Biosensor Architectures for High-Fidelity Reporting of Cellular Signaling

Understanding mechanisms of information processing in cellular signaling networks requires quantitative measurements of protein activities in living cells. Biosensors are molecular probes that have been developed to directly track the activity of specific signaling proteins and their use is revolutionizing our understanding of signal transduction. The use of biosensors relies on the assumption that their activity is linearly proportional to the activity of the signaling protein they have been engineered to track. We use mechanistic mathematical models of common biosensor architectures (single-chain FRET-based biosensors), which include both intramolecular and intermolecular reactions, to study the validity of the linearity assumption. As a result of the classic mechanism of zero-order ultrasensitivity, we find that biosensor activity can be highly nonlinear so that small changes in signaling protein activity can give rise to large changes in biosensor activity and vice versa. This nonlinearity is abolished in architectures that favor the formation of biosensor oligomers, but oligomeric biosensors produce complicated FRET states. Based on this finding, we show that high-fidelity reporting is possible when a single-chain intermolecular biosensor is used that cannot undergo intramolecular reactions and is restricted to forming dimers. We provide phase diagrams that compare various trade-offs, including observer effects, which further highlight the utility of biosensor architectures that favor intermolecular over intramolecular binding. We discuss challenges in calibrating and constructing biosensors and highlight the utility of mathematical models in designing novel probes for cellular signaling.     

Biosensor Architectures for High-Fidelity Reporting of Cellular Signaling

Understanding mechanisms of information processing in cellular signaling networks requires quantitative measurements of protein activities in living cells. Biosensors are molecular probes that have been developed to directly track the activity of specific signaling proteins and their use is revolutionizing our understanding of signal transduction. The use of biosensors relies on the assumption that their activity is linearly proportional to the activity of the signaling protein they have been engineered to track. We use mechanistic mathematical models of common biosensor architectures (single-chain FRET-based biosensors), which include both intramolecular and intermolecular reactions, to study the validity of the linearity assumption. As a result of the classic mechanism of zero-order ultrasensitivity, we find that biosensor activity can be highly nonlinear so that small changes in signaling protein activity can give rise to large changes in biosensor activity and vice versa. This nonlinearity is abolished in architectures that favor the formation of biosensor oligomers, but oligomeric biosensors produce complicated FRET states. Based on this finding, we show that high-fidelity reporting is possible when a single-chain intermolecular biosensor is used that cannot undergo intramolecular reactions and is restricted to forming dimers. We provide phase diagrams that compare various trade-offs, including observer effects, which further highlight the utility of biosensor architectures that favor intermolecular over intramolecular binding. We discuss challenges in calibrating and constructing biosensors and highlight the utility of mathematical models in designing novel probes for cellular signaling.     

Small is beautiful: models of small neuronal networks

Modeling has contributed a great deal to our understanding of how individual neurons and neuronal networks function. In this review, we focus on models of the small neuronal networks of invertebrates, especially rhythmically active CPG networks. Models have elucidated many aspects of these networks, from identifying key interacting membrane properties to pointing out gaps in our understanding, for example missing neurons. Even the complex CPGs of vertebrates, such as those that underlie respiration, have been reduced to small network models to great effect. Modeling of these networks spans from simplified models, which are amenable to mathematical analyses, to very complicated biophysical models. Some researchers have now adopted a population approach, where they generate and analyze many related models that differ in a few to several judiciously chosen free parameters; often these parameters show variability across animals and thus justify the approach. Models of small neuronal networks will continue to expand and refine our understanding of how neuronal networks in all animals program motor output, process sensory information and learn.     

A model-based strategy to investigate the role of <Emphasis Type="Italic">microRNA</Emphasis> regulation in cancer signalling networks

In this paper we present and discuss a model-based approach to link miRNA translational control with cell signalling networks. MicroRNAs are small regulatory RNAs that are able to regulate the activity and the stability of specific messenger RNA and have been implicated in tumour progression due to their ability to translationally regulate critical oncogenes and tumour suppressors. In our approach, data on protein–protein interactions and miRNA regulation, obtained from bioinformatics databases, are integrated with quantitative experimental data using mathematical modelling. Predictive computational simulations and qualitative (bifurcation) analyses of those mathematical models are employed to further support the investigation of such multifactorial networks in the context of cancer progression. We illustrate our approach with the C-Myc/E2F signalling network, involved in the progression of several tumour subtypes, including colorectal cancer.     

