Dynamics of Boolean networks controlled by biologically meaningful functions

The remarkably stable dynamics displayed by randomly constructed Boolean networks is one of the most striking examples of the spontaneous emergence of self-organization in model systems composed of many interacting elements (Kauffman, S., J. theor. Biol.22, 437-467, 1969; The Origins of Order, Oxford University Press, Oxford, 1993). The dynamics of such networks is most stable for a connectivity of two inputs per element, and decreases dramatically with increasing number of connections. Whereas the simplicity of this model system allows the tracing of the dynamical trajectories, it leaves out many features of real biological connections. For instance, the dynamics has been studied in detail only for networks constructed by allowing all theoretically possible Boolean rules, whereas only a subset of them make sense in the material world. This paper analyses the effect on the dynamics of using only Boolean functions which are meaningful in a biological sense. This analysis is particularly relevant for nets with more than two inputs per element because biological networks generally appear to be more extensively interconnected. Sets of the meaningful functions were assembled for up to four inputs per element. The use of these rules results in a smaller number of distinct attractors which have a shorter length, with relatively little sensitivity to the size of the network and to the number of inputs per element. Forcing away the activator/inhibitor ratio from the expected value of 50% further enhances the stability. This effect is more pronounced for networks consisting of a majority of activators than for networks with a corresponding majority of inhibitors, indicating that the former allow the evolution of larger genetic networks. The data further support the idea of the usefulness of logical networks as a conceptual framework for the understanding of real-world phenomena.     

Poisson-Boltzmann continuum-solvation models: applications to pH-dependent properties of biomolecules

All molecules can be viewed as either discrete or continuous assemblies of electric charges, and electrostatics plays a major role in intermolecular and intramolecular interactions. Moreover, charge distribution within molecules may fluctuate due to the presence of ionizable groups capable of exchanging protons with the environment, leading to pH-dependence of phenomena involving such molecules. Electrostatic aspects of complex shapes and environments of biological molecules, in vitro and in vivo, are relatively well amenable to treatment by Poisson-Boltzmann models, which are attractive in that they possess a clear physical meaning, and can be readily solved by several mathematically sound methods. Here we describe applications of these models to obtain valuable insights into some biologically important pH-dependent properties of biomolecules, such as stability, binding of ligands (including potential drugs), enzymatic activity, conformational transitions, membrane transport and viral entry.     

Temporal dynamics of natural enemy–pest interactions in a changing environment

Agroecosystems contain complex networks of interacting organisms and these interaction webs are structured by the relative timing of key biological and ecological events. Recent intensification of land management and global changes in climate threaten to desynchronize the temporal structure of interaction webs and disrupt the provisioning of ecosystem services, such as biological control by natural enemies. It is therefore critical to recognize the central role of temporal dynamics in driving predator–prey interactions in agroecosystems. Specifically, ecological dynamics in crop fields routinely behave as periodic oscillations, or cycles. Familiar examples include phenological cycles, diel activity rhythms, and crop-management cycles. The relative timing and the degree of overlap among ecological cycles determine the nature and magnitude of the ecological interactions among organisms, and ultimately determine whether ecosystem services, such as biological control, can be provided. Additionally, the ecological dynamics in many cropping systems are characterized by a pattern of frequent disturbances due to management actions such as harvest, sowing and pesticide applications. These disturbance cycles cause agroecosystems to be dominated by dispersal and repopulation dynamics. However, they also serve as selective filters that regulate which animals can persist in agroecosystems over larger temporal scales. Here, we review key concepts and examples from the literature on temporal dynamics in ecological systems, and provide a framework to guide biological control strategies for sustainable pest management in a changing world.     

Neural model of the genetic network

Many cell control processes consist of networks of interacting elements that affect the state of each other over time. Such an arrangement resembles the principles of artificial neural networks, in which the state of a particular node depends on the combination of the states of other neurons. The lambda bacteriophage lysis/lysogeny decision circuit can be represented by such a network. It is used here as a model for testing the validity of a neural approach to the analysis of genetic networks. The model considers multigenic regulation including positive and negative feedback. It is used to simulate the dynamics of the lambda phage regulatory system; the results are compared with experimental observation. The comparison proves that the neural network model describes behavior of the system in full agreement with experiments; moreover, it predicts its function in experimentally inaccessible situations and explains the experimental observations. The application of the principles of neural networks to the cell control system leads to conclusions about the stability and redundancy of genetic networks and the cell functionality. Reverse engineering of the biochemical pathways from proteomics and DNA micro array data using the suggested neural network model is discussed.     

