Molecular basis for evolving modularity in the yeast protein interaction network

Scale-free networks are generically defined by a power-law distribution of node connectivities. Vastly different graph topologies fit this law, ranging from the assortative, with frequent similar-degree node connections, to a modular structure. Using a metric to determine the extent of modularity, we examined the yeast protein network and found it to be significantly self-dissimilar. By orthologous node categorization, we established the evolutionary trend in the network, from an “emerging” assortative network to a present-day modular topology. The evolving topology fits a generic connectivity distribution but with a progressive enrichment in intramodule hubs that avoid each other. Primeval tolerance to random node failure is shown to evolve toward resilience to hub failure, thus removing the fragility often ascribed to scale-free networks. This trend is algorithmically reproduced by adopting a connectivity accretion law that disfavors like-degree connections for large-degree nodes. The selective advantage of this trend relates to the need to prevent a failed hub from inducing failure in an adjacent hub. The molecular basis for the evolutionary trend is likely rooted in the high-entropy penalty entailed in the association of two intramodular hubs.     

Towards a large-scale model of patient-specific epileptic spike-wave discharges

Clinical electroencephalographic (EEG) recordings of the transition into generalised epileptic seizures show a sudden onset of spike-wave dynamics from a low-amplitude irregular background. In addition, non-trivial and variable spatio-temporal dynamics are widely reported in combined EEG/fMRI studies on the scale of the whole cortex. It is unknown whether these characteristics can be accounted for in a large-scale mathematical model with fixed heterogeneous long-range connectivities. Here, we develop a modelling framework with which to investigate such EEG features. We show that a neural field model composed of a few coupled compartments can serve as a low-dimensional prototype for the transition between irregular background dynamics and spike-wave activity. This prototype then serves as a node in a large-scale network with long-range connectivities derived from human diffusion-tensor imaging data. We examine multivariate properties in 42 clinical EEG seizure recordings from 10 patients diagnosed with typical absence epilepsy and 50 simulated seizures from the large-scale model using 10 DTI connectivity sets from humans. The model can reproduce the clinical feature of stereotypy where seizures are more similar within a patient than between patients, essentially creating a patient-specific fingerprint. We propose the approach as a feasible technique for the investigation of patient-specific large-scale epileptic features in space and time.     

Rules for connectivity of secondary structure elements in protein: Two–layer αβ sandwiches

In protein structures, the fold is described according to the spatial arrangement of secondary structure elements (SSEs: α‐helices and β‐strands) and their connectivity. The connectivity or the pattern of links among SSEs is one of the most important factors for understanding the variety of protein folds. In this study, we introduced the connectivity strings that encode the connectivities by using the types, positions, and connections of SSEs, and computationally enumerated all the connectivities of two‐layer αβ sandwiches. The calculated connectivities were compared with those in natural proteins determined using MICAN, a nonsequential structure comparison method. For 2α‐4β, among 23,000 of all connectivities, only 48 were free from irregular connectivities such as loop crossing. Of these, only 20 were found in natural proteins and the superfamilies were biased toward certain types of connectivities. A similar disproportional distribution was confirmed for most of other spatial arrangements of SSEs in the two‐layer αβ sandwiches. We found two connectivity rules that explain the bias well: the abundances of interlayer connecting loops that bridge SSEs in the distinct layers; and nonlocal β‐strand pairs, two spatially adjacent β‐strands located at discontinuous positions in the amino acid sequence. A two‐dimensional plot of these two properties indicated that the two connectivity rules are not independent, which may be interpreted as a rule for the cooperativity of proteins.     

SERPINE2 is a possible candidate promotor for lymph node metastasis in testicular cancer

