Recent advances in integrated electronic devices motivated the use of Wireless Sensor Networks (WSNs) in many applications including domain surveillance and mobile target tracking, where a number of sensors are scattered within a sensitive region to detect the presence of intruders and forward related events to some analysis center(s). Obviously, sensor deployment should guarantee an optimal event detection rate and should reduce coverage holes. Most of the coverage control approaches proposed in the literature deal with two-dimensional zones and do not develop strategies to handle coverage in three-dimensional domains, which is becoming a requirement for many applications including water monitoring, indoor surveillance, and projectile tracking. This paper proposes efficient techniques to detect coverage holes in a 3D domain using a finite set of sensors, repair the holes, and track hostile targets. To this end, we use the concepts of Voronoi tessellation, Vietoris complex, and retract by deformation. We show in particular that, through a set of iterative transformations of the Vietoris complex corresponding to the deployed sensors, the number of coverage holes can be computed with a low complexity. Mobility strategies are also proposed to repair holes by moving appropriately sensors towards the uncovered zones. The tracking objective is to set a non-uniform WSN coverage within the monitored domain to allow detecting the target(s) by the set of sensors. We show, in particular, how the proposed algorithms adapt to cope with obstacles. Simulation experiments are carried out to analyze the efficiency of the proposed models. To our knowledge, repairing and tracking is addressed for the first time in 3D spaces with different sensor coverage schemes. This is because a sensor can detect the occurrence of events or the presence of hostile targets only if they are within its sensing range. Coverage reflects how well a zone is monitored or a system is tracked by sensors. Therefore, the WSN detection performance depends on how well the wireless sensors observe the physical space under control.Several metrics have been provided in the literature to measure the quality of coverage. Among these metrics, one can mention the following: (a) the number of coverage holes; (b) the proportion of uncovered area with respect to the area under monitoring; and (c) the so called Average Linear Uncovered Length (ALUL), which has been developed in 2D zones to estimate the average distance a mobile target can traverse before being detected by one sensor . The ALUObstacles in monitored 3D domains may complicate seriously the role of the monitoring sensors, increase their power consumption, and limit the coverage efficiency of the process providing coverage control ,3. ProceThe definition proposed to distributively reduce the Rips complex associated to the sensors is general, in the sense that it applies to a large variety of sensor, detection techniques, monitored domains, and obstacles.The proposed cooperative coverage repairing approach considerably reduces the uncovered areas and provides efficient handling of obstacles with respect to existing methods. The detection and localization of holes is done with low complexity.We show that the higher-order Voronoi tessellations we utilize are useful for performing multiple tasks including activity scheduling and coordination. In addition, we show that local coverage information, when gathered using the Voronoi diagram, can be used to implement coverage preserving mobility models.This paper proposes a coverage assessment approach amenable to implement advanced target tracking functionalities. First, it provides a technique based on the concept of retraction by deformation applied to a special space, called the Rips complex, associated with the deployment of a set of sensors to develop a low complexity algorithm for locating coverage holes. Second, it constructs a collaborative mechanism to repair coverage holes, assuming that the sensors have mobility capabilities. Third, the paper builds on higher-order Voronoi diagrams to define an efficient scheme to coordinate tracking activities of single and multiple targets. To the best of our knowledge, this is the first time where retraction by deformation and higher-order Voronoi tessellations are used for hole assessment and target tracking in 3D domains with obstacles using sensors. The major contributions of this paper are as follows:The remaining part of this paper is organized as follows: Section 2 describes the state of the art of coverage control in various areas in general and in 3D spaces in particular. Section 3 surveys the definition of the mathematical objects needed for coverage and tracking control, the Vietoris complex and the Voronoi diagram and discusses the retraction by deformation. Section 4 discusses different schemes based on the Vietoris complex to detect and count the coverage holes in 3D domains, locate these holes, and repair them. It also defines a special procedure to reduce the complexity of the Vietoris complexes without modifying their topological properties. Section 5 sets up models for coverage assessment, sensor mobility, and target tracking. Section 6 analyzes the complexity of the algorithms constructed in this paper and sets some extensions of our results to more general types of sensors. Section 7 develops simulation experiments to evaluate the performance of a monitoring system implementing our techniques. Section 8 concludes this paper.2.Studies on coverage, holes, and boundary detection have been addressed using three main categories of techniques: geometric methods, statistical/probabilistic methods, and topological methods.et al.  and passing by its middle point and by H the half space of R3 containing the p and delimited by B. Thus, B and H are expressed as follows:Let us assume that the sensors in MH  and MB  the intersection of H and B with M, respectively.We also denote by p ∈ S is nothing but the common area to the (|S| − 1) closed half spaces containing p involving the other sensors. Therefore, the Voronoi cell generated by p is expressed by:The Voronoi cell generated by SV(p) ∩ SV(q) is included in H. It can be a plane, a half plane, an edge, a point, or an empty set. The Voronoi diagram associated to the set S of sensors deployed to monitor M is the unique subdivision defined in R3 by the Voronoi cells associated to all sensors. Thus, every cell of the subdivision contains the nearest neighbors defined in S for a sensor p. The Voronoi diagram of S is the set of point belonging to the all the Voronoi cell. Hence we have:The Voronoi cell of a sensor is convex and contractible. The common boundary of two Voronoi cells DV(S) has no vertices and no edges when the sensors are located at collinear points. In that case, the faces of the Voronoi diagram are parallel planes. In addition, one can notice that when p ∈ S lies on the boundary of the convex hull of S, then the Voronoi cell of p is unbounded in R3.In particular, the Voronoi diagram M into cells according to k-nearest neighbors in S, for a given integer 1 ≤ k ≤ n − 1, we turn now to the definition of the High-order Voronoi diagrams, as they are