Alternative time representation in dopamine models

Dopaminergic neuron activity has been modeled during learning and appetitive behavior, most commonly using the temporal-difference (TD) algorithm. However, a proper representation of elapsed time and of the exact task is usually required for the model to work. Most models use timing elements such as delay-line representations of time that are not biologically realistic for intervals in the range of seconds. The interval-timing literature provides several alternatives. One of them is that timing could emerge from general network dynamics, instead of coming from a dedicated circuit. Here, we present a general rate-based learning model based on long short-term memory (LSTM) networks that learns a time representation when needed. Using a naïve network learning its environment in conjunction with TD, we reproduce dopamine activity in appetitive trace conditioning with a constant CS-US interval, including probe trials with unexpected delays. The proposed model learns a representation of the environment dynamics in an adaptive biologically plausible framework, without recourse to delay lines or other special-purpose circuits. Instead, the model predicts that the task-dependent representation of time is learned by experience, is encoded in ramp-like changes in single-neuron activity distributed across small neural networks, and reflects a temporal integration mechanism resulting from the inherent dynamics of recurrent loops within the network. The model also reproduces the known finding that trace conditioning is more difficult than delay conditioning and that the learned representation of the task can be highly dependent on the types of trials experienced during training. Finally, it suggests that the phasic dopaminergic signal could facilitate learning in the cortex.     

Predicting the unpredictable: Recent structure–activity studies on peptide-based macrocycles

Heterocycle-containing macrocycles are an emerging class of molecules that have therapeutic efficacy. Many biologically active natural products that have interesting biological properties fall into this class of molecules. The highly specific and selective biological activity is often attributed to the unique conformation of these macrocycles, which is affected by the elements of the macrocycles as well as its surroundings in biological systems. In this review, the structure–activity relationship studies of several recently developed biologically active heterocycle-containing macrocycles have been discussed in order to facilitate an understanding on how unpredictable structures can be controlled.     

Attraction Basins as Gauges of Robustness against Boundary Conditions in Biological Complex Systems

One fundamental concept in the context of biological systems on which researches have flourished in the past decade is that of the apparent robustness of these systems, i.e., their ability to resist to perturbations or constraints induced by external or boundary elements such as electromagnetic fields acting on neural networks, micro-RNAs acting on genetic networks and even hormone flows acting both on neural and genetic networks. Recent studies have shown the importance of addressing the question of the environmental robustness of biological networks such as neural and genetic networks. In some cases, external regulatory elements can be given a relevant formal representation by assimilating them to or modeling them by boundary conditions. This article presents a generic mathematical approach to understand the influence of boundary elements on the dynamics of regulation networks, considering their attraction basins as gauges of their robustness. The application of this method on a real genetic regulation network will point out a mathematical explanation of a biological phenomenon which has only been observed experimentally until now, namely the necessity of the presence of gibberellin for the flower of the plant Arabidopsis thaliana to develop normally.     

Automata network theories in immunology: Their utility and their underdetermination

Small networks of threshold automata are used to model complex interactions between populations of regulatory cells (helpers and suppressors, antigen specific and anti-idiotypic) which participate in the immune response. The models, being discrete and semiquantitative, are well adapted to the situation of incomplete information often encounteredin vivo. However, the dynamics of many different network structures usually end up in the same attractor set. Thus, many different theories are equivalent in their explicative power for the same facts. This property, known as underdetermination of the theories by the facts, is given a quantitative estimate. It appears that such an underdetermination, as a kind of irreductible complexity, can be expected in manyin vivo biological processes, even when the number of interacting and functionally coupled elements is relatively small.     

