Models Of Biomolecular Networks Research Articles

Aggregates of Monotonic Step Response Systems: A Structural Classification

Complex dynamical networks can often be analyzed as the interconnection of subsystems: This allows us to considerably simplify the model and better understand the global behavior. Some biological networks can be conveniently analyzed as aggregates of monotone subsystems. Yet, monotonicity is a strong requirement; it relies on the knowledge of the state representation and imposes a severe restriction on the Jacobian (which must be a Metzler matrix). Systems with a monotonic step response (MSR), which include input–output monotone systems as a special case, are a broader class and still have interesting features. The property of having a monotonically increasing step response (or, equivalently, in the linear case, a positive impulse response) can be evinced from experimental data, without an explicit model of the system. We consider networks that can be decomposed as aggregates of MSR subsystems and we provide a structural (parameter-free) classification of oscillatory and multistationary behaviors. The classification is based on the exclusive or concurrent presence of negative and positive cycles in the system aggregate graph , whose nodes are the MSR subsystems. The result is analogous to our earlier classification for aggregates of monotone subsystems. Models of biomolecular networks are discussed to demonstrate the applicability of our classification, which helps build synthetic biomolecular circuits that, by design, are well suited to exhibit the desired dynamics.

Target Control in Logical Models Using the Domain of Influence of Nodes.

Dynamical models of biomolecular networks are successfully used to understand the mechanisms underlying complex diseases and to design therapeutic strategies. Network control and its special case of target control, is a promising avenue toward developing disease therapies. In target control it is assumed that a small subset of nodes is most relevant to the system's state and the goal is to drive the target nodes into their desired states. An example of target control would be driving a cell to commit to apoptosis (programmed cell death). From the experimental perspective, gene knockout, pharmacological inhibition of proteins, and providing sustained external signals are among practical intervention techniques. We identify methodologies to use the stabilizing effect of sustained interventions for target control in Boolean network models of biomolecular networks. Specifically, we define the domain of influence (DOI) of a node (in a certain state) to be the nodes (and their corresponding states) that will be ultimately stabilized by the sustained state of this node regardless of the initial state of the system. We also define the related concept of the logical domain of influence (LDOI) of a node, and develop an algorithm for its identification using an auxiliary network that incorporates the regulatory logic. This way a solution to the target control problem is a set of nodes whose DOI can cover the desired target node states. We perform greedy randomized adaptive search in node state space to find such solutions. We apply our strategy to in silico biological network models of real systems to demonstrate its effectiveness.

The Design Space of the Embryonic Cell Cycle Oscillator

One of the main tasks in the analysis of models of biomolecular networks is to characterize the domain of the parameter space that corresponds to a specific behavior. Given the large number of parameters in most models, this is no trivial task. We use a model of the embryonic cell cycle to illustrate the approaches that can be used to characterize the domain of parameter space corresponding to limit cycle oscillations, a regime that coordinates periodic entry into and exit from mitosis. Our approach relies on geometric construction of bifurcation sets, numerical continuation, and random sampling of parameters. We delineate the multidimensional oscillatory domain and use it to quantify the robustness of periodic trajectories. Although some of our techniques explore the specific features of the chosen system, the general approach can be extended to other models of the cell cycle engine and other biomolecular networks.

The research on molecular network models of complex disease

Complex diseases such as cardiovascular disease, cancer and diabetes are major killers of human health. Unlike single gene defect diseases, complex diseases are usually believed to be associated with the interactions among genes and the interactions among genes and environmental factors. The underlying complex pathogeneses make both the early diagnosis and treatment difficult. Therefore the research of complex diseases is one of the major challenges of biomedical research in this century. Recently, the rapid accumulation of biological knowledge and multi-level high-throughput omics data, revolutionarily changed the research paradigm on complex disease. Instead of only focusing on single molecular, researchers are gradually extending their research to systematically analyzing genome-wide biomolecular interactions, i.e., biomolecular networks. In this context, bio-molecular network, which is a powerful tool to study complex diseases, enables systematically integration of high throughput biological data and plenty of biological knowledge. Recently, a large number of biological networks have been constructed, including protein interaction network, transcriptional regulation network, signal transduction network, metabolic network and so on. These studies have played a significant role in revealing the pathogeneses of complex diseases and promoting treatment or prevention of diseases. However, the biomolecular network research on complex diseases is still in its infancy. Due to the complexity of mechanisms and disease-related biological data, many challenges remain to be further explored and resolved. In this thesis, we use mathematical models of biomolecular networks to address some main challenges in the research of complex diseases. Specifically, we study molecular networks step by step from static, node dynamic, edge dynamic, to module dynamic of network construction and network analysis, and build several mathematical models to deepen the complex disease study by biomolecular networks concept.

Modeling approaches for qualitative and semi-quantitative analysis of cellular signaling networks.