Testicular germ cell tumors (TGCTs) commonly metastasize to the lymph node or lung. However, it remains unclear which genes are associated with TGCT metastasis. The aim of this study was to identify gene(s) that promoted human TGCT metastasis. We intraperitoneally administered conditioned medium (CM) from JKT-1, a cell-line from a human testicular seminoma, or JKT-HM, a JKT-1 cell sub-line with high metastatic potential, into mice with JKT-1 xenografts. Administration of CM from JKT-HM significantly promoted lymph node metastasis. A cDNA microarray analysis showed that JKT-HM cells highly expressed the Serpine peptidase inhibitor, clade E, member 2 (SERPINE2), which encodes a secreted protein. Administration of CM from SERPINE2-silenced JKT-HM cells inhibited lymph node metastasis in the xenograft model, compared with administration of CM from JKT-HM cells. There was no significant difference in xenograft volume. Moreover, administration of CM from SERPINE2-over-expressing JKT-1 was likely to promote lymph node metastasis in the xenograft model. There was no difference in the in vitro proliferation or migration of JKT-1 cells cultured with CM from JKT-HM cells, compared to that with CM from JKT-1. There was no promotion of proliferation or lymphangiogenesis in the xenografts, as measured by Ki-67 and LYVE-1 immunohistochemistry, respectively. Although we could not clarify how SERPINE2 promoted lymph node metastasis, it may be a promoter in the development of lymph node metastasis in the human seminoma cells in a mouse xenograft model.     

Partial correlation analysis for the identification of synaptic connections

In this paper, we investigate the use of partial correlation analysis for the identification of functional neural connectivity from simultaneously recorded neural spike trains. Partial correlation analysis allows one to distinguish between direct and indirect connectivities by removing the portion of the relationship between two neural spike trains that can be attributed to linear relationships with recorded spike trains from other neurons. As an alternative to the common frequency domain approach based on the partial spectral coherence we propose a new statistic in the time domain. The new scaled partial covariance density provides additional information on the direction and the type, excitatory or inhibitory, of the connectivities. In simulation studies, we investigated the power and limitations of the new statistic. The simulations show that the detectability of various connectivity patterns depends on various parameters such as connectivity strength and background activity. In particular, the detectability decreases with the number of neurons included in the analysis and increases with the recording time. Further, we show that the method can also be used to detect multiple direct connectivities between two neurons. Finally, the methods of this paper are illustrated by an application to neurophysiological data from spinal dorsal horn neurons.     

Identification of subpopulations from connectivity matrices

Dispersal on the landscape/seascape scale may lead to complex spatial population structure with non‐synchronous demography and genetic divergence. In this study we present a novel approach to identify subpopulations and dispersal barriers based on estimates of dispersal probabilities on the landscape scale. A theoretical framework is presented where the landscape connectivity matrix is analyzed for clusters as a signature of partially isolated subpopulations. Identification of subpopulations is formulated as a minimization problem with a tuneable penalty term that makes it possible to generate population subdivisions with varying degree of dispersal restrictions. We show that this approach produces superior results compared to alternative standard methods. We apply this theory to a dataset of modeled dispersal probabilities for a sessile marine invertebrate with free‐swimming larvae in the Baltic Sea. For a range of critical connectivities we produce a hierarchical partitioning into subpopulations spanning dispersal probabilities that are typical for both genetic divergence and demographic independence. The mapping of subpopulations suggests that the Baltic Sea includes a fine‐scale (100–600 km) mosaic of invisible dispersal barriers. An analysis of the present network of marine protected areas reveal that protection is very unevenly distributed among the suggested subpopulations. Our approach can be used to assess the location and strength of dispersal barriers in the landscape, and identify conservation units when extensive genotyping is prohibitively costly to cover necessary spatial and temporal scales, e.g. in spatial management of marine populations.     

Global snapshot of a protein interaction network-a percolation based approach

MOTIVATION: Biologically significant information can be revealed by modeling large-scale protein interaction data using graph theory based network analysis techniques. However, the methods that are currently being used draw conclusions about the global features of the network from local connectivity data. A more systematic approach would be to define global quantities that measure (1) how strongly a protein ties with the other parts of the network and (2) how significantly an interaction contributes to the integrity of the network, and connect them with phenotype data from other sources. In this paper, we introduce such global connectivity measures and develop a stochastic algorithm based upon percolation in random graphs to compute them. RESULTS: We show that, in terms of global connectivities, the distribution of essential proteins is distinct from the background. This observation highlights a fundamental difference between the essential and the non-essential proteins in the network. We also find that the interaction data obtained from different experimental methods such as immunoprecipitation and two-hybrid techniques contribute differently to network integrities. Such difference between different experimental methods can provide insight into the systematic bias present among these techniques. SUPPLEMENTARY INFORMATION: The full list of our results can be found in the supplemental web site http://www.nas.nasa.gov/Groups/SciTech/nano/msamanta/projects/percolation/index.php     