Dynamics of a simple regulatory switch

We consider the dynamics of a model toggle switch abstracted from the genetic interactions operative in a fungal stress response circuit. The switch transduces an external signal and propagates it forward by mediating the transport between compartments of two interacting gene products. The transport between compartments is assumed to be related to the degree of association between the interacting proteins, a fact for which there exists a wealth of biological evidence. The ubiquity and modularity of this cellular control mechanism warrants a detailed study of the dynamics entailed by various modelling assumptions. Specifically, we consider a general gate model in which both of the associating proteins are freely transportable between compartments. A more restrictive, but biologically supported model, is considered in which only one of the two proteins undergoes transport. Under the strong assumption that the disassociation of the interacting proteins is unidirectional we show that the qualitative dynamics of the two models are similar; that is they both converge to unique periodic orbits. From a biophysical perspective the assumption of unidirectional dissociation is unrealistic. We show that the same result holds for the more restrictive model when one weakens the assumption of unidirectional binding or disassociation. We speculate that this is not true for the more general model. This difference in dynamics may have important biological implications and certainly points to promising avenues of research.     

Site-specific terminal and internal labeling of RNA by poly(A) polymerase tailing and copper-catalyzed or copper-free strain-promoted click chemistry

The modification of RNA with fluorophores, affinity tags and reactive moieties is of enormous utility for studying RNA localization, structure and dynamics as well as diverse biological phenomena involving RNA as an interacting partner. Here we report a labeling approach in which the RNA of interest--of either synthetic or biological origin--is modified at its 3'-end by a poly(A) polymerase with an azido-derivatized nucleotide. The azide is later on conjugated via copper-catalyzed or strain-promoted azide-alkyne click reaction. Under optimized conditions, a single modified nucleotide of choice (A, C, G, U) containing an azide at the 2'-position can be incorporated site-specifically. We have identified ligases that tolerate the presence of a 2'-azido group at the ligation site. This azide is subsequently reacted with a fluorophore alkyne. With this stepwise approach, we are able to achieve site-specific, internal backbone-labeling of de novo synthesized RNA molecules.     

Dynamical and integrative cell signaling: challenges for the new biology

Years of careful experimental analysis have revealed that signaling molecules are organized into complex networks of biochemical reactions exquisitely regulated in time and space to provide a cell with high-fidelity information about an extremely noisy and volatile environment. A new view of signaling networks as systems consisting of multiple complex elements interacting in a multifarious fashion is emerging, a view that conflicts with the single-gene or protein-centric approach common in biological research. The postgenomic era has brought about a different, network-centric methodology of analysis, suddenly forcing researchers toward the opposite extreme of complexity, where the networks being explored are, to a certain extent, intractable and uninterpretable. Both the cartoons of simple pathways and the very large "hair-ball" diagrams of large intracellular networks are also representations of static worlds, superficially devoid of dynamics and chemistry. These representations are often viewed as being analogous to stably linked computer and neural networks rather than dynamically changing networks of chemical interactions, where the notions of concentration, compartmentalization, and diffusion may be the primary determinants of connectivity. Arguably, the systems biology approach, relying on computational modeling coupled with various experimental techniques and methodologies, will be an essential component of analysis of the behavior of signal transduction pathways. Combining the dynamical view of rapidly evolving responses and the structural view arising from high-throughput analyses of the interacting species will be the best approach toward efforts toward greater understanding of intracellular signaling processes.     

Finding biologically relevant protein domain interactions: conserved binding mode analysis

Proteins evolved through the shuffling of functional domains, and therefore, the same domain can be found in different proteins and species. Interactions between such conserved domains often involve specific, well-determined binding surfaces reflecting their important biological role in a cell. To find biologically relevant interactions we developed a method of systematically comparing and classifying protein domain interactions from the structural data. As a result, a set of conserved binding modes (CBMs) was created using the atomic detail of structure alignment data and the protein domain classification of the Conserved Domain Database. A conserved binding mode is inferred when different members of interacting domain families dock in the same way, such that their structural complexes superimpose well. Such domain interactions with recurring structural themes have greater significance to be biologically relevant, unlike spurious crystal packing interactions. Consequently, this study gives lower and upper bounds on the number of different types of interacting domain pairs in the structure database on the order of 1000-2000. We use CBMs to create domain interaction networks, which highlight functionally significant connections by avoiding many infrequent links between highly connected nodes. The CBMs also constitute a library of docking templates that may be used in molecular modeling to infer the characteristics of an unknown binding surface, just as conserved domains may be used to infer the structure of an unknown protein. The method's ability to sort through and classify large numbers of putative interacting domain pairs is demonstrated on the oligomeric interactions of globins.     

