Virtual stimulation of the interictal EEG network localizes the EZ as a measure of cortical excitability.

Introduction: For patients with drug-resistant epilepsy, successful localization and surgical treatment of the epileptogenic zone (EZ) can bring seizure freedom. However, surgical success rates vary widely because there are currently no clinically validated biomarkers of the EZ. Highly epileptogenic regions often display increased levels of cortical excitability, which can be probed using single-pulse electrical stimulation (SPES), where brief pulses of electrical current are delivered to brain tissue. It has been shown that high-amplitude responses to SPES can localize EZ regions, indicating a decreased threshold of excitability. However, performing extensive SPES in the epilepsy monitoring unit (EMU) is time-consuming. Thus, we built patient-specific in silico dynamical network models from interictal intracranial EEG (iEEG) to test whether virtual stimulation could reveal information about the underlying network to identify highly excitable brain regions similar to physical stimulation of the brain. Methods: We performed virtual stimulation in 69 patients that were evaluated at five centers and assessed for clinical outcome 1 year post surgery. We further investigated differences in observed SPES iEEG responses of 14 patients stratified by surgical outcome. Results: Clinically-labeled EZ cortical regions exhibited higher excitability from virtual stimulation than non-EZ regions with most significant differences in successful patients and little difference in failure patients. These trends were also observed in responses to extensive SPES performed in the EMU. Finally, when excitability was used to predict whether a channel is in the EZ or not, the classifier achieved an accuracy of 91%. Discussion: This study demonstrates how excitability determined via virtual stimulation can capture valuable information about the EZ from interictal intracranial EEG.

Improving and Extending STERGM Approximations Based on Cross-Sectional Data and Tie Durations.

Temporal exponential-family random graph models (TERGMs) are a flexible class of models for network ties that change over time. Separable TERGMs (STERGMs) are a subclass of TERGMs in which the dynamics of tie formation and dissolution can be separated within each discrete time step and may depend on different factors. The Carnegie et al. (2015) approximation improves estimation efficiency for a subclass of STERGMs, allowing them to be reliably estimated from inexpensive cross-sectional study designs. This approximation adapts to cross-sectional data by attempting to construct a STERGM with two specific properties: a cross-sectional equilibrium distribution defined by an exponential-family random graph model (ERGM) for the network structure, and geometric tie duration distributions defined by constant hazards for tie dissolution. In this paper we focus on approaches for improving the behavior of the Carnegie et al. approximation and increasing its scope of application. We begin with Carnegie et al.'s observation that the exact result is tractable when the ERGM is dyad-independent, and then show that taking the sparse limit of the exact result leads to a different approximation than the one they presented. We show that the new approximation outperforms theirs for sparse, dyad-independent models, and observe that the errors tend to increase with the strength of dependence for dyad-dependent models. We then develop theoretical results in the dyad-dependent case, showing that when the ERGM is allowed to have arbitrary dyad-dependent terms and some dyad-dependent constraints, both the old and new approximations are asymptotically exact as the size of the STERGM time step goes to zero. We note that the continuous-time limit of the discrete-time approximations has the desired cross-sectional equilibrium distribution and exponential tie duration distributions with the desired means. We show that our results extend to hypergraphs, and we propose an extension of the Carnegie et al. framework to dissolution hazards that depend on tie age.

Development of a Dynamic Network Model to Identify Temporal Patterns of Structural Malformations in Zebrafish Embryos Exposed to a Model Toxicant, Tris(4-chlorophenyl)methanol.

Embryogenesis is a well-coordinated process relying on precise cues and environmental signals that direct spatiotemporal embryonic patterning. Quite often, when one error in this process occurs, others tend to co-occur. We posit that investigating the co-occurrence of these abnormalities over time would yield additional information about the mode of toxicity for chemicals. Here, we use the environmental contaminant tris(4-chlorophenyl)methanol (TCPMOH) as a model toxicant to assess the relationship between exposures and co-occurrence of developmental abnormalities in zebrafish embryos. We propose a dynamic network modeling approach to study the co-occurrence of abnormalities, including pericardial edema, yolk sac edema, cranial malformation, spinal deformity, delayed/failed swim bladder inflation, and mortality induced by TCPMOH exposure. TCPMOH-exposed samples revealed increased abnormality co-occurrence when compared to controls. The abnormalities were represented as nodes in the dynamic network model. Abnormalities with high co-occurrence over time were identified using network centrality scores. We found that the temporal patterns of abnormality co-occurrence varied between exposure groups. In particular, the high TCPMOH exposure group experienced abnormality co-occurrence earlier than the low exposure group. The network model also revealed that pericardial and yolk sac edema are the most common critical nodes among all TCPMOH exposure levels, preceding further abnormalities. Overall, this study introduces a dynamic network model as a tool for assessing developmental toxicology, integrating structural and temporal features with a concentration response.

