Template-based intervention in Boolean network models of biological systems

Motivation

A grand challenge in the modeling of biological systems is the identification of key variables which can act as targets for intervention. Boolean networks are among the simplest of models, yet they have been shown to adequately model many of the complex dynamics of biological systems. In our recent work, we utilized a logic minimization approach to identify quality single variable targets for intervention from the state space of a Boolean network. However, as the number of variables in a network increases, the more likely it is that a successful intervention strategy will require multiple variables. Thus, for larger networks, such an approach is required in order to identify more complex intervention strategies while working within the limited view of the network’s state space. Specifically, we address three primary challenges for the large network arena: the first challenge is how to consider many subsets of variables, the second is to design clear methods and measures to identify the best targets for intervention in a systematic way, and the third is to work with an intractable state space through sampling.

Results

We introduce a multiple variable intervention target called a template and show through simulation studies of random networks that these templates are able to identify top intervention targets in increasingly large Boolean networks. We first show that, when other methods show drastic loss in performance, template methods show no significant performance loss between fully explored and partially sampled Boolean state spaces. We also show that, when other methods show a complete inability to produce viable intervention targets in sampled Boolean state spaces, template methods maintain significantly consistent success rates even as state space sizes increase exponentially with larger networks. Finally, we show the utility of the template approach on a real-world Boolean network modeling T-LGL leukemia.

Conclusions

Overall, these results demonstrate how template-based approaches now effectively take over for our previous single variable approaches and produce quality intervention targets in larger networks requiring sampled state spaces.

     

Boolean dynamics of Kauffman models with a scale-free network

We studied the Boolean dynamics of the "quenched" Kauffman models with a directed scale-free network, comparing with that of the original directed random Kauffman networks and that of the directed exponential-fluctuation networks. We have numerically investigated the distributions of the state cycle lengths and its changes as the network size N and the average degree k of nodes increase. In the relatively small network (N approximately 150), the median, the mean value and the standard deviation grow exponentially with N in the directed scale-free and the directed exponential-fluctuation networks with k=2, where the function forms of the distributions are given as an almost exponential. We have found that for the relatively large N approximately 10(3) the growth of the median of the distribution over the attractor lengths asymptotically changes from algebraic type to exponential one as the average degree k goes to k=2. The result supports the existence of the transition at k(c)=2 derived in the annealed model.     

Boolean network simulations for life scientists

Background

We present a C++ class library for Monte Carlo simulation of molecular systems, including proteins in solution. The design is generic and highly modular, enabling multiple developers to easily implement additional features. The statistical mechanical methods are documented by extensive use of code comments that – subsequently – are collected to automatically build a web-based manual.

Results

We show how an object oriented design can be used to create an intuitively appealing coding framework for molecular simulation. This is exemplified in a minimalistic C++ program that can calculate protein protonation states. We further discuss performance issues related to high level coding abstraction.

Conclusion

C++ and the Standard Template Library (STL) provide a high-performance platform for generic molecular modeling. Automatic generation of code documentation from inline comments has proven particularly useful in that no separate manual needs to be maintained.     

Likelihood-based inference for stochastic models of sexual network formation

Sexually-transmitted diseases (STDs) constitute a major public health concern. Mathematical models for the transmission dynamics of STDs indicate that heterogeneity in sexual activity level allow them to persist even when the typical behavior of the population would not support endemicity. This insight focuses attention on the distribution of sexual activity level in a population. In this paper, we develop several stochastic process models for the formation of sexual partnership networks. Using likelihood-based model selection procedures, we assess the fit of the different models to three large distributions of sexual partner counts: (1) Rakai, Uganda, (2) Sweden, and (3) the USA. Five of the six single-sex networks were fit best by the negative binomial model. The American women's network was best fit by a power-law model, the Yule. For most networks, several competing models fit approximately equally well. These results suggest three conclusions: (1) no single unitary process clearly underlies the formation of these sexual networks, (2) behavioral heterogeneity plays an essential role in network structure, (3) substantial model uncertainty exists for sexual network degree distributions. Behavioral research focused on the mechanisms of partnership formation will play an essential role in specifying the best model for empirical degree distributions. We discuss the limitations of inferences from such data, and the utility of degree-based epidemiological models more generally.     

Identification of control targets in Boolean molecular network models via computational algebra

Background

Many problems in biomedicine and other areas of the life sciences can be characterized as control problems, with the goal of finding strategies to change a disease or otherwise undesirable state of a biological system into another, more desirable, state through an intervention, such as a drug or other therapeutic treatment. The identification of such strategies is typically based on a mathematical model of the process to be altered through targeted control inputs. This paper focuses on processes at the molecular level that determine the state of an individual cell, involving signaling or gene regulation. The mathematical model type considered is that of Boolean networks. The potential control targets can be represented by a set of nodes and edges that can be manipulated to produce a desired effect on the system.