On the number of experiments required to find the causal structure of complex systems

The need to capture the complexity of biological systems in a simpler formalism is the underlying impetus of biological sciences. Understanding the function of many biological complex systems, such as genetic networks or molecular signalling pathways, requires precise identification of the interactions between their individual components. A number of questions in the study of complex systems are then important-in particular, what can be inferred about the interactions in a complex system from an arbitrary set of experiments, and, what is the minimum number of experiments required to characterize the system? This paper shows that the problem of finding the minimal causal structure of a system based on a set of observations is computationally intractable for even moderately sized systems (it is NP-hard), but a reasonable approximation can be found in a relatively short (polynomial) time. Next, it is shown that the number of experiments required to characterize a complex system grows exponentially with the upper bound on the number of immediate upstream influences of each element, but only logarithmically with the number of elements in the system. This makes it possible to study biological systems with extremely large number of interacting elements and relatively sparse interconnections, such as gene regulatory and cell signalling networks. Finally, the construction of a randomized experimental sequence which achieves this bound is discussed.     

Protein interaction networks in bacteria

The complement of expressed cellular proteins - the proteome - is organized into functional, structured networks of protein interactions that mediate assembly of molecular machines and dynamic cellular pathways. Recent studies reveal the biological roles of protein interactions in bacteriophage T7 and Helicobacter pylori, and new methods allow to compare and to predict interaction networks in other species. Smaller scale networks provide biological insights into DNA replication and chromosome dynamics in Bacillus subtilis and Archeoglobus fulgidus, and into the assembly of multiprotein complexes such as the type IV secretion system of Agrobacterium tumefaciens, and the cell division machinery of Escherichia coli. Genome-wide interaction networks in several species are needed to obtain a biologically meaningful view of the higher order organization of the proteome in bacteria.     

Engineering biological systems with synthetic RNA molecules

RNA molecules play diverse functional roles in natural biological systems. There has been growing interest in designing synthetic RNA counterparts for programming biological function. The design of synthetic RNA molecules that exhibit diverse activities, including sensing, regulatory, information processing, and scaffolding activities, has highlighted the advantages of RNA as a programmable design substrate. Recent advances in implementing these engineered RNA molecules as key control elements in synthetic genetic networks are highlighting the functional relevance of this class of synthetic elements in programming cellular behaviors.     

Usefulness and limitations of dK random graph models to predict interactions and functional homogeneity in biological networks under a pseudo-likelihood parameter estimation approach

Background  

Many aspects of biological functions can be modeled by biological networks, such as protein interaction networks, metabolic networks, and gene coexpression networks. Studying the statistical properties of these networks in turn allows us to infer biological function. Complex statistical network models can potentially more accurately describe the networks, but it is not clear whether such complex models are better suited to find biologically meaningful subnetworks.     

Understanding of the roles of phospholipase D and phosphatidic acid through their binding partners

Phospholipase D (PLD) is a phosphatidyl choline (PC)-hydrolyzing enzyme that generates phosphatidic acid (PA), a lipid second messenger that modulates diverse intracellular signaling. Through interactions with signaling molecules, both PLD and PA can mediate a variety of cellular functions, such as, growth/proliferation, vesicle trafficking, cytoskeleton modulation, development, and morphogenesis. Therefore, systemic approaches for investigating PLD networks including interrelationship between PLD and PA and theirs binding partners, such as proteins and lipids, can enhance fundamental knowledge of roles of PLD and PA in diverse biological processes. In this review, we summarize previously reported protein-protein and protein-lipid interactions of PLD and PA and their binding partners. In addition, we describe the functional roles played by PLD and PA in these interactions, and provide PLD network that summarizes these interactions. The PLD network suggests that PLD and PA could act as a decision maker and/or as a coordinator of signal dynamics. This viewpoint provides a turning point for understanding the roles of PLD-PA as a dynamic signaling hub.