Identifying responsive modules by mathematical programming: an application to budding yeast cell cycle

High-throughput biological data offer an unprecedented opportunity to fully characterize biological processes. However, how to extract meaningful biological information from these datasets is a significant challenge. Recently, pathway-based analysis has gained much progress in identifying biomarkers for some phenotypes. Nevertheless, these so-called pathway-based methods are mainly individual-gene-based or molecule-complex-based analyses. In this paper, we developed a novel module-based method to reveal causal or dependent relations between network modules and biological phenotypes by integrating both gene expression data and protein-protein interaction network. Specifically, we first formulated the identification problem of the responsive modules underlying biological phenotypes as a mathematical programming model by exploiting phenotype difference, which can also be viewed as a multi-classification problem. Then, we applied it to study cell-cycle process of budding yeast from microarray data based on our biological experiments, and identified important phenotype- and transition-based responsive modules for different stages of cell-cycle process. The resulting responsive modules provide new insight into the regulation mechanisms of cell-cycle process from a network viewpoint. Moreover, the identification of transition modules provides a new way to study dynamical processes at a functional module level. In particular, we found that the dysfunction of a well-known module and two new modules may directly result in cell cycle arresting at S phase. In addition to our biological experiments, the identified responsive modules were also validated by two independent datasets on budding yeast cell cycle.     

Functional genomic analysis reveals the utility of the I/LWEQ module as a predictor of protein:actin interaction

The I/LWEQ module is a conserved sequence that we have identified as an actin-binding motif in the metazoan focal adhesion protein talin and the yeast protein Sla2p. Both of these proteins are associated with the actin cytoskeleton in cells. To better establish the value of the I/LWEQ module for prediction of actin-binding function, we have applied a functional genomics approach. Analysis of the 23 available I/LWEQ module sequences supports the division of I/LWEQ protein superfamily into four groups: (1) metazoan talin, (2) Dictyostelium discoideum talin homologs TalA/B, (3) metazoan Hip1p, and (4) yeast Sla2p. We show here that I/LWEQ modules from each major group bind to F-actin in vitro and that GFP-fusion proteins of the I/LWEQ modules of talin and Sla2p bind to F-actin in vivo. Therefore, the presence of an I/LWEQ module is strongly predictive of protein-actin interactions. The structural and functional conservation of the I/LWEQ module across the phylogenetic distance between cellular slime molds and mammals implies that the role of the I/LWEQ module is to connect diverse proteins involved in distinct cellular processes, including cell adhesion, cytoskeletal organization, and cell differentiation, to the actin cytoskeleton.     

Electrophorus electricus as a model system for the study of membrane excitability

The stunning sensations produced by electric fish, particularly the electric eel, Electrophorus electricus, have fascinated scientists for centuries. Within the last 50 years, however, electric cells of Electrophorus have provided a unique model system that is both specialized and appropriate for the study of excitable cell membrane electrophysiology and biochemistry. Electric tissue generates whole animal electrical discharges by means of membrane potentials that are remarkably similar to those of mammalian neurons, myocytes and secretory cells. Electrocytes express ion channels, ATPases and signal transduction proteins common to these other excitable cells. Action potentials of electrocytes represent the specialized end function of electric tissue whereas other excitable cells use membrane potential changes to trigger sophisticated cellular processes, such as myofilament cross-bridging for contraction, or exocytosis for secretion. Because electric tissue lacks these functions and the proteins associated with them, it provides a highly specialized membrane model system. This review examines the basic mechanisms involved in the generation of the electrical discharge of the electric eel and the membrane proteins involved. The valuable contributions that electric tissue continues to make toward the understanding of excitable cell physiology and biochemistry are summarized, particularly those studies using electrocytes as a model system for the study of the regulation of membrane excitability by second messengers and signal transduction pathways.     