Results

This paper presents a method for the identification of potential intervention targets in Boolean molecular network models using algebraic techniques. The approach exploits an algebraic representation of Boolean networks to encode the control candidates in the network wiring diagram as the solutions of a system of polynomials equations, and then uses computational algebra techniques to find such controllers. The control methods in this paper are validated through the identification of combinatorial interventions in the signaling pathways of previously reported control targets in two well studied systems, a p53-mdm2 network and a blood T cell lymphocyte granular leukemia survival signaling network. Supplementary data is available online and our code in Macaulay2 and Matlab are available via http://www.ms.uky.edu/~dmu228/ControlAlg.

Conclusions

This paper presents a novel method for the identification of intervention targets in Boolean network models. The results in this paper show that the proposed methods are useful and efficient for moderately large networks.

     

Analysis of feedback loops and robustness in network evolution based on Boolean models

Background  

Many biological networks such as protein-protein interaction networks, signaling networks, and metabolic networks have topological characteristics of a scale-free degree distribution. Preferential attachment has been considered as the most plausible evolutionary growth model to explain this topological property. Although various studies have been undertaken to investigate the structural characteristics of a network obtained using this growth model, its dynamical characteristics have received relatively less attention.     

Ribonucleic acid within the extracellular matrix during embryonic tooth formation

During embryonic tooth formation, interactions between epithelial and mesenchymal cells results in the formation of a metachromatic interface or extracellular matrix. The cervical or germinative region of this epidermal organ system is populated by an increasing gradient of cellular differentiation and an extracellular matrix which is the progenitor for subsequent dentine organic matrix formation. Embryonic rabbit tooth primordia can be maintained in culture enabling kinetic studies of labeled precursor incorporation. Autoradiographs of tooth organ cultures continusly incubated with labeled uridine for periods up to eight hours, demonstrated initial cellular incorporation with subsequent transfer of 2% of the grain density to the extracellular matrix by four hours. The grain density was removed by ribonuclease treatment. No incorporation of tritiated thymidine into the matrix was observed. The incorporation of C¹⁴-uridine during organ culture was inhibited by actinomycin D. Micrurgy was employed to isolate the extracellular matrix free of adherent cells. Electron microscopy demonstrated membrane-bound, electron dense bodies within the matrix, presumably cytoplasmic extensions. No cells per se were observed on the isolated matrix. Several experimental criteria suggested that uridine incorporation into the extracellular matrix was regulated by epithelial and mesenchymal cells. Phenol extraction procedures of labeled cervical matrices demonstrated an ultraviolet absorption maximum at 260 μU. Both spectrophotometric determinations and orcinol assays found RNA to be 0.4–0.5% of the cervical extracellular matrix. These results are interpreted to indicate that RNA is a component of the metachromatic extracellular matrix during epithelio-mensenchymal interactions associated with tooth formation. The functional significance of these observations is premature at this time.     

Brain extracellular matrix

The extracellular matrix of the adult brain tissue has a uniquecomposition. The striking feature of this matrix is the prominenceof lecticans, proteoglycans that contain a lectin domain anda hyaluronic acid-binding domain. Hyaluronic acid and tenascinfamily adhesive/anti-adhesive proteins are also abundant. Matrixproteins common in other tissues are nearly absent in adultbrain. The brain extracellular matrix appears to have trophiceffects on neuronal cells and affect neurite outgrowth. Theunique composition of this matrix may be responsible for theresistance of brain tissue toward invasion by tumors of non-neuronalorigin. extracellular matrix lectican versican review     

Disjunctive models of Boolean category learning

Four connectionistic/neural models which are capable of learning arbitrary Boolean functions are presented. Three are provably convergent, but of differing generalization power. The fourth is not necessarily convergent, but its empirical behavior is quite good. The time and space characteristics of the four models are compared over a diverse range of functions and testing conditions. These include the ability to learn specific instances, to effectively generalize, and to deal with irrelevant or redundant information. Trade-offs between time and space are demonstrated by the various approaches.     

Mean-field Boolean network model of a signal transduction network

In this paper we provide a mean-field Boolean network model for a signal transduction network of a generic fibroblast cell. The network consists of several main signaling pathways, including the receptor tyrosine kinase, the G-protein coupled receptor, and the Integrin signaling pathway. The network consists of 130 nodes, each representing a signaling molecule (mainly proteins). Nodes are governed by Boolean dynamics including canalizing functions as well as totalistic Boolean functions that depend only on the overall fraction of active nodes. We categorize the Boolean functions into several different classes. Using a mean-field approach we generate a mathematical formula for the probability of a node becoming active at any time step. The model is shown to be a good match for the actual network. This is done by iterating both the actual network and the model and comparing the results numerically. Using the Boolean model it is shown that the system is stable under a variety of parameter combinations. It is also shown that this model is suitable for assessing the dynamics of the network under protein mutations. Analytical results support the numerical observations that in the long-run at most half of the nodes of the network are active.     