A central goal of systems biology is the construction of predictive models of bio-molecular networks. Cellular networks of moderate size have been modeled successfully in a quantitative way based on differential equations. However, in large-scale networks, knowledge of mechanistic details and kinetic parameters is often too limited to allow for the set-up of predictive quantitative models.Here, we review methodologies for qualitative and semi-quantitative modeling of cellular signal transduction networks. In particular, we focus on three different but related formalisms facilitating modeling of signaling processes with different levels of detail: interaction graphs, logical/Boolean networks, and logic-based ordinary differential equations (ODEs). Albeit the simplest models possible, interaction graphs allow the identification of important network properties such as signaling paths, feedback loops, or global interdependencies. Logical or Boolean models can be derived from interaction graphs by constraining the logical combination of edges. Logical models can be used to study the basic input–output behavior of the system under investigation and to analyze its qualitative dynamic properties by discrete simulations. They also provide a suitable framework to identify proper intervention strategies enforcing or repressing certain behaviors. Finally, as a third formalism, Boolean networks can be transformed into logic-based ODEs enabling studies on essential quantitative and dynamic features of a signaling network, where time and states are continuous.We describe and illustrate key methods and applications of the different modeling formalisms and discuss their relationships. In particular, as one important aspect for model reuse, we will show how these three modeling approaches can be combined to a modeling pipeline (or model hierarchy) allowing one to start with the simplest representation of a signaling network (interaction graph), which can later be refined to logical and eventually to logic-based ODE models. Importantly, systems and network properties determined in the rougher representation are conserved during these transformations.

Design of biomolecular network modifications to achieve adaptation

A biomolecular network is called adaptive if its output returns to the original value after a transient response even under a persisting stimulus. The conditions for adaptation have been investigated thoroughly with systems theory approaches in the literature and it is easy to check whether they are satisfied in the linear approximation. In contrast, it is in general not easy to modify a non-adaptive network model such that it gains adaptive behaviour, especially for medium- and large-scale networks. The authors present a systematic approach based on the notion of kinetic perturbations to construct adaptive biomolecular network models from non-adaptive ones. An advantage of kinetic perturbations in this application is that neither the stoichiometry nor the steady state of the system is changed. Furthermore, the method covers both parameter and network structure modifications and can be applied to any reaction rate formalism and even to medium-scale or partially unknown models. The approach is exemplified at a small- and a medium-sized biomolecular network, illustrating its potential to systematically evaluate the different network modifications for adaptation. The proposed method will be useful either in iterative model building to construct mathematical models of adaptive biomolecular networks, or in synthetic biology where it can be applied to design or modify synthetic networks for adaptation.

Model reduction of multi-scale chemical Langevin equations

This paper addresses the model reduction problem for a class of stiff chemical Langevin equations that arise as models of biomolecular networks with fast and slow reactions and can be described as continuous Markov processes. Initially, a coordinate transformation is sought that allows the decoupling of fast and slow variables in the model equations. Necessary and sufficient conditions are derived for such a linear transformation to exist, along with an explicit change of variables which achieves the desired decoupling. For the systems for which this step is applicable, the method of adiabatic elimination is applied to determine a representation of the slow dynamics. Theoretical concepts and results are illustrated with simple examples.

Accelerated search for biomolecular network models to interpret high-throughput experimental data.

BackgroundThe functions of human cells are carried out by biomolecular networks, which include proteins, genes, and regulatory sites within DNA that encode and control protein expression. Models of biomolecular network structure and dynamics can be inferred from high-throughput measurements of gene and protein expression. We build on our previously developed fuzzy logic method for bridging quantitative and qualitative biological data to address the challenges of noisy, low resolution high-throughput measurements, i.e., from gene expression microarrays. We employ an evolutionary search algorithm to accelerate the search for hypothetical fuzzy biomolecular network models consistent with a biological data set. We also develop a method to estimate the probability of a potential network model fitting a set of data by chance. The resulting metric provides an estimate of both model quality and dataset quality, identifying data that are too noisy to identify meaningful correlations between the measured variables.ResultsOptimal parameters for the evolutionary search were identified based on artificial data, and the algorithm showed scalable and consistent performance for as many as 150 variables. The method was tested on previously published human cell cycle gene expression microarray data sets. The evolutionary search method was found to converge to the results of exhaustive search. The randomized evolutionary search was able to converge on a set of similar best-fitting network models on different training data sets after 30 generations running 30 models per generation. Consistent results were found regardless of which of the published data sets were used to train or verify the quantitative predictions of the best-fitting models for cell cycle gene dynamics.ConclusionOur results demonstrate the capability of scalable evolutionary search for fuzzy network models to address the problem of inferring models based on complex, noisy biomolecular data sets. This approach yields multiple alternative models that are consistent with the data, yielding a constrained set of hypotheses that can be used to optimally design subsequent experiments.