useful concepts to define these sets and support target tracking. An order k Voronoi diagram is defined as follows: Let T ⊂ S containing k sensors, the T-generated cell is defined byk Voronoi diagram is given by:Since in this paper, we are rather interested in partitioning a domain DSV, that V(T) can be empty, and that DV(S) induces a partition on the domain M into bounded components.One can easily see that the order 1 Voronoi diagram 3.2.S = {v1,..., nv} corresponding to the locations of a set of sensor nodes in a 3D space. For brevity, (iv)i≤n1≤ will be simply referring indifferently to as sensor nodes and points. We suppose that each sensor is capable of covering a disk of radius cr and communicate with the other sensors within a distance i,rcv = {x ∈ ℝ3 : ||ix − v|| ≤ cr}.We consider a set of points k-simplex (or a simplex of dimension k) σ is an unordered set σ = {v0, v1, .., kv} ⊆ S, where i ≠ vjv and δ, for all i ≠ j. A face of the k-simplex σ is a (k − 1)-simplex formed by k elements (or vertices) of σ. Clearly, any k-simplex has exactly k + 1 faces. The collection of all k-simplices of S is called the abstract associated with Γ(S). In fact, an abstract simplicial complex X is a finite collection of simplices which is closed with respect to the inclusion of faces; meaning that, if σ ∈ X, then all faces of σ are also in X. It is noteworthy that a simplicial complex is a generalization of a graph; that is, the connectivity graph is nothing but the set of 1-simplices of the simplicial complex associated to a set V of points in the 3D space.A Now let us discuss the definition of the Vietoris-Rips complex. This complex captures the features related to connectivity and coverage of WSNs.Definition 3.1. ε(Vietoris-rips complex) Let S be a set of points in a 3D space and a given radius ε. The Vietoris-rips complex of S, denoted by R(S), is the simplicial complex whose k-simplices correspond to unordered (k + 1)-tuples of points in S which are pairwise within Euclidean distance ε of each other.k + 1 points in S determine a k-simplex of for the Vietoris-rips complex if, and only if, each of these points lies within the intersection of the balls of radius ε centered at the other k points.A subset of iv broadcasts its identity to its neighbors. Upon receipt of the message, each sensors builds the list, denoted by Initialization: Every sensor iv appends its identity to the vertices in in of its neighbors. Then it informs its neighbors about the 1-simplices it built.Edge construction: Sensor iv starts building the lists j ≤ in, by simply adding appropriately the structures it has received to the ones it has already constructed.Simplicial iteration: On receiving the information from its neighbors, sensor The reader, however, may wonder whether such topological structure can be computed in practice by tiny motes equipped with radio devices and limited storage capabilities. To answer this question, we propose a simple mechanism allowing a fully distributed construction of the Vietoris-rips complex. Through a 3-step broadcast of connectivity information, each sensor node can be aware of what simplices it belongs to, and what other simplices its neighbors belong to. To this end, we assume that every sensor node has a unique identifier  and has enough space to maintain a table of identifiers. The protocol performs as follows:i, j, and k, provided that i ≠ j, i ≠ k, j ≠ k. The rules used for the following iterations are similar.An informal explanation of the construction algorithm is as follows. Simplices of higher dimension are constructed iteratively. In the first iteration, the 2-simplices are constructed by applying the following rule:3.3.X and Y be two topological spaces and f, g : X → Y be two maps (or continuous functions). We say that f and g are homotopic if there is a map F :  ×  → X such thatLet x0 ∈ X be a given basepoint of X. A loop based on x0 is a map α :  → X, such that x0 = α(0) = α(1). An equivalence relation on the set of all loops based at x0 can be defined by stating that loops α1 and α2 are equivalent if they are homotopic with respect to x0; meaning that there exists a homotopy F between α1 and α2 such thatLet α :  → X based at x0 by [α] and call it the based homotopy class of the loop α. The set of equivalence classes of loops based at x0 is denoted by π1 and is called the fundamental group. It can be equipped with a multiplication defined by [α1] ★ [α2] = [α1.α2], for all loops [α1] and [α2] based at x0, where α1.α2 is the loop obtained by attaching α1 to α2. A second group of homotopy, denoted by π2 can be defined as the set of homotopy equivalence classes of applications β : 2 → X, based at x0. It is an Abelian group,  → X such that:A deformation retraction of a space A is a retraction by deformation of the space X if, starting from the original space X at time 0, we can continuously deform X until it becomes the subspace A at time 1 and deformation is performed without ever moving the subspace A in the process. It is obvious that, if A is a retraction by deformation of X, then X and A are homotopically equivalent.In other words, The subset K be complex, a retraction filtration of K is a nested finite sequence of subcomplexes iK,k ≥ 0, kK is a retract by deformation of kK+1. Thus, it can be shown easily that, K0 and nK have the same type of homotopy and the same homotopy group.Finally, let T = {p1, .., kp} be a simplex and A T1 = {p2, .., kp} be one of its faces. Then A = T −(T1 − ∂T1) be the part of the boundary of T that is not internal to T1. Then A is a deformation retract of T.Let R(S) be the Rips complex associated with S, repeating the process of retraction of simplexes that are on the boundary of R(S), with faces external to R(S), would lead to a filtration of R(S), say kK, 0 ≤ k ≤ n, such that, for all k ≥ 0, kK is a retract by deformation of kK+1 and kK+1 is obtained from kK by adding one simplex, external to kK and belonging to R(S). The object K0 has no simplex with external face that is retractible.Let 4.In this section, we propose a novel distributed technique to count the coverage holes of WSN using the retraction theory of spaces. In particular, we show that the Vietoris-rips complex associated with the WSN can be reduced to a simpler space that is tightly related to the number of holes.D ⊆ ℝ3 be a compact domain in the 3D space ℝ3 and ∂D be its boundary. We consider that D contains no obstacles. We also consider that a collection S = {v1, .., nv} is deployed over domain D and that the sensors are equipped with local communication and sensing capabilities. In fact, each sensor is capable of communicating directly with other sensors in its proximity (within a given distance br) and has a limited sensing range ε.In the following, let 4.1.We assume, in this subsection, a complete absence of localization capabilities and metric information, in the sense that the sensors in the network can determine neither distance nor direction. Under these assumptions, we are interested in designing distributed algorithms for coverage assessment and hole detection.Retract, that reduces the size of the Vietoris-rips complex while keeping its type of homotopy. Repeating this procedure several times