The influence of extracellular matrix on reversible gap junction formation in vitro

In vivo gap junctions (gj) are common in the subumbrellar plate endoderm of anthomedusa. When isolated and cultivated in artificial sea water the tissue, consisting of one cell type only, forms a spheroid in which all gap junctions disappear. Gap junction (gj) formation can, however, be induced by attachment and consecutive spreading of the endodermal tissue (spheroid) on stretched extracellular matrix (ECM) material isolated from the polyp stage (with Ca2+-Mg2+-free sea water, without EDTA). Formation, and loss of gj is reversible and strictly corresponds with the alteration from the monolayer 'spread' (on stretched ECM) to 'spheroid' arrangement (no ECM) of the endodermal cells. The functional competence of induced gj is ascertained by injection of Lucifer Yellow, and the transfer of the dye is used to map the pattern of communication. The experimental conditions that result in gj formation simulate the in vivo situation of the endoderm. The influence of the ECM on gj formation, and the structural organization of the isolated endodermal tissue in this well defined in vitro system are discussed.     

Studies of extracellular fibronectin matrix formation with fluoresceinated fibronectin and fibronectin fragments

Fluorescein isothiocyanate conjugated human plasma fibronectin, 70-kDa collagen-binding, 60-kDa central, 60-kDa heparin-binding, 180-kDa heparin, collagen-binding fibronectin fragments and gelatin were used to study extracellular fibronectin matrix formation. Exogenous fibronectin, gelatin, 70-kDa collagen-binding and 180-kDa heparin, collagen-binding fragments were shown to be able to bind specifically to preexisting extracellular matrix of living fibroblasts. The results suggest that: (i) Fibronectin matrix formation may occur through a self-assembly process; (ii) the NH2-terminal part of fibronectin is responsible for fibronectin-fibronectin interaction during fibronectin fibril formation; (iii) plasma fibronectin may be the source for tissue fibronectin.     

Spatial anisotropies and temporal fluctuations in extracellular matrix network texture during early embryogenesis

Early stages of vertebrate embryogenesis are characterized by a remarkable series of shape changes. The resulting morphological complexity is driven by molecular, cellular, and tissue-scale biophysical alterations. Operating at the cellular level, extracellular matrix (ECM) networks facilitate cell motility. At the tissue level, ECM networks provide material properties required to accommodate the large-scale deformations and forces that shape amniote embryos. In other words, the primordial biomaterial from which reptilian, avian, and mammalian embryos are molded is a dynamic composite comprised of cells and ECM. Despite its central importance during early morphogenesis we know little about the intrinsic micrometer-scale surface properties of primordial ECM networks. Here we computed, using avian embryos, five textural properties of fluorescently tagged ECM networks--(a) inertia, (b) correlation, (c) uniformity, (d) homogeneity, and (e) entropy. We analyzed fibronectin and fibrillin-2 as examples of fibrous ECM constituents. Our quantitative data demonstrated differences in the surface texture between the fibronectin and fibrillin-2 network in Day 1 (gastrulating) embryos, with the fibronectin network being relatively coarse compared to the fibrillin-2 network. Stage-specific regional anisotropy in fibronectin texture was also discovered. Relatively smooth fibronectin texture was exhibited in medial regions adjoining the primitive streak (PS) compared with the fibronectin network investing the lateral plate mesoderm (LPM), at embryonic stage 5. However, the texture differences had changed by embryonic stage 6, with the LPM fibronectin network exhibiting a relatively smooth texture compared with the medial PS-oriented network. Our data identify, and partially characterize, stage-specific regional anisotropy of fibronectin texture within tissues of a warm-blooded embryo. The data suggest that changes in ECM textural properties reflect orderly time-dependent rearrangements of a primordial biomaterial. We conclude that the ECM microenvironment changes markedly in time and space during the most important period of amniote morphogenesis--as determined by fluctuating textural properties.     

Cellular transglutaminase has affinity for extracellular matrix

Summary Cellular transglutaminase (TGase) was demonstrated as an intracellular enzyme by immunofluorescence in WI-38 cells. Following cell membrane perturbation by Triton X-100 treatment, TGase was bound to the extracellular matrix and was found to coexist with fibronectin as visualized by immunofluorescence microscopy. The binding of TGase to the cell matrix was blocked by anti-fibronectin antibody. Exogenous sources of soluble TGase were transferred to the extracellular matrix of an untreated or methanol fixed cell. The experimental data indicated that “particulate bound” TGase is a consequence of soluble TGase binding to the extracellular matrix following cell rupture. Editor's statement This report suggest that “particulate bound” transglutaminase may be a consequence of affinity of soluble enzyme for specific molecules in extracellular matrix and opens up a means to characterize transglutaminase binding sites in the matrix.