Hormonal regulation of root growth: integrating local activities into global behaviour

To date, plant researchers have probed the control of root growth by studying the roles of individual regulatory components or cellular processes. However, recent studies in the Arabidopsis (Arabidopsis thaliana) root have shown that different hormones control organ growth by regulating specific growth processes (cell proliferation, differentiation or expansion) in distinct tissues. We discuss key issues raised by these new insights and hypothesise that novel tissue-to-tissue signals exist to coordinate organ growth. We conclude by describing how multiscale models can help probe the interplay between the different scales at which hormones and their regulatory networks operate in different cells and tissues. Such approaches promise to generate new insights into the mechanisms that control root growth.     

BIOCOMPUTATION: Some history and prospects

At first glance, biology and computer science are diametrically opposed sciences. Biology deals with carbon based life forms shaped by evolution and natural selection. Computer Science deals with electronic machines designed by engineers and guided by mathematical algorithms. In this brief paper, we review biologically inspired computing. We discuss several models of computation which have arisen from various biological studies. We show what these have in common, and conjecture how biology can still suggest answers and models for the next generation of computing problems. We discuss computation and argue that these biologically inspired models do not extend the theoretical limits on computation. We suggest that, in practice, biological models may give more succinct representations of various problems, and we mention a few cases in which biological models have proved useful. We also discuss the reciprocal impact of computer science on biology and cite a few significant contributions to biological science.     

A survey on methods for modeling and analyzing integrated biological networks

Understanding how cellular systems build up integrated responses to their dynamically changing environment is one of the open questions in Systems Biology. Despite their intertwinement, signaling networks, gene regulation and metabolism have been frequently modeled independently in the context of well-defined subsystems. For this purpose, several mathematical formalisms have been developed according to the features of each particular network under study. Nonetheless, a deeper understanding of cellular behavior requires the integration of these various systems into a model capable of capturing how they operate as an ensemble. With the recent advances in the "omics" technologies, more data is becoming available and, thus, recent efforts have been driven toward this integrated modeling approach. We herein review and discuss methodological frameworks currently available for modeling and analyzing integrated biological networks, in particular metabolic, gene regulatory and signaling networks. These include network-based methods and Chemical Organization Theory, Flux-Balance Analysis and its extensions, logical discrete modeling, Petri Nets, traditional kinetic modeling, Hybrid Systems and stochastic models. Comparisons are also established regarding data requirements, scalability with network size and computational burden. The methods are illustrated with successful case studies in large-scale genome models and in particular subsystems of various organisms.     

Network modeling of signal transduction: establishing the global view

Embryonic development and adult tissue homeostasis are controlled through activation of intracellular signal transduction pathways by extracellular growth factors. In the past, signal transduction has largely been regarded as a linear process. However, more recent data from large-scale and high-throughput experiments indicate that there is extensive cross-talk between individual signaling cascades leading to the notion of a signaling network. The behavior of such complex networks cannot be predicted by simple intuitive approaches but requires sophisticated models and computational simulations. The purpose of such models is to generate experimentally testable hypotheses and to find explanations for unexpected experimental results. Here, we discuss the need for, and the future impact of, mathematical models for exploring signal transduction in different biological contexts such as for example development.     

Using theoretical models to explore dispersal variation and fragmentation in urban environments

Cities are fundamentally changing the environment that plants inhabit, most notably through habitat fragmentation. Urban plant habitat patches are separated by impervious surfaces like buildings and roads and may vary from small, isolated green spaces to large green spaces like parks. Understanding the consequences of this urban fragmentation on seed dispersal is essential to both maintain urban biodiversity and mitigate the spread of unwanted weeds or invasive species but we currently lack enough empirical data to draw generalities. Theoretical reasoning (via both verbal and mathematical models) is well positioned to contribute to this knowledge gap in dispersal by providing useful predictions when empirical data are lacking. Variation in dispersal can easily be captured by models by incorporating different dispersal kernel shapes, and multiple habitat configurations can be examined. Urban environments are rarely considered by mathematical models, and our literature review indicates that most models that include dispersal variation via a dispersal kernel use only one or two shapes, suggesting a gap in the theoretical literature as well. We present a proof-of-concept model of fragmentation in an urban environment illustrating how varying habitat width can lead to different outcomes depending on the dispersal kernel. We also provide some thoughts for future directions on the application of mathematical models in urban areas.     