Modular organization of protein interaction networks

MOTIVATION: Accumulating evidence suggests that biological systems are composed of interacting, separable, functional modules. Identifying these modules is essential to understand the organization of biological systems. RESULT: In this paper, we present a framework to identify modules within biological networks. In this approach, the concept of degree is extended from the single vertex to the sub-graph, and a formal definition of module in a network is used. A new agglomerative algorithm was developed to identify modules from the network by combining the new module definition with the relative edge order generated by the Girvan-Newman (G-N) algorithm. A JAVA program, MoNet, was developed to implement the algorithm. Applying MoNet to the yeast core protein interaction network from the database of interacting proteins (DIP) identified 86 simple modules with sizes larger than three proteins. The modules obtained are significantly enriched in proteins with related biological process Gene Ontology terms. A comparison between the MoNet modules and modules defined by Radicchi et al. (2004) indicates that MoNet modules show stronger co-clustering of related genes and are more robust to ties in betweenness values. Further, the MoNet output retains the adjacent relationships between modules and allows the construction of an interaction web of modules providing insight regarding the relationships between different functional modules. Thus, MoNet provides an objective approach to understand the organization and interactions of biological processes in cellular systems. AVAILABILITY: MoNet is available upon request from the authors.     

Building the cellular puzzle: control in multi-level reaction networks

Quantitative conceptual tools dealing with control and regulation of cellular processes have been mostly developed for and applied to the pathways of intermediary metabolism. Yet, cellular processes are organized in different levels, metabolism forming the lowest level in a cascade of processes. Well-known examples are the DNA-mRNA-enzyme-metabolism cascade and the signal transduction cascades consisting of covalent modification cycles. The reaction network that constitutes each level can be viewed as a "module" in which reactions are linked by mass transfer. Although in principle all of these cellular modules are ultimately linked by mass transfer, in practice they can often be regarded as "isolated" from each other in terms of mass transfer. Here modules can interact with each other only by means of regulatory or catalytic effects-a chemical species in one module may affect the rate of a reaction in another module by binding to an enzyme or transport system or by acting as a catalyst. This paper seeks to answer two questions about the control and regulation of such multi-level reaction networks: (i) How can the control properties of the system as a whole be expressed in terms of the control properties of individual modules and the effects between modules? (ii) How do the control properties of a module in its isolated state change when it is embedded in the whole system through its connections with the other modules? In order to answer these questions a quantitative theoretical framework is developed and applied to systems containing two, three or four fully interacting modules; it is shown how it can be extended in principle to n modules. This newly developed theory therefore makes it possible to quantitatively dissect intermodular, internal and external regulation in multi-level systems.     

Cellular mechanics of wound formation in single cell layer under cyclic stretching

Wounds can be produced when cells and tissues are subjected to excessive forces, for instance, under pathological conditions or nonphysiological loading. However, the cellular behaviors in the wound formation process are not clear. Here we tested the behaviors of wound formation in the epithelial layer with an in-suit uniaxial stretching device. We found that the wound often nucleates at the position where the cells are dividing. The polarization direction of cells near the wound is preferentially along the wound edge, whereas the cells far from the wound are preferentially perpendicular to the stretching direction. The larger the wound area is, the higher is the aspect ratio of the cells around the wound. Increasing the cell density will strengthen the cell layer. The higher the cell density is, the smaller is the area of the wounds, and the weaker is the effect of stretching on the polarization of the cells. Furthermore, we built a coarse-grained cell model that can explicitly consider the elasticity and viscoelasticity of cells, cell-cell interaction, and cell active stress, by which we simulated the wound formation process and quantitatively analyzed the force and stress fields in the cell layer, particularly around the wound. These analyses reveal the cellular mechanisms of wound formation behaviors in the cell layer under stretching and shed useful light on tissue engineering and regenerative medicine for biomedical applications.     

Dynamic-module redundancy confers robustness to the gene regulatory network involved in hair patterning of Arabidopsis epidermis

Redundancy among dynamic modules is emerging as a potentially generic trait in gene regulatory networks. Moreover, module redundancy could play an important role in network robustness to perturbations. We explored the effect of dynamic-module redundancy in the networks associated to hair patterning in Arabidopsis root and leaf epidermis. Recent studies have put forward several dynamic modules belonging to these networks. We defined these modules in a discrete dynamical framework that was previously reported. Then, we addressed whether these modules are sufficient or necessary for recovering epidermal cell types and patterning. After defining two quantitative estimates of the system's robustness, we also compared the robustness of each separate module with that of a network coupling all the leaf or root modules. We found that, considering certain assumptions, all the dynamic modules proposed so far are sufficient on their own for pattern formation, but reinforce each other during epidermal development. Furthermore, we found that networks of coupled modules are more robust to perturbations than single modules. These results suggest that dynamic-module redundancy might be an important trait in gene regulatory networks and point at central questions regarding network evolution, module coupling, pattern robustness and the evolution of development.     