PlantSimLab - a modeling and simulation web tool for plant biologists.

BACKGROUND: At the molecular level, nonlinear networks of heterogeneous molecules control many biological processes, so that systems biology provides a valuable approach in this field, building on the integration of experimental biology with mathematical modeling. One of the biggest challenges to making this integration a reality is that many life scientists do not possess the mathematical expertise needed to build and manipulate mathematical models well enough to use them as tools for hypothesis generation. Available modeling software packages often assume some modeling expertise. There is a need for software tools that are easy to use and intuitive for experimentalists. RESULTS: This paper introduces PlantSimLab, a web-based application developed to allow plant biologists to construct dynamic mathematical models of molecular networks, interrogate them in a manner similar to what is done in the laboratory, and use them as a tool for biological hypothesis generation. It is designed to be used by experimentalists, without direct assistance from mathematical modelers. CONCLUSIONS: Mathematical modeling techniques are a useful tool for analyzing complex biological systems, and there is a need for accessible, efficient analysis tools within the biological community. PlantSimLab enables users to build, validate, and use intuitive qualitative dynamic computer models, with a graphical user interface that does not require mathematical modeling expertise. It makes analysis of complex models accessible to a larger community, as it is platform-independent and does not require extensive mathematical expertise.

Parameter Estimation for Gene Regulatory Networks from Microarray Data: Cold Shock Response in Saccharomyces cerevisiae.

We investigated the dynamics of a gene regulatory network controlling the cold shock response in budding yeast, Saccharomyces cerevisiae. The medium-scale network, derived from published genome-wide location data, consists of 21 transcription factors that regulate one another through 31 directed edges. The expression levels of the individual transcription factors were modeled using mass balance ordinary differential equations with a sigmoidal production function. Each equation includes a production rate, a degradation rate, weights that denote the magnitude and type of influence of the connected transcription factors (activation or repression), and a threshold of expression. The inverse problem of determining model parameters from observed data is our primary interest. We fit the differential equation model to published microarray data using a penalized nonlinear least squares approach. Model predictions fit the experimental data well, within the 95% confidence interval. Tests of the model using randomized initial guesses and model-generated data also lend confidence to the fit. The results have revealed activation and repression relationships between the transcription factors. Sensitivity analysis indicates that the model is most sensitive to changes in the production rate parameters, weights, and thresholds of Yap1, Rox1, and Yap6, which form a densely connected core in the network. The modeling results newly suggest that Rap1, Fhl1, Msn4, Rph1, and Hsf1 play an important role in regulating the early response to cold shock in yeast. Our results demonstrate that estimation for a large number of parameters can be successfully performed for nonlinear dynamic gene regulatory networks using sparse, noisy microarray data.

Infectious disease transmission and contact networks in wildlife and livestock.

The use of social and contact networks to answer basic and applied questions about infectious disease transmission in wildlife and livestock is receiving increased attention. Through social network analysis, we understand that wild animal and livestock populations, including farmed fish and poultry, often have a heterogeneous contact structure owing to social structure or trade networks. Network modelling is a flexible tool used to capture the heterogeneous contacts of a population in order to test hypotheses about the mechanisms of disease transmission, simulate and predict disease spread, and test disease control strategies. This review highlights how to use animal contact data, including social networks, for network modelling, and emphasizes that researchers should have a pathogen of interest in mind before collecting or using contact data. This paper describes the rising popularity of network approaches for understanding transmission dynamics in wild animal and livestock populations; discusses the common mismatch between contact networks as measured in animal behaviour and relevant parasites to match those networks; and highlights knowledge gaps in how to collect and analyse contact data. Opportunities for the future include increased attention to experiments, pathogen genetic markers and novel computational tools.

Understanding quantitative genetics in the systems biology era.

Biology is now entering the new era of systems biology and exerting a growing influence on the future development of various disciplines within life sciences. In early classical and molecular periods of Biology, the theoretical frames of classical and molecular quantitative genetics have been systematically established, respectively. With the new advent of systems biology, there is occurring a paradigm shift in the field of quantitative genetics. Where and how the quantitative genetics would develop after having undergone its classical and molecular periods? This is a difficult question to answer exactly. In this perspective article, the major effort was made to discuss the possible development of quantitative genetics in the systems biology era, and for which there is a high potentiality to develop towards "systems quantitative genetics". In our opinion, the systems quantitative genetics can be defined as a new discipline to address the generalized genetic laws of bioalleles controlling the heritable phenotypes of complex traits following a new dynamic network model. Other issues from quantitative genetic perspective relating to the genetical genomics, the updates of network model, and the future research prospects were also discussed.