The layer-oriented approach to declarative languages for biological modeling

We present a new approach to modeling languages for computational biology, which we call the layer-oriented approach. The approach stems from the observation that many diverse biological phenomena are described using a small set of mathematical formalisms (e.g. differential equations), while at the same time different domains and subdomains of computational biology require that models are structured according to the accepted terminology and classification of that domain. Our approach uses distinct semantic layers to represent the domain-specific biological concepts and the underlying mathematical formalisms. Additional functionality can be transparently added to the language by adding more layers. This approach is specifically concerned with declarative languages, and throughout the paper we note some of the limitations inherent to declarative approaches. The layer-oriented approach is a way to specify explicitly how high-level biological modeling concepts are mapped to a computational representation, while abstracting away details of particular programming languages and simulation environments. To illustrate this process, we define an example language for describing models of ionic currents, and use a general mathematical notation for semantic transformations to show how to generate model simulation code for various simulation environments. We use the example language to describe a Purkinje neuron model and demonstrate how the layer-oriented approach can be used for solving several practical issues of computational neuroscience model development. We discuss the advantages and limitations of the approach in comparison with other modeling language efforts in the domain of computational biology and outline some principles for extensible, flexible modeling language design. We conclude by describing in detail the semantic transformations defined for our language.     

METANNOGEN: compiling features of biochemical reactions needed for the reconstruction of metabolic networks

Background  

One central goal of computational systems biology is the mathematical modelling of complex metabolic reaction networks. The first and most time-consuming step in the development of such models consists in the stoichiometric reconstruction of the network, i. e. compilation of all metabolites, reactions and transport processes relevant to the considered network and their assignment to the various cellular compartments. Therefore an information system is required to collect and manage data from different databases and scientific literature in order to generate a metabolic network of biochemical reactions that can be subjected to further computational analyses.     

Competing to coordinate cell fate decisions: the MST2-Raf-1 signaling device

How do biochemical signaling pathways generate biological specificity? This question is fundamental to modern biology, and its enigma has been accentuated by the discovery that most proteins in signaling networks serve multifunctional roles. An answer to this question may lie in analyzing network properties rather than individual traits of proteins in order to elucidate design principles of biochemical networks that enable biological decision-making. We discuss how this is achieved in the MST2/Hippo-Raf-1 signaling network with the help of mathematical modeling and model-based analysis, which showed that competing protein interactions with affinities controlled by dynamic protein modifications can function as Boolean computing devices that determine cell fate decisions. In addition, we discuss areas of interest for future research and highlight how systems approaches would be of benefit.     

Mathematical approaches to differentiation and gene regulation

We consider some mathematical issues raised by the modelling of gene networks. The expression of genes is governed by a complex set of regulations, which is often described symbolically by interaction graphs. These are finite oriented graphs where vertices are the genes involved in the biological system of interest and arrows describe their interactions: a positive (resp. negative) arrow from a gene to another represents an activation (resp. inhibition) of the expression of the latter gene by some product of the former. Once such an interaction graph has been established, there remains the difficult task to decide which dynamical properties of the gene network can be inferred from it, in the absence of precise quantitative data about their regulation. There mathematical tools, among others, can be of some help. In this paper we discuss a rule proposed by Thomas according to which the possibility for the network to have several stationary states implies the existence of a positive circuit in the corresponding interaction graph. We prove that, when properly formulated in rigorous terms, this rule becomes a theorem valid for several different types of formal models of gene networks. This result is already known for models of differential [C. Soulé, Graphic requirements for multistationarity, ComPlexUs 1 (2003) 123-133] or Boolean [E. Rémy, P. Ruet, D. Thieffry, Graphic requirements for multistability and attractive cycles in a boolean dynamical framework, 2005, Preprint] type. We show here that a stronger version of it holds in the differential setup when the decay of protein concentrations is taken into account. This allows us to verify also the validity of Thomas' rule in the context of piecewise-linear models. We then discuss open problems.     