will eliminate all the 3-cells of the Vietoris-rips complex.To this end, we need first to introduce a special procedure, called εR(S) be the Vietoris-rips complex. Let {v0, ..., v3} be a 3-simplex in εR(S) such that one of the 2-cell {v0, v1, v2} does not belong to another 3-simplex in εR(S). If such a situation does not exist, then one can easily deduce that εR(S) has no 3-cells. Let X1 and A1 be the set of points x ∈ εR(S) belonging to simplex {v0, v1, v2} and the subset of X1 generated by the other two faces, respectively. Then its is easy to construct a map h1 : X1 ×  → X1 such that:Let h1 can be easily extended to a mapA is εR(S) − X1) ∪ A1.Map Retract several times will lead to eliminating all the 3-simplices in εR(S). The map Retract can also be reapplied several times to delete all 2-simplices and 1-simplices that a free face. The resulting space, say Repeating the map Proposition 4.1. εLet S be a set of sensors. If R(S) is path-connected, then satisfies the following properties:εis homotopy equivalent to R(S)the number of holes delimited by εis equal to the number of holes of the vietoris space R(S)Proof. Applying the map Retract several times helps creating a retraction filtration of εR(S) such that:n is number of 3-simplices in εR(S). Since, for every i, iK is homotopy equivalent to iK+1, we can deduce that εR(S).εR(S)).a holes is a path connected component that is surrounded by the delimiting space (εR(S) may enlarge a hole but does not eliminate it.Retracting a 3-simplex in The retraction process does not create holes since it operates on the simplices that have free faces.The second statement of the theorem can be deduced from the following features:4.2.εR(S). This is the subset of S containing all the nodes occurring on free faces and facing the boundary ∂D of the domain. In the second step, we define an algorithm that detects holes by progressively transforming the external boundary by retracting all its external simplices. In the third step, the following process is repeated: one external 2 simplex is deflated, the Retract map is applied several times to reduce appearing simplices with free faces, and the external boundary is updated. The number of iterations of this process gives the number of coverage holes.To count and locate holes, we set up a 3-step algorithm. In the first step, we construct the external boundary of 4.2.1.D of the domain D under monitoring can be seen (or detected) by the sensors in S and that the nodes in S broadcast periodically their unique ID numbers. The construction is based on the three following actions:D or finding itself on an external facet sends this information to its neighbors.Every sensor node detecting a boundary component of εR(S), by simply allowing every sensor node to know which neighbor is on the external boundary.The information related to boundary detection, when received by sensors should be put together to form the external boundary of εR(S) so that every node on the boundary can have a precise picture of the boundary.The nodes broadcast information related the external boundary of Let us assume that the boundary ∂4.2.2.nC be a n-simplex on the boundary of εR(S) and Cn−1 be one of its external faces, then nC can be retracted using the procedure Retract and the boundary is updated by adding a new node (the one in nC − Cn−1), if n ≥ 2, or by deleting the node occurring in Cn−1, if n = 1.Boundary retraction: Let S (in charge of the counter) selects one of the nodes of the new external boundary, withdraws it from the boundary, and increments the counter.Boundary deflation: When all the simplices on the boundary of have been retracted, a pre-selected node in Counting the coverage holes can be set up by an algorithm that repeats iteratively the following major procedures:4.2.3.εR(S) is applied after retraction is complete, a hole is reduced from the coverage zone. This because the selected node, for deflation, is observing the hole, since it is one of the nearest nodes surrounding the reduced hole. Thus, this node can start the construction of the boundary of the reduced hole by determining the list of the nodes surrounding immediately the hole.It is worth noticing that, when a deflation of a 2-simplex on the boundary One can conclude, therefore, that any time a deflation is operated, a hole can be located by simply constructing its boundary using the nearest nodes to that hole.4.3.D under monitoring has no obstacles and let us denote by χ (χ = 4πε3/3) the volume of the area covered by a sensor and by Vol(D) the volume of D. One can state that the number |S| of sensors in S should be higher than the number N0 = Vol(D)/χ to be able to guarantee full coverage of D, at least after hole detection and coverage optimization. Therefore, we will assume in the sequel that this condition is satisfied. Finally, we assume that the sensors are able to move and detect the external boundary of D, when they are close to it, like in the above subsection.Let us here assume that the 3D domain M should keep seeing the boundary when it moves.A node detecting the external boundary ∂εR(S) should move towards the uncovered area, when it does not see the boundary.A node on the external boundary of εR(S) are separated by a distance higher than a predefined threshold, say θ1, and one of them is not seeing the boundary of D, then the sensor unable to see the boundary asks its successor  to move towards the external boundary.When two neighbor nodes on the external boundary of A node seeing the boundary should inform its neighbors so that they can move accordingly.s and its neighbors on the boundary of a hole is lower than a predefined value, say θ2, then s should move in the opposite direction of the hole, while the other sensors should move towards the hole so that when they see each other, s can withdraw itself from the minimal surface after informing its neighbors.When the distance between a sensor A node on the external boundary, finding itself unable to move informs, its successor to move towards its direction.Repairing holes aims at extending the coverage by eliminating the holes, or at least by shrinking considerably their size. An algorithm can be defined to this purpose. It can be built based on the following general rules:5.In this section, we use 3D Voronoi diagrams to optimize sensor coverage and target tracking performance. We first propose a strategy to measure the uncovered zones of the monitored region. Then, we develop two mobility models that provide target tracking using order k Voronoi diagrams and optimize the coverage ratio of a zone using Voronoi cells. Finally, we extend these models to multiple target tracking. We assume in this section that the sensors have spherical coverage. The vector-guided case can be addressed using similar techniques.5.1.x within the surveillance area is not covered by any sensor. Let ℒ define the Linear Uncovered Length (LUL) at location x with direction θ. This is the undetected path length of a target traveling from location x with direction θ = , for 0 ≤ θ1 ≤ 2π, −π/2 ≤ θ2 ≤ π/2).Assume that a location ALUL(x), introduced in [The Average Linear Uncovered Length (ALUL), denoted by duced in ,21, for A is a subregion of the 3D