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.     

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.

     

Effects of boron derivatives on extracellular matrix formation

Boric acid solution (3%) dramatically improves wound healing through action on the extracellular matrix, a finding that has been obtained in vitro. Consequently, investigations are presently underway to produce boronated compounds having a therapeutical effectiveness similar to that of boric acid. On the basis of experimental results obtained with boric acid, we examined the effects of boron derivatives on extracellular matrix formation and degradation and analyzed their potential toxicity by using two biological models (chick embryo cartilage and human fibroblasts). The four boron derivatives tested in this study (triethanolamine borate; N-diethyl-phosphoramidate-propylboronique acid; 2,2 dimethylhexyl-1,3-propanediol-aminopropylboronate and 1,2 propanediol-aminopropylboronate) mimicked the effects of boric acid. They induced a decrease of intracellular concentrations in extracellular matrix macromolecules (proteoglycans, proteins)-associated with an increase of their release in culture medium and stimulated the activity of intra- and extracellular proteases. Similarly to boric acid, these actions occurred after exposure of the cells to concentrations of all boron derivatives without apparent toxic effects. The compounds were found to be more toxic than boric acid itself when concentrations were calculated according to their molecular weight. Nevertheless, these in vitro preliminary results demonstrate effects of boron derivatives that may be of therapeutic benefit in wound repair.     

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.

     

A viscoelastic two-dimensional network model of the lung extracellular matrix

Biomechanics and Modeling in Mechanobiology - The extracellular matrix (ECM) comprises a large proportion of the lung parenchymal tissue and is an important contributor to the mechanical properties...     

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.     

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.     

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     

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.     

Activity-dependent formation and functions of chondroitin sulfate-rich extracellular matrix of perineuronal nets

Extracellular matrix molecules--including chondroitin sulfate proteoglycans, hyaluronan, and tenascin-R--are enriched in perineuronal nets (PNs) associated with subsets of neurons in the brain and spinal cord. In the present study, we show that similar cell type-dependent extracellular matrix aggregates are formed in dissociated cell cultures prepared from early postnatal mouse hippocampus. Starting from the 5th day in culture, accumulations of lattice-like extracellular structures labeled with Wisteria floribunda agglutinin were detected at the cell surface of parvalbumin-expressing interneurons, which developed after 2-3 weeks into conspicuous PNs localized around synaptic contacts at somata and proximal dendrites, as well as around axon initial segments. Physiological recording and intracellular labeling of PN-expressing neurons revealed that these are large fast-spiking interneurons with morphological characteristics of basket cells. To study mechanisms of activity-dependent formation of PNs, we performed pharmacological analysis and found that blockade of action potentials, transmitter release, Ca2+ permeable AMPA subtype of glutamate receptors or L-type Ca2+ voltage-gated channels strongly decreased the extracellular accumulation of PN components in cultured neurons. Thus, we suggest that Ca2+ influx via AMPA receptors and L-type channels is necessary for activity-dependent formation of PNs. To study functions of chondroitin sulfate-rich PNs, we treated cultures with chondroitinase ABC that resulted in a prominent reduction of several major PN components. Removal of PNs did not affect the number and distribution of perisomatic GABAergic contacts but increased the excitability of interneurons in cultures, implicating the extracellular matrix of PNs in regulation of interneuronal activity.     

The extracellular matrix and blood vessel formation: not just a scaffold

The extracellular matrix plays a number of important roles, among them providing structural support and information to cellular structures such as blood vessels imbedded within it. As more complex organisms have evolved, the matrix ability to direct signalling towards the vasculature and remodel in response to signalling from the vasculature has assumed progressively greater importance. This review will focus on the molecules of the extracellular matrix, specifically relating to vessel formation and their ability to signal to the surrounding cells to initiate or terminate processes involved in blood vessel formation.     

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.     

State reduction for network intervention in probabilistic Boolean networks

MOTIVATION: A key goal of studying biological systems is to design therapeutic intervention strategies. Probabilistic Boolean networks (PBNs) constitute a mathematical model which enables modeling, predicting and intervening in their long-run behavior using Markov chain theory. The long-run dynamics of a PBN, as represented by its steady-state distribution (SSD), can guide the design of effective intervention strategies for the modeled systems. A major obstacle for its application is the large state space of the underlying Markov chain, which poses a serious computational challenge. Hence, it is critical to reduce the model complexity of PBNs for practical applications. RESULTS: We propose a strategy to reduce the state space of the underlying Markov chain of a PBN based on a criterion that the reduction least distorts the proportional change of stationary masses for critical states, for instance, the network attractors. In comparison to previous reduction methods, we reduce the state space directly, without deleting genes. We then derive stationary control policies on the reduced network that can be naturally induced back to the original network. Computational experiments study the effects of the reduction on model complexity and the performance of designed control policies which is measured by the shift of stationary mass away from undesirable states, those associated with undesirable phenotypes. We consider randomly generated networks as well as a 17-gene gastrointestinal cancer network, which, if not reduced, has a 2(17) × 2(17) transition probability matrix. Such a dimension is too large for direct application of many previously proposed PBN intervention strategies.