Multiple interactions networks: towards more realistic descriptions of the web of life

Ecological communities are defined by species interacting dynamically in a given location at a given time, and can be conveniently represented as networks of interactions. Pairwise interactions can be ascribed to one of five main types, depending on their outcome for the species involved: amensalism, antagonism (including predation, parasitism and disease), commensalism, competition or mutualism. While most studies have dealt so far with networks involving one single type of interaction at a time, often focusing on a specific clade and/or guild, recent studies are being developed that consider networks with more than one interaction type and across several levels of biological organisation. We review these developments and suggest that three main frameworks are in use to investigate the properties of multiple interactions networks: ‘expanded food‐webs’, ‘multilayer networks’ and ‘equal footing networks’. They differ on how interactions are classified and implemented in mathematical models, and on whether the effect of different interaction types is expressed in the same units. We analyse the mathematical and ecological assumptions of these three approaches, and identify some of the questions that can be addressed with each one of them. Since the overwhelming majority of studies on multiple interactions are theoretical and use artificially generated data, we also provide recommendations for the incorporation of field data in such studies.     

EXAMINE: a computational approach to reconstructing gene regulatory networks

Reverse-engineering of gene networks using linear models often results in an underdetermined system because of excessive unknown parameters. In addition, the practical utility of linear models has remained unclear. We address these problems by developing an improved method, EXpression Array MINing Engine (EXAMINE), to infer gene regulatory networks from time-series gene expression data sets. EXAMINE takes advantage of sparse graph theory to overcome the excessive-parameter problem with an adaptive-connectivity model and fitting algorithm. EXAMINE also guarantees that the most parsimonious network structure will be found with its incremental adaptive fitting process. Compared to previous linear models, where a fully connected model is used, EXAMINE reduces the number of parameters by O(N), thereby increasing the chance of recovering the underlying regulatory network. The fitting algorithm increments the connectivity during the fitting process until a satisfactory fit is obtained. We performed a systematic study to explore the data mining ability of linear models. A guideline for using linear models is provided: If the system is small (3-20 elements), more than 90% of the regulation pathways can be determined correctly. For a large-scale system, either clustering is needed or it is necessary to integrate information in addition to expression profile. Coupled with the clustering method, we applied EXAMINE to rat central nervous system development (CNS) data with 112 genes. We were able to efficiently generate regulatory networks with statistically significant pathways that have been predicted previously.     

Generative probabilistic models for protein-protein interaction networks--the biclique perspective

MOTIVATION: Much of the large-scale molecular data from living cells can be represented in terms of networks. Such networks occupy a central position in cellular systems biology. In the protein-protein interaction (PPI) network, nodes represent proteins and edges represent connections between them, based on experimental evidence. As PPI networks are rich and complex, a mathematical model is sought to capture their properties and shed light on PPI evolution. The mathematical literature contains various generative models of random graphs. It is a major, still largely open question, which of these models (if any) can properly reproduce various biologically interesting networks. Here, we consider this problem where the graph at hand is the PPI network of Saccharomyces cerevisiae. We are trying to distinguishing between a model family which performs a process of copying neighbors, represented by the duplication-divergence (DD) model, and models which do not copy neighbors, with the Barabási-Albert (BA) preferential attachment model as a leading example. RESULTS: The observed property of the network is the distribution of maximal bicliques in the graph. This is a novel criterion to distinguish between models in this area. It is particularly appropriate for this purpose, since it reflects the graph's growth pattern under either model. This test clearly favors the DD model. In particular, for the BA model, the vast majority (92.9%) of the bicliques with both sides ≥4 must be already embedded in the model's seed graph, whereas the corresponding figure for the DD model is only 5.1%. Our results, based on the biclique perspective, conclusively show that a na?ve unmodified DD model can capture a key aspect of PPI networks.