domain under supervision, the Average Linear Uncovered Length related to A, ALUL(A), that a target can travel within A without been detected by a sensor is given by the expression:A|| is the volume of A.More generally, when x, θ, t), that defines the Linear Uncovered Length at location x with direction θ, at time t. Based on this reasoning, we define the metric mALUL representing the ALUL in a location x at time t and given by:the ALUL metric was developed to deal with a static deployment, which is not the case of our study. When a mobility model is implemented, the topology of the WSN is no longer static. To overcome this, we extend this notion so as to support sensor node mobility. The ALUL should also vary according to time and should use a function, denoted by the ℒ can be computed by ALUL(x) by mALUL(x).Finally, mALUL gives information about the coverage-preserving capabilities of the mobility model. It can be used to state whether the steady state is rapidly reached, and whether the mobility model affect the detection performance of the sensor network.mALUL(A) provides information about the long-term behavior of the mobility model. It can be used to evaluate the impact of mobility on the possibility for a target to be undetected within the monitored region.From the performance evaluation perspective, two important points should be highlighted:5.2.The first model is called k-mobility model. Sensor nodes in this model move toward the regions where the hostile target is supposed to be and collaborate to keep the target controlled by k sensors all the time, To this end, the order k Voronoi diagrams are used and maintained all the time.The second model is called simplified model. It relies on estimating the uncovered zones within the Voronoi cells, using the ALUL metrics and moving sensor nodes toward the “uncovered zones”.In this section, we show how the Voronoi cells can be used to implement target tracking using a sensor mobility model. In fact, we define two mobility models:While the first model is triggered by the occurrence of targets, the second model aims at adapting the covered area so that the targets can be detected with higher probabilities. Obviously, the k-mobility model is more energy-consuming than the second since it encompasses the prediction of the target position and requires tracking using k sensor nodes. Therefore, we suppose that the second model can be used when energy resources become scarce. The performance of both models will be assessed in Section 7. Moreover, one can notice that the prediction function we are using is tightly related to the coverage of the zones where the targets are expected and that the mobility models assume that nearest sensor nodes can move to these zones while reducing the coverage of other zones where targets are not expected. In fact, the greater is the number of target detection signals, the better is the prediction precision to command sensor movements.5.2.1.k−covered area and (b) a target crossing non k−covered zone.In the following, we distinguish two cases: (a) a target crossing a 5.2.2.The mobility algorithm is triggered upon the detection of a target presence. Every detecting sensor sends its detection signal to the relevant intermediate sensor . The latter collects all detection signals, verifies their integrity, deduces the current zone where the target might be, estimates the positions of the target in the next of time slot, and commands k sensors to move to monitor the new zone to ensure tracking continuity.k−covered.Typically, the selected zone of target presence is taken among other zones (when more then k sensors detect the target presence). These zones are ordered according to the probability of presence of the target. The zone selected is the one presenting the highest probability among those which are k′ sensors detect the target (k′ > k). The k′ sensors is, 1 ≤ i ≤ k′, send their detection data id to an intermediate node under the form:t,ir = δ is the Euclidean distance separating is from the position t,iz of the target as seen by i, θt,is =  is the direction of the vector t,iτ is the detection instant.Assume that k of them) at a unique node IS, which verifies first the authentication of the messages.In the case where detection signals are sent to different intermediate nodes; the intermediate coordinate to gather all signals (or at least The zone of target presence τZ(t). Several strategies can be used for this including selecting the largest intersection of k zones of the form T be the set of k sensors involved in the definition of τZ (t).The most likely target presence zone IS constructs:SV(T). Obviously, it contains τZ (t).Then, IS computes the order k Voronoi cell Zτ,+(t), where target tz is likely to be in the next time slot. Several strategies can be used for this estimation including extrapolation of older positions or some information related to target direction and speed. It also estimates the most likely new position of tz.IS estimates the zone k sensors based on a specific criteria and order them to move towards Zτ,+(t) to increase its coverage. If no criteria is used, then the order goes to the sensors in T. A criteria can simply to reduce sensor movement.IS selects The mobility algorithm is defined through five steps:k″ sensors) may belong to T and the other (say k−k″) have to be added among the neighbors of T. This situation is addressed in the following subsection.When a criteria is applied for the selection of k sensors to cover the new position, some of the selected sensors (say 5.2.3.k′ (k′ ≤ k) detection signals are received by the intermediate sensor IS, which should proceeds at the construction of the probable current zone of presence of the target the way the preceding algorithms does. Then it starts the selection of the remaining (k − k′) required signals. Then, it orders the movement of the k sensor provide k monitoring to the target. For this purpose, IS executes the following steps:tz using the k′ reports from k′ sensors denoted by s1, ..., k′s.IS computes the most likely zone of target presence let i ≤ k′, IS selects the nearest k sensors to is. It computes the related k−Voronoi cell For each i ≤ k′, IS gets the number of sensors ik”, 0 ≤ ik” < k, that have sent detection signals to IS.For each k− Voronoi cells according to the value of ik”. The greater ik” is, the most important is the probability of presence of the target in jk” induces that the target is going in or out the cell IS classifies the k sensors involved in ik” = maxj≤k′jk, and guides the (k −k”) added sensors (among the nearest sensors to is) to move towards ir ≥  such that δ ≥ δ. and x, y ∈ iv and iv is the set of the vertices of the boundary ∂iV, iπ = k”/k is the probability of presence of the target in IS selects the nearest In this case, only k−coverage. To this purpose, for each mobility step, the sensors define randomly groups of k members for each, the latter are not required to be the nearest neighbors. Each group chooses randomly a head which chooses the first mobility step. The remaining members of the group take into account this choice to determine their next mobility step. By this way, every sensor’s mobility will depend on the integrating group. Furthermore, a sensor may move from one group to another in each mobility step. This model enables the definition of overlapping k−Voronoi groups which increases the guarantee of having a k−coverage.To enhance coverage while keeping more mobility freedom, we implement a group mobility model in which ground sensors move in groups in order to preserve the 5.2.4.We propose hereafter a mobility model which is based on the use of simple Voronoi diagram to identify and reduce coverage holes.