Comparing structural and functional graph theory features in the human brain using multimodal MRI

Recent advances in magnetic resonance imaging (MRI) are allowing neuroscientists to gain critical insights into the neural networks mediating a variety of cognitive processes. This work investigates structural and functional connectivity in the human brain under different experimental conditions through multimodal MRI acquisitions. To define the nodes of a full-brain network, a set of regions was identified from resting-state functional MRI (fMRI) data using spatial independent component analysis (sICA) and a hierarchical clustering technique. Diffusion-weighted imaging (DWI) data were acquired from the same subjects and a probabilistic fiber tracking method was used to estimate the structure of this network. Using features originating from graph theory, such as small-world properties and network efficiency, we characterized the structural and functional connectivities of the full-brain network and we compared them quantitatively. We showed that structural and functional networks shared some properties in terms of topology as measured by the distribution of the node degrees, hence supporting the existence of an underlying anatomical substrate for functional networks.     

The signaling petri net-based simulator: a non-parametric strategy for characterizing the dynamics of cell-specific signaling networks

Reconstructing cellular signaling networks and understanding how they work are major endeavors in cell biology. The scale and complexity of these networks, however, render their analysis using experimental biology approaches alone very challenging. As a result, computational methods have been developed and combined with experimental biology approaches, producing powerful tools for the analysis of these networks. These computational methods mostly fall on either end of a spectrum of model parameterization. On one end is a class of structural network analysis methods; these typically use the network connectivity alone to generate hypotheses about global properties. On the other end is a class of dynamic network analysis methods; these use, in addition to the connectivity, kinetic parameters of the biochemical reactions to predict the network's dynamic behavior. These predictions provide detailed insights into the properties that determine aspects of the network's structure and behavior. However, the difficulty of obtaining numerical values of kinetic parameters is widely recognized to limit the applicability of this latter class of methods. Several researchers have observed that the connectivity of a network alone can provide significant insights into its dynamics. Motivated by this fundamental observation, we present the signaling Petri net, a non-parametric model of cellular signaling networks, and the signaling Petri net-based simulator, a Petri net execution strategy for characterizing the dynamics of signal flow through a signaling network using token distribution and sampling. The result is a very fast method, which can analyze large-scale networks, and provide insights into the trends of molecules' activity-levels in response to an external stimulus, based solely on the network's connectivity. We have implemented the signaling Petri net-based simulator in the PathwayOracle toolkit, which is publicly available at http://bioinfo.cs.rice.edu/pathwayoracle. Using this method, we studied a MAPK1,2 and AKT signaling network downstream from EGFR in two breast tumor cell lines. We analyzed, both experimentally and computationally, the activity level of several molecules in response to a targeted manipulation of TSC2 and mTOR-Raptor. The results from our method agreed with experimental results in greater than 90% of the cases considered, and in those where they did not agree, our approach provided valuable insights into discrepancies between known network connectivities and experimental observations.     

Estimation of Directed Effective Connectivity from fMRI Functional Connectivity Hints at Asymmetries of Cortical Connectome

The brain exhibits complex spatio-temporal patterns of activity. This phenomenon is governed by an interplay between the internal neural dynamics of cortical areas and their connectivity. Uncovering this complex relationship has raised much interest, both for theory and the interpretation of experimental data (e.g., fMRI recordings) using dynamical models. Here we focus on the so-called inverse problem: the inference of network parameters in a cortical model to reproduce empirically observed activity. Although it has received a lot of interest, recovering directed connectivity for large networks has been rather unsuccessful so far. The present study specifically addresses this point for a noise-diffusion network model. We develop a Lyapunov optimization that iteratively tunes the network connectivity in order to reproduce second-order moments of the node activity, or functional connectivity. We show theoretically and numerically that the use of covariances with both zero and non-zero time shifts is the key to infer directed connectivity. The first main theoretical finding is that an accurate estimation of the underlying network connectivity requires that the time shift for covariances is matched with the time constant of the dynamical system. In addition to the network connectivity, we also adjust the intrinsic noise received by each network node. The framework is applied to experimental fMRI data recorded for subjects at rest. Diffusion-weighted MRI data provide an estimate of anatomical connections, which is incorporated to constrain the cortical model. The empirical covariance structure is reproduced faithfully, especially its temporal component (i.e., time-shifted covariances) in addition to the spatial component that is usually the focus of studies. We find that the cortical interactions, referred to as effective connectivity, in the tuned model are not reciprocal. In particular, hubs are either receptors or feeders: they do not exhibit both strong incoming and outgoing connections. Our results sets a quantitative ground to explore the propagation of activity in the cortex.     