Steady-State Kinetic Modeling Constrains Cellular Resting States and Dynamic Behavior

A defining characteristic of living cells is the ability to respond dynamically to external stimuli while maintaining homeostasis under resting conditions. Capturing both of these features in a single kinetic model is difficult because the model must be able to reproduce both behaviors using the same set of molecular components. Here, we show how combining small, well-defined steady-state networks provides an efficient means of constructing large-scale kinetic models that exhibit realistic resting and dynamic behaviors. By requiring each kinetic module to be homeostatic (at steady state under resting conditions), the method proceeds by (i) computing steady-state solutions to a system of ordinary differential equations for each module, (ii) applying principal component analysis to each set of solutions to capture the steady-state solution space of each module network, and (iii) combining optimal search directions from all modules to form a global steady-state space that is searched for accurate simulation of the time-dependent behavior of the whole system upon perturbation. Importantly, this stepwise approach retains the nonlinear rate expressions that govern each reaction in the system and enforces constraints on the range of allowable concentration states for the full-scale model. These constraints not only reduce the computational cost of fitting experimental time-series data but can also provide insight into limitations on system concentrations and architecture. To demonstrate application of the method, we show how small kinetic perturbations in a modular model of platelet P2Y₁ signaling can cause widespread compensatory effects on cellular resting states.     

Spatiotemporal organization and mechanosensory function of podosomes

Podosomes are small, circular adhesions formed by cells such as osteoclasts, macrophages, dendritic cells, and endothelial cells. They comprise a protrusive actin core module and an adhesive ring module composed of integrins and cytoskeletal adaptor proteins such as vinculin and talin. Furthermore, podosomes are associated with an actin network and often organize into large clusters. Recent results from our laboratory and others have shed new light on podosome structure and dynamics, suggesting a revision of the classical “core-ring” model. Also, these studies demonstrate that the adhesive and protrusive module are functionally linked by the actin network likely facilitating mechanotransduction as well as providing feedback between these two modules. In this commentary, we briefly summarize these recent advances with respect to the knowledge on podosome structure and discuss force distribution mechanisms within podosomes and their emerging role in mechanotransduction.     

Meristems, metamers and modules and the development of shoot and root systems

BARLOW, P. W., 1989. Meristems, metamers and modules in the development of shoot and root systems . Root and shoot systems are hierarchical organizations whose levels are represented, in part, by cells and meristems. Meristems produce modules which in turn construct the architectural model. The latter is species specific and its structure depends on the geometrical interrelationships between the modular elements. The place of the metamer within this hierarchical scheme is discussed. Metamers derive directly from meristem activity and are externally recognizable as reiterated sub-units of the module. Another sub-unit of module construction, the cellular complex, or merophyte, is also a product of meristem activity, but, in contrast to the metamer, it is an internal, rather than an external, anatomical feature. Being cellular, it increases the ‘span’ of the cell level rather than constituting a level in its own right. Although the physical boundaries of metamer and merophyte can overlap, or even coincide, the two units belong to different conceptual schemes of module structure: the metamer is defined from a ‘classical’ morphological viewpoint, whereas the merophyte derives from a cellular conception of plant structure. Both the merophyte and the metamer have a role in clarifying the understanding of plant development since both provide insights into the functioning of the meristems from which they are derived and the structure of the module to which they contribute. For example, modules which lack an obvious metameric construction can usefully be analysed in terms of their merophytic organization. This is particularly true of roots of lower plants. Here, the merophytes reflect the presence and activity of a specialized meristematic apical cell. On the other hand, modules of higher plants, which lack such apical cells, also lack clearly defined merophytes, but their shoots have obvious metamers which reflect the activity of the meristem as a whole. It should be possible to represent the development of modules from cells, via their intermediate sub-structures of meristems and metamers, by means of formal languages of automata theory. One of these, a graphical algorithm (Petri net), is applied in this developmental context.     