ρ-distant from it. If such nodes exist, the sensor node moves toward the most distant neighbor, denoted by fn, with a distance This model can serve to implement a mobility strategy where a sensor node looks for one or more neighbors that are at least 2k-covered using the simplified algorithm. It uses a set, denoted by X), which defined the set of intersection points expressed as follows:R ⊆ R3, denotes the boundary of R.The following result extends this strategy to the case where the monitored region is required to be For the sake of parsimony, we do not provide proofs for these corollaries in this paper.Lemma 5.1. i in S, if |NFor s)D| < k, where |.| denotes set cardinality, then V(is) i in S, if |Xis not k-covered. For s)D| < k, then V(is) is not k-covered.This lemma shows how simple Voronoi diagrams can be used to detect the coverage holes based on the distance between the sensor node and the edges of its Voronoi cell. It is based on the concept that the Voronoi tessellation is a partition of the points belonging to the monitored area according to their proximity to the sensor nodes. In other terms, if a point is not detected by the sensor node located at the generator of the Voronoi cell it belongs to, it cannot be detected by any other sensor node. If a sensor detects that the distance to one among the edges of its Voronoi edges is more than its coverage range, it has to move towards this edge to cover the corresponding hole. The uncovered can therefore be gradually reduced using this distributed strategy. However, a sensor node can detect that more than one of its Voronoi neighbors do not fulfill the condition of the lemma, it will therefore move towards the most distant neighbor.k-coverage while the advanced model proposed in the previous subsection is based on order k Voronoi tessellations which are more complex to build.The major advantage of this strategy, with respect to the advanced strategy, is that it relies on simple Voronoi diagrams to deal with A more accurate comparison between the two models will be carried out in the simulation section.5.3.S. Let tz and tz′ be the reported positions.The two tracking models presented in the above can be extended to the tracking of multiple targets. To describe the extension let us assume, for the sake of clarity, only two targets are detected by sensors in Only one node has detected the presence of the two targets: In that case, the sensor keeps monitoring one of the targets and invites the nearest neighbor to the second target to monitor the second and provides it with relevant information it collects.More than one node have detected the targets: In that case, two sensor among those that have detected the targets are selected to keep monitoring the targets independently.The extension of the simplified model considers two cases:On the other hand, the k-mobility model extends in following way: if d nodes detect the targets, these sensors are divided into two subsets, each in charge of monitoring one target, then the subsets are extended so that any of them contains k sensors.6.6.1.The number of messages exchanged between the sensors during the execution of the algorithm.The number of additions and deletions of simplices to the Vietoris complex.The number of sensor movements made during the execution of an algorithm.In this section, we analyze the complexity of the different algorithms we have developed in the previous sections for the detect and locate holes or to repair coverage holes. Our approach to estimate the complexity can be based on the following metrics:i.e., on the boundary of Vietoris complex). They also can be used to construct the initial boundary of Rips complex, or used to reduce the external boundary. They also can be sent after the retraction or the deflation of a simplex, or they are sent by a leader node the command a coordinated movement of sensors.Some other operations can be added for a more accurate estimation of complexity. These metrics may include, for example, the number of storing operations made at the node level to update the related data structures. The messages exchanged during the execution of an algorithm can be of different types. In particular, they can be sent to a neighbor to tell it to change its status from internal (to the Vietoris complex) to external . Let also p the number of vertices at the initial boundary of the Rips complex.For the sake of clarity, we will focus on the complexity on the detection and counting of coverage hole. In this case, let N1 of messages sent is given by:p is the number of external vertices. This result can be deduced from the preceding and the fact that p ≤ |S|.The number of messages sent during the execution of the algorithm should be lower or equal to the number of messages exchanged if all the polyhedra  have been retracted first and that after deflation all the facets have been retracted. In that case, one can state that the number S has at most v neighbors . Then, one can conclude that e is smaller than v × |S|, we deduce thatNow let us assume, without loss of generality, that the deployment of sensors  guarantees that every node in the Rips complex of 6.2.The results presented in the previous sections can be extended in two dimensions: the type of the sensors and the occurrence of obstacles in the domain under monitoring.Coping with obstacles. The algorithms developed in the preceding sections can be adapted to the occurrence of obstacles. Obstacles in monitored 3D areas may complicate seriously the role of monitoring sensors, increase their power consumption, and limit the coverage efficiency. Two particular objects have to be modified in our algorithms. First, the coverage holes that have to be counted should not contain obstacles. one can assume for this that the sensors are able to recognize an obstacle). Second, the mobility model used to increase coverage or to provide tracking should consider moving the sensor vertically as an alternative.Coping with semi spherical. The algorithms developed in the preceding sections can be extended to semi-spherical sensors . It is worth noticing, at this point, that this type is sufficiently general to represent various sensors-base applications. In particular, the model can be used to represent fire and smoking-based sensors or camera-based sensors. To cope with semi-spherical sensors, one can notice that the concepts of Vietoris-rips and Voronoi diagram can be extended, so that coverage holes can be handles in a similar way. However, when repairing a hole, the mobility model of the sensor should include rotating a sensor to increase the coverage of a specific area by the sensor.It is worth noticing that the additions made to the developed