive model of psychopathology, encompassing a common explanatory model for mental disorders, as well as novel definitions of associated concepts such as mental health, resilience, vulnerability and liability. In addition, the network theory has direct implications for how to understand diagnosis and treatment, and suggests a clear agenda for future research in psychiatry and associated disciplines.     

Using network dynamic fMRI for detection of epileptogenic foci

Background

Epilepsy is one of the most prevalent neurological disorders. It remains medically intractable for about one-third of patients with focal epilepsy, for whom precise localization of the epileptogenic zone responsible for seizure initiation may be critical for successful surgery. Existing fMRI literature points to widespread network disturbances in functional connectivity. Per previous scalp and intracranial EEG studies and consistent with excessive local synchronization during interictal discharges, we hypothesized that, relative to same regions in healthy controls, epileptogenic foci would exhibit less chaotic dynamics, identifiable via entropic analyses of resting state fMRI time series.

Methods

In order to first validate this hypothesis on a cohort of patients with known ground truth, here we test individuals with well-defined epileptogenic foci (left mesial temporal lobe epilepsy). We analyzed voxel-wise resting-state fMRI time-series using the autocorrelation function (ACF), an entropic measure of regulation and feedback, and performed follow-up seed-to-voxel functional connectivity analysis. Disruptions in connectivity of the region exhibiting abnormal dynamics were examined in relation to duration of epilepsy and patients’ cognitive performance using a delayed verbal memory recall task.

Results

ACF analysis revealed constrained (less chaotic) functional dynamics in left temporal lobe epilepsy patients, primarily localized to ipsilateral temporal pole, proximal to presumed focal points. Autocorrelation decay rates differentiated, with 100 % accuracy, between patients and healthy controls on a subject-by-subject basis within a leave-one-subject out classification framework. Regions identified via ACF analysis formed a less efficient network in patients, as compared to controls. Constrained dynamics were linked with locally increased and long-range decreased connectivity that, in turn, correlated significantly with impaired memory (local left temporal connectivity) and epilepsy duration (left temporal – posterior cingulate cortex connectivity).

Conclusions

Our current results suggest that data driven functional MRI methods that target network dynamics hold promise in providing clinically valuable tools for identification of epileptic regions.