城市生态网络空间评价及其格局优化

合理的城市生态网络空间格局对于保障城市生态环境可持续发展具有重要意义。以哈尔滨中心城区为研究区,基于景观生态学"斑块-廊道-基质"理论,识别研究区生态源、生态廊道、生态节点和生态基质,分析生态网络连接度强弱的空间分布情况,运用GIS技术和CA-Marcov模型对生态网络格局进行模拟优化。研究结果表明:(1)研究区内部生态源较外部生态源与外界联系较密切;周边地区生态源或生态节点与生态廊道连接数目较少;中北部与西南部生态廊道连接度较差,东部生态廊道连接度处于中等水平,中部个别生态廊道连接度较好;转入的大型生态用地大片集中,转入的小型生态用地零星分布。(2)优化后的生态源地在东西方向与南北方向形成集中连片态势,大型生态源地间彼此连接程度较高;大型生态源之间,以及大型生态源与小型生态源之间构成大型生态廊道,是研究区内主要生态廊道网络;研究区小型生态源之间构成小型生态廊道,是研究区内次要生态廊道网络;研究区周边及研究区中心处60%的区域为生态节点盲区,应加强生态节点盲区生态建设;新增加的大部分生态用地,主要集中分布在水域生态源地周边,还有部分分布在绿地生态源地和风景区生态源地周边,其余少量新增加的生态用地零星分布在林地生态源地周边。研究成果为中心城区尺度的生态环境保护和城市规划提供科学的依据。     

Bacterial Protein Interaction Networks: Connectivity is Ruled by Gene Conservation,Essentiality and Function

BackgroundProtein-protein interaction (PPI) networks are the backbone of all processes in living cells. In this work, we relate conservation, essentiality and functional repertoire of a gene to the connectivity k (i.e. the number of interactions, links) of the corresponding protein in the PPI network.MethodsOn a set of 42 bacterial genomes of different sizes, and with reasonably separated evolutionary trajectories, we investigate three issues: i) whether the distribution of connectivities changes between PPI subnetworks of essential and nonessential genes; ii) how gene conservation, measured both by the evolutionary retention index (ERI) and by evolutionary pressures, is related to the connectivity of the corresponding protein; iii) how PPI connectivities are modulated by evolutionary and functional relationships, as represented by the Clusters of Orthologous Genes (COGs).ResultsWe show that conservation, essentiality and functional specialisation of genes constrain the connectivity of the corresponding proteins in bacterial PPI networks. In particular, we isolated a core of highly connected proteins (connectivities k≥40), which is ubiquitous among the species considered here, though mostly visible in the degree distributions of bacteria with small genomes (less than 1000 genes).ConclusionThe genes that support this highly connected core are conserved, essential and, in most cases, belong to the COG cluster J, related to ribosomal functions and the processing of genetic information.     

Optimizing the connectivity in disulfide-rich peptides: alpha-conotoxin SII as a case study

We describe a strategy for the efficient, unambiguous assignment of disulfide connectivities in alpha-conotoxin SII, of which approximately 30% of its mass is cysteine, as an example of a generalizable technique for investigation of cysteine-rich peptides. alpha-Conotoxin SII was shown to possess 3-8, 2-18, and 4-14 disulfide bond connectivity. Sequential disulfide bond connectivity analysis was performed by partial reduction with Tris(2-carboxyethyl)phosphine and real-time mass monitoring by direct-infusion electrospray mass spectrometry (ESMS). This method achieved high yields of the differentially reduced disulfide bonded intermediates and economic use of reduced peptide. Intermediates were alkylated with either N-phenylmaleimide or 4-vinylpyridine. The resulting alkyl products were assigned by ESMS and their alkyl positions sequentially identified via conventional Edman degradation. The methodology described allows a more efficient, rapid, and reliable assignment of disulfide bond connectivity in synthetic and native cysteine-rich peptides.     