algorithms do not modify significantly the complexity of the algorithms. In particular, the complexity of the hole counter remains linear (as shown in the simulation discussed in the following section).7.In this section, we carry out a set of experiments to prove the efficiency of the proposed techniques. We first address the coverage hole problem by evaluating the performance of the higher-order Voronoi-based strategy for coverage optimization. To this purpose, we define a metric representing the ratio of uncovered area with respect to the total area of the monitored region. Second, We assess the target tracking approach by estimating the maximum linear distance that can be made by a hostile target without being detected. Finally, we evaluate the complexity of our coverage control and mobility techniques. We use the number of transmitted messages as a main criterion to estimate this complexity since data transmission consumes much more power than computational steps in WSNs.7.1.The first experiment aims at evaluating the hole reduction strategy based on three-dimensional Voronoi tessellations with spherical coverage. We define the following metric to evaluate the performance of hole reduction.μ according to the number of iterations of the coverage hole reduction algorithm. We compared the Voronoi-based hole reduction strategy with the Homotopy-based strategy proposed in Section 4. It can be noticed that the increase in terms of normalized uncovered proportion is about 15% when the number of iteration is low. In addition, when the number of iteration exceeds 30, both approaches perform well since the normalized sum of uncovered areas becomes higher than 90%.μ according to the number of iterations of the coverage hole reduction algorithm and compares it to the Voronoi-based hole reduction strategy with the Homotopy-based strategy. One can conclude that while the homotopy-based approach is less complex, since linear for detection and localization, the Voronoi-based method reaches better results. In addition, a comparison between the results obtained for spherical sensors and semi spherical sensors shows the following:The approach performs better with spherical sensors for the first iterations. Indeed, the normalized uncovered proportion reaches 70%, with spherical sensors, after 10 iterations, while it stays under 10% for semi spherical sensors.The approach performs the same for both types of sensors after 30 iterations.A similar experiment is conducted for vector guided sensors, assuming that at every step of the iteration, the mobility is provided along with an orientation of the vector to achieve better coverage. This can be explained by the fact that the density of sensors is the same for both types and, therefore, it takes more mobility for semi spherical sensors the coverage holes.7.2.x, θ), gives an approximation of the average distance that can be made by a target, moving in 3D space, before being detected by the sensor network. The metric mALUL representing the ALUL in a location x at time t is given by:The Average Linear Uncovered Length (ALUL), denoted by ℒ(mALUL(A) provides information on the coverage-preserving capabilities of the mobility model and the long-term behavior of the mobility model.From the performance evaluation perspective, 2-size monitored zone, the coverage degree considerably varies according proximity to the mobile target. In fact, after 5 mobility steps, the local sensor density is less than 1 in regions that are far from the target location ) and reaches 2.7 in points that are close to this target.In order to visually illustrate the performance of coverage reduction models, we use the local node density distribution that gives the number of sensors that cover every point of the monitored region. More interestingly, m metric to evaluate the evolution of the uncovered area with respect to time. In fact, this allows to know whether uncovered regions are created due to the density increase in the zones that are close to the target. We compared our scheme to four known mobility models, which are: the random walk model, the random waypoint model, the random direction model, and the Gauss-Markov model. The results of this comparison are depicted in To confirm these results, we used the ALULWe notice that the proposed mobility models, denoted by Advanced Voronoi-based Mobility Model (AVBMM) and Distributed Voronoi-based Mobility Model (DVBMM), clearly outperform the existing models. They also return a better performance than the Density-Preserving Mobility Model. This is because the latter model, despite its ability to guarantee a nearly uniform node density within the monitored area, does not take into account the presence of hostile targets in the zone of interest.7.3.In this subsection, we evaluate the communication overhead resulting from the proposed retract-based coverage control approach. To this end, we only consider the complexity of the detection and localization steps in our algorithm and do not address the complexity of the repair step, since the repair step complexity is mainly dependent on the first deployment. However, one can easily deduce that if the deployment guarantees that holes size do not exceed a threshold, then the linear complexity can be verified.2 to 5 sensors per m2. The major remark is that this number is nearly linear with respect to the number of sensors per area unit.We considered that the dimensions of the monitored zone are 10 m × 10 m × 3 m. We varied the number of nodes deployed within this zone and we measured the number of messages required to setup our coverage control protocol. We first supposed that all sensor nodes have a spherical coverage of range 0.5 m. The number of exchanged messages is independent of the density. It is close to 4 for the spherical sensors and 10 for semi spherical sensors. This fact may appear strange; however, one can notice that when a deployment is performed, the detection and location will only search for holes surrounded by the Vietoris space. The latter is reduced when the density is low.The number of messages exchanged by the semi spherical sensors for detection and localization is 2.5 times higher than the number observed for spherical. Two reasons can be mentioned for this. First, the area covered by a semi spherical sensors is half the area covered by spherical sensors. Second, the guiding vectors is randomly oriented.Moreover, we considered the case where sensors have semi-spherical coverage (with the same range). 8.This paper developed a low complexity approach to detect and localize sensing holes in 3D spaces. It also constructed efficient algorithms to repair holes and track (multiple targets). Our approach has built on two concepts, the Vietoris complex and the Voronoi diagram, and demonstrated that the technique called retraction by deformation achieves low complexity algorithms for the detection of coverage holes in WSNs.Our approach can be easily extended to more general sensors, for which the Vietoris complex and the Voronoi diagram can be defined. Such sensors can be called conical sensors or vector guided sensors and can represent camera sensors.