Dynamical systems for predictive control of autonomous robots

Summary Regularities in the environment are accessible to an autonomous agents as reproducible relations between actions and perceptions and can be exploited by unsupervised learning. Our approach is based on the possibility to perform and to verify predictions about perceivable consequences of actions. It is implemented as a three-layer neural network that combines predictive perception, internal-state transitions and action selection into a loop which closes via the environment. In addition to minimizing prediction errors, the goal of network adaptation comprises also an optimization of the minimization rate such that new behaviors are favored over already learned ones, which would result in a vanishing improvement of predictability. Previously learned behaviors are reactivated or continued if triggering stimuli are available and an externally or otherwise given reward overcompensates the decay of the learning rate. In the model, behavior learning and learning behavior are brought about by the same mechanism, namely the drive to continuously experience learning success. Behavior learning comprises representation and storage of learned behaviors and finally their inhibition such that a further exploration of the environment is possible. Learning behavior, in contrast, detects the frontiers of the manifold of learned behaviors and provides estimates of the learnability of behaviors leading outwards the field of expertise. The network module has been implemented in a Khepera miniature robot. We also consider hierarchical architectures consisting of several modules in one agent as well as groups of several agents, which are controlled by such networks.     

Spatiotemporal organization and mechanosensory function of podosomes

Podosomes are small, circular adhesions formed by cells such as osteoclasts, macrophages, dendritic cells, and endothelial cells. They comprise a protrusive actin core module and an adhesive ring module composed of integrins and cytoskeletal adaptor proteins such as vinculin and talin. Furthermore, podosomes are associated with an actin network and often organize into large clusters. Recent results from our laboratory and others have shed new light on podosome structure and dynamics, suggesting a revision of the classical “core-ring” model. Also, these studies demonstrate that the adhesive and protrusive module are functionally linked by the actin network likely facilitating mechanotransduction as well as providing feedback between these two modules. In this commentary, we briefly summarize these recent advances with respect to the knowledge on podosome structure and discuss force distribution mechanisms within podosomes and their emerging role in mechanotransduction.     

The C-terminal region of E1A: a molecular tool for cellular cartography

The adenovirus E1A proteins function via protein-protein interactions. By making many connections with the cellular protein network, individual modules of this virally encoded hub reprogram numerous aspects of cell function and behavior. Although many of these interactions have been thoroughly studied, those mediated by the C-terminal region of E1A are less well understood. This review focuses on how this region of E1A affects cell cycle progression, apoptosis, senescence, transformation, and conversion of cells to an epithelial state through interactions with CTBP1/2, DYRK1A/B, FOXK1/2, and importin-α. Furthermore, novel potential pathways that the C-terminus of E1A influences through these connections with the cellular interaction network are discussed.     

Methods in clonal analysis and applications

During development, embryonic cells display a large variety of behaviors that lead to the formation of embryonic structures that are frequently transient. Simultaneously, cells progress towards a specific fate. The current challenge for embryologists is to resolve how these two distinct aspects of development co-exist. As cell behaviors (including elementary cellular operations such as motility, adhesiveness, polarization, change in shape, division and death) and their control are much less well understood than the genetic aspects of cell fate determination, there is currently much interest in the study of cell behaviors. This mainly consists of labeling groups of cells or, less frequently, single cells and observing their descendants. In this review, we describe a few techniques for labeling groups of cells and we discuss prospective and retrospective clonal analysis, in particular the LaacZ system, in detail. We examine the information generated by these approaches.     

A multi-approach and multi-scale platform to model CD4+ T cells responding to infections

Immune responses rely on a complex adaptive system in which the body and infections interact at multiple scales and in different compartments. We developed a modular model of CD4+ T cells, which uses four modeling approaches to integrate processes at three spatial scales in different tissues. In each cell, signal transduction and gene regulation are described by a logical model, metabolism by constraint-based models. Cell population dynamics are described by an agent-based model and systemic cytokine concentrations by ordinary differential equations. A Monte Carlo simulation algorithm allows information to flow efficiently between the four modules by separating the time scales. Such modularity improves computational performance and versatility and facilitates data integration. We validated our technology by reproducing known experimental results, including differentiation patterns of CD4+ T cells triggered by different combinations of cytokines, metabolic regulation by IL2 in these cells, and their response to influenza infection. In doing so, we added multi-scale insights to single-scale studies and demonstrated its predictive power by discovering switch-like and oscillatory behaviors of CD4+ T cells that arise from nonlinear dynamics interwoven across three scales. We identified the inflamed lymph node’s ability to retain naive CD4+ T cells as a key mechanism in generating these emergent behaviors. We envision our model and the generic framework encompassing it to serve as a tool for understanding cellular and molecular immunological problems through the lens of systems immunology.