CD-Based Indices for Link Prediction in Complex Network

Lots of similarity-based algorithms have been designed to deal with the problem of link prediction in the past decade. In order to improve prediction accuracy, a novel cosine similarity index CD based on distance between nodes and cosine value between vectors is proposed in this paper. Firstly, node coordinate matrix can be obtained by node distances which are different from distance matrix and row vectors of the matrix are regarded as coordinates of nodes. Then, cosine value between node coordinates is used as their similarity index. A local community density index LD is also proposed. Then, a series of CD-based indices include CD-LD-k, CD*LD-k, CD-k and CDI are presented and applied in ten real networks. Experimental results demonstrate the effectiveness of CD-based indices. The effects of network clustering coefficient and assortative coefficient on prediction accuracy of indices are analyzed. CD-LD-k and CD*LD-k can improve prediction accuracy without considering the assortative coefficient of network is negative or positive. According to analysis of relative precision of each method on each network, CD-LD-k and CD*LD-k indices have excellent average performance and robustness. CD and CD-k indices perform better on positive assortative networks than on negative assortative networks. For negative assortative networks, we improve and refine CD index, referred as CDI index, combining the advantages of CD index and evolutionary mechanism of the network model BA. Experimental results reveal that CDI index can increase prediction accuracy of CD on negative assortative networks.     

Hyperthermia-Induced Disruption of Functional Connectivity in the Human Brain Network

Background

Passive hyperthermia is a potential risk factor to human cognitive performance and work behavior in many extreme work environments. Previous studies have demonstrated significant effects of passive hyperthermia on human cognitive performance and work behavior. However, there is a lack of a clear understanding of the exact affected brain regions and inter-regional connectivities.

Methodology and Principal Findings

We simulated 1 hour environmental heat exposure to thirty-six participants under two environmental temperature conditions (25°C and 50°C), and collected resting-state functional brain activity. The functional connectivities with a preselected region of interest (ROI) in the posterior cingulate cortex and precuneus (PCC/PCu), furthermore, inter-regional connectivities throughout the entire brain using a prior Anatomical Automatic Labeling (AAL) atlas were calculated. We identified decreased correlations of a set of regions with the PCC/PCu, including the medial orbitofrontal cortex (mOFC) and bilateral medial temporal cortex, as well as increased correlations with the partial orbitofrontal cortex particularly in the bilateral orbital superior frontal gyrus. Compared with the normal control (NC) group, the hyperthermia (HT) group showed 65 disturbed functional connectivities with 50 of them being decreased and 15 of them being increased. While the decreased correlations mainly involved with the mOFC, temporal lobe and occipital lobe, increased correlations were mainly located within the limbic system. In consideration of physiological system changes, we explored the correlations of the number of significantly altered inter-regional connectivities with differential rectal temperatures and weight loss, but failed to obtain significant correlations. More importantly, during the attention network test (ANT) we found that the number of significantly altered functional connectivities was positively correlated with an increase in executive control reaction time.

Conclusions/Significance

We first identified the hyperthermia-induced altered functional connectivity patterns. The changes in the functional connectivity network might be a possible explanation for the cognitive performance and work behavior alteration.     

Structure and folding of disulfide-rich miniproteins: insights from molecular dynamics simulations and MM-PBSA free energy calculations

The fold of small disulfide-rich proteins largely relies on two or more disulfide bridges that are main components of the hydrophobic core. Because of the small size of these proteins and their high cystine content, the cysteine connectivity has been difficult to ascertain in some cases, leading to uncertainties and debates in the literature. Here, we use molecular dynamics simulations and MM-PBSA free energy calculations to compare similar folds with different disulfide pairings in two disulfide-rich miniprotein families, namely the knottins and the short-chain scorpion toxins, for which the connectivity has been discussed. We first show that the MM-PBSA approach is able to discriminate the correct knotted topology of knottins from the laddered one. Interestingly, a comparison of the free energy components for kalata B1 and MCoTI-II suggests that cyclotides and squash inhibitors, although sharing the same scaffold, are stabilized through different interactions. Application to short-chain scorpion toxins suggests that the conventional cysteine pairing found in many homologous toxins is significantly more stable than the unconventional pairing reported for maurotoxin and for spinoxin. This would mean that native maurotoxin and spinoxin are not at the lowest free energy minimum and might result from kinetically rather than thermodynamically driven oxidative folding processes. For both knottins and toxins, the correct or conventional disulfide connectivities provide lower flexibilities and smaller deviations from the initial conformations. Overall, our work suggests that molecular dynamics simulations and the MM-PBSA approach to estimate free energies are useful tools to analyze and compare disulfide bridge connectivities in miniproteins.     