Cliques  in protein-protein interaction (PPI) network are an important resource used to analyze protein complexes and functional modules. Clique-based methods of predicting PPI complement the data defection from biological experiments. However, clique-based predicting methods only depend on the topology of network. The false-positive and false-negative interactions in a network usually interfere with prediction. Therefore, we propose a method combining clique-based method of prediction and gene ontology (GO) annotations to overcome the shortcoming and improve the accuracy of predictions. According to different GO correcting rules, we generate two predicted interaction sets which guarantee the quality and quantity of predicted protein interactions. The proposed method is applied to the PPI network from the Database of Interacting Proteins (DIP) and most of the predicted interactions are verified by another biological database, BioGRID. The predicted protein interactions are appended to the original protein network, which leads to clique extension and shows the significance of biological meaning. Identifying protein-protein interaction (PPI) and constructing biological networks are vital to understand the molecular function and cellular organization . In receApplying different GO rules, we generate two predicted PPI sets, that is, CORE and ALL which insure the quality and quantity of predictions, respectively. The proposed method is applied on DIP dataset . The twoG =  to represent a PPI network, where V is the set of all nodes (proteins) and E is the set of all edges (interactions) in graph G.A PPI network is used to describe a set of protein pairs, and it can be modeled as a graph. We use an undirected graph We propose an iterative method based on cliques and GO annotations to predict PPI see . First, Mining cliques in a PPI network is a NP-complete problem according to graph computing theory . HoweverNot all cliques participate in the process of predicting PPI. We set a minimum threshold of clique size. Only the cliques whose sizes are more than that threshold have the qualification to participate in PPI prediction. Furthermore, we set a clique confidence score to avoid that the selected cliques include many predicted PPIs. The clique confidence is determined by sum score of all the edges in it. That is,λ of the clique score for PPI prediction. Obviously, cliques selected as the participants for predicting PPI must satisfy with the two mentioned thresholds.We set a threshold k-clique, the appending of one edge extends it to (k + 1)-clique(s). Corresponding to the direct connection, the missing edge that links the nodes in and out of the clique to form a larger clique is a predicted interaction. As to a given k-clique, the description of prediction with missing-one-edge method is as below.We count the number of the nodes connected with the members of the known cliques. Based on a known C = N(n1) ∪ N(n2)∪⋯∪N(nk)−{n1, n2,…, nk}, where ni is the node in k-clique and N(ni) represents the neighbor set of ni.C ← C − {n | Degree(n) < k − 1, n ∈ C}, where Degree(n) represents the number of the neighbors of node n.w in C.Getting a node i making niw ∉ Eall and ∀j, njw ∈ Eall, j = 1,2,…, k, j ≠ i, where Eall = E ∪ {predictions}.Judging whether ∃niw is a new predicted PPI.If condition (2) is satisfied, C have been reached.Repeating (1) until all of the nodes in Proteins in a complex always have same cellular components, and proteins in a function module often perform similar biological roles. Therefore, GO terms contribute to reducing false-positive predictions  before tTwo proteins in the predicted interaction should have a common cellular component at least.Two proteins in the predicted interaction should have a common molecular function at least.If only k-cliques are mined based on the (k − 1)-cliques until the maximum cliques are found.After we obtain the predicted PPIs of the first round, the new predictions are merely related with the cliques including interactions just predicted in the previous round. Therefore, we design an appropriate method to generate cliques only based on the predicted interactions to minimize the computational cost. Mining cliques is a recursively bottom-up procedure, as illustrated in Saccharomyces cerevisiae downloaded from the Database of Interacting Proteins  [Our method is applied on a dataset of PPIs in 10/6/14) . DIP is The maximum size of mined clique is 10. According to this maximum size, we set the minimum size of clique participating in predicting PPI to be 6. The threshold of clique confidence score is set to be 0.7. Based on the PPI network of the original DIP dataset, 442 PPI predictions are generated. Then, according to the cliques derived from these predictions and different GO rules, CORE and ALL are generated, respectively. CORE includes 352 predictions and ALL contains 874. Adding these predictions into the original dataset, the size of the maximum clique is enlarged to 16 and the number of small cliques is reduced, that is, consolidation of smaller cliques into larger ones.Saccharomyces cerevisiae from primary literatures. Therefore, we compare CORE and ALL with the dataset of BioGRID (version 3.2.98) and find that the overlaps between them are very high. Of 352 predictions in CORE, 323 are found in BioGRID and the overlapping ratio is near 92%. Of 874 predictions in ALL, 774 are found in BioGRID and the overlapping ratio is nearly 89%. The process of predicting and validating PPI in each round is shown in Tables We expect predictions in CORE and ALL to be validated by the other records of biological experiments. Database BioGRID collects sufficient and reliable data in L, that is, L = (P+/G+)/(P−/G−). P+ is the number of repaired edges of cliques contained in the true-positive GS set. P− is the number in the true-negative GS set. G+ is the number of the true-positive set of GS and G− is the number of the true-negative set of GS. Jansen et al. [L > 600. G+ and G− are constant and equal to 8250 and 2705844, respectively. The estimation of value L in CORE and ALL is listed in L values of two predicted PPI sets are more than the acceptable threshold. The predicting quality of CORE is obviously better than ALL.A statistical method based on gold standard (GS) datasets is introduced to estimate the PPI predictions , where tn et al.  have poiBased on a network topology to predict protein interactions, clique methods are usually more reliable and accurate than clustering methods in the dense region of protein interaction network. Therefore, we select two methods based on cliques to compare with our method. The first is DC method of Yu et al. , which pt to 0.8. These parameters of two compared methods are set to be stricter than applied in the original papers for getting better results. DC method predicts 465 protein-protein interactions and 407 are hit in the BioGRID dataset. Furthermore, value L is estimated in GS datasets. There are 70 in true positives and 26 in true negatives based on gold standard datasets, and the value L is 883. IPC-MCE algorithm generates 496 predicted interactions and 436 are hit in BioGRID. And 79 are in true-positive dataset and 31 are in true-negatives based on gold standard datasets. The value L is 