Optimal Balance of the Striatal Medium Spiny Neuron Network

Slowly varying activity in the striatum, the main Basal Ganglia input structure, is important for the learning and execution of movement sequences. Striatal medium spiny neurons (MSNs) form cell assemblies whose population firing rates vary coherently on slow behaviourally relevant timescales. It has been shown that such activity emerges in a model of a local MSN network but only at realistic connectivities of and only when MSN generated inhibitory post-synaptic potentials (IPSPs) are realistically sized. Here we suggest a reason for this. We investigate how MSN network generated population activity interacts with temporally varying cortical driving activity, as would occur in a behavioural task. We find that at unrealistically high connectivity a stable winners-take-all type regime is found where network activity separates into fixed stimulus dependent regularly firing and quiescent components. In this regime only a small number of population firing rate components interact with cortical stimulus variations. Around connectivity a transition to a more dynamically active regime occurs where all cells constantly switch between activity and quiescence. In this low connectivity regime, MSN population components wander randomly and here too are independent of variations in cortical driving. Only in the transition regime do weak changes in cortical driving interact with many population components so that sequential cell assemblies are reproducibly activated for many hundreds of milliseconds after stimulus onset and peri-stimulus time histograms display strong stimulus and temporal specificity. We show that, remarkably, this activity is maximized at striatally realistic connectivities and IPSP sizes. Thus, we suggest the local MSN network has optimal characteristics – it is neither too stable to respond in a dynamically complex temporally extended way to cortical variations, nor is it too unstable to respond in a consistent repeatable way. Rather, it is optimized to generate stimulus dependent activity patterns for long periods after variations in cortical excitation.     

Solution structure of recombinant somatomedin B domain from vitronectin produced in Pichia pastoris

The cysteine-rich somatomedin B domain (SMB) of the matrix protein vitronectin is involved in several important biological processes. First, it stabilizes the active conformation of the plasminogen activator inhibitor (PAI-1); second, it provides the recognition motif for cell adhesion via the cognate integrins (alpha(v)beta(3), alpha(v)beta(5), and alpha(IIb)beta(3)); and third, it binds the complex between urokinase-type plasminogen activator (uPA) and its glycolipid-anchored receptor (uPAR). Previous structural studies on SMB have used recombinant protein expressed in Escherichia coli or SMB released from plasma-derived vitronectin by CNBr cleavage. However, different disulfide patterns and three-dimensional structures for SMB were reported. In the present study, we have expressed recombinant human SMB by two different eukaryotic expression systems, Pichia pastoris and Drosophila melanogaster S2-cells, both yielding structurally and functionally homogeneous protein preparations. Importantly, the entire population of our purified, recombinant SMB has a solvent exposure, both as a free domain and in complex with PAI-1, which is indistinguishable from that of plasma-derived SMB as assessed by amide hydrogen ((1)H/(2)H) exchange. This solvent exposure was only reproduced by one of three synthetic SMB products with predefined disulfide connectivities corresponding to those published previously. Furthermore, this connectivity was also the only one to yield a folded and functional domain. The NMR structure was determined for free SMB produced by Pichia and is largely consistent with that solved by X-ray crystallography for SMB in complex with PAI-1.     

Quantifying gene network connectivity in silico: scalability and accuracy of a modular approach

Large, complex data sets that are generated from microarray experiments, create a need for systematic analysis techniques to unravel the underlying connectivity of gene regulatory networks. A modular approach, previously proposed by Kholodenko and co-workers, helps to scale down the network complexity into more computationally manageable entities called modules. A functional module includes a gene's mRNA, promoter and resulting products, thus encompassing a large set of interacting states. The essential elements of this approach are described in detail for a three-gene model network and later extended to a ten-gene model network, demonstrating scalability. The network architecture is identified by analysing in silico steady-state changes in the activities of only the module outputs, communicating intermediates, that result from specific perturbations applied to the network modules one at a time. These steady-state changes form the system response matrix, which is used to compute the network connectivity or network interaction map. By employing a known biochemical network, the accuracy of the modular approach and its sensitivity to key assumptions are evaluated.