836. The results compared between various methods are shown in Using DC method, the parameters of nonoverlapping size and overlapping size of a clique are, respectively, sets 3 and 4 . The lowThere are 321 interactions between CORE and ALL, as shown in section (2) of The predicted PPIs using our methods can well complement missing interactions to extend potential cliques see . We consCliques in the PPI network are good resource and worth to study properly. Predicting PPIs by recursively extending cliques results in a quantity increase of predicted PPIs. And the quality of predictions is significantly improved via combining GO annotations with clique-based method. Obviously, iteratively finding cliques is a time-consuming task. Especially, the PPI network is frequently extended by new PPIs. Therefore, we design a special and novel method based only on the new predictions to mine cliques. This method is feasible and efficient in practice, which decreases the solution searching space and obtains high performance. Our work also partly solves the problem of missing cliques due to the false negative interactions. The clique size increases with continuously appending the predicted PPIs into the original network. Most enlarged cliques show good biological meaning with GO annotations. Besides, the predicted PPIs can complement data defection associated with protein complexes which are too large to detect all of its components with biological experiments. In the future, our methods on predicting PPIs and extending cliques will be applied to other PPI networks, such as human protein network, to help us associate disease relationship in the cliques.


Mycobacterium tuberculosis (M. tuberculosis), is thus vital. We have implemented improved screening methods for protein–protein interactions based on affinity purification followed by high-resolution mass spectrometry. This method can be efficiently applied to both medium- and high-throughput studies aiming to characterize protein–protein interaction networks of tubercle bacilli. Of the 4 tested epitopes FLAG, enhanced green fluorescent protein (eGFP), protein A and haemagglutinin, the eGFP tag was found to be most useful on account of its easily monitored expression and its ability to function as a simultaneous tool for subcellular localization studies. It presents a relatively low background with cost-effective purification. RNA polymerase subunit A (RpoA) was used as a model for investigation of a large protein complex. When used as bait, it co-purified with all remaining RNA polymerase core subunits as well as many accessory proteins. The amount of RpoA strongly correlated with the amount of quantification peptide used as part of the tagging system in this study (SH), making it applicable for semi-quantification studies. Interactions between the components of the RpoA-eGFP protein complex were further confirmed using protein cross-linking. Dynamic changes in the composition of protein complexes under induction of UV damage were observed when UvrA-eGFP expressing cells treated with UV light were used to co-purify UvrA interaction partners.Tuberculosis is a leading cause of death in developing countries. Efforts are being made to both prevent its spread and improve curability rates. Understanding the biology of the bacteria causing the disease,  Mycobacterium tuberculosis, the causative agent of tuberculosis (TB), is a deadly human pathogen, and it has emerged as an epidemic in many developing countries. The latest WHO report states that 8.6 million new cases of TB occurred in 2012. Moreover, TB threatens the lives of HIV-positive individuals, killing 3,20,000 of HIV-positive patients in 2012. Emergence of multidrug-resistant (MDR)-TB and totally drug-resistant (TDR)-TB strains has created an urgent need for profound investigation of the tubercle bacilli's physiology and pathogenicity. Understanding its biology is fundamental for developing new effective strategies to combat TB. Genomic and proteomic methods are being utilized to broaden this knowledge and to understand the network of protein–protein interactions for a variety of organisms, including pathogenic bacteria, in order to elucidate the regulation and dynamics of important cellular functions and processes including DNA replication, transcription and virulence.M. tuberculosis, representing approximately 80% of its total predicted number of genes Mycoplasma pneumoniaeHelicobacter pyloriSaccharomyces cerevisiaeDrosophila melanogasterRecent proteogenomic analysis identified 3,176 proteins from M. tuberculosis proteome was built using the bacterial two-hybrid (B2H) system Escherichia coli (E. coli). This three-hybrid system was used for the RD1 complex of M. tuberculosisM. smegmatis host. This method presents a clear advantage of studying protein complex formation under physiological conditions and was successfully implemented both for soluble as well as for membrane proteins The most comprehensive protein–protein interaction network for the Mycobacterium. To determine the most efficient epitope, we designed 4 constructs containing 4 different fusion tags to be tested with targeted proteins. For further experiments, we selected FLAG, haemagglutinin (HA), protein A (ProtA) and enhanced green fluorescent protein (eGFP) epitopes. We employed a localization and affinity purification (LAP) method coupled with tandem mass spectrometry (LC–MS/MS), an efficient tool to investigate protein–protein interactions in living cells under close-to-physiological conditions Here we propose a single-epitope affinity purification (AP) technique combined with LC–MS/MS as a screening method for studying protein–protein interactions specifically in Mycobacterium, dynamic changes in UvrABC DNA repair protein complex composition after UV irradiation. We strongly believe that the experimental system along with computational and informatics strategies , boiled for 5 min and resolved on a 4%–12% gradient NuPage Bis–Tris gel (Invitrogen) using MES running buffer (Invitrogen) at 125 V. The PageRuler prestained protein ladder (Fermentas) was used as a molecular weight standard. The gels were stained with Coomassie for 2 h and destained overnight.4HCO3 and subjected to a standard procedure of trypsin digestion: the proteins were reduced with 10 mM DTT for 30 min at 56°C, alkylated with 55 mM iodoacetamide in darkness for 45 min at RT and digested overnight with 10 ng/μl trypsin. The resulting peptide mixtures were applied to RP-18 pre-columns of an HPLC system (Waters) using water containing 0.1% trifluoroacetic acid as the mobile phase, and transferred to a nano-HPLC RP-18 column  using an acetonitrile gradient (0%–35% ACN in 160 min) in the presence of 0.1% trifluoroacetic acid at a flow rate of 250 nl/min. The column outlet was directly coupled to the ion source of an Orbitrap Velos mass spectrometer (Thermo Scientific). A blank run ensured absence of cross-contamination from preceding samples.The protein pellets were dissolved in 50 μl of 100 mM NHThe mass spectrometer was operated in a data-dependent mode to automatically switch between Orbitrap MS and LTQ–MS/MS acquisition. Survey full-scan MS spectra (from m/z 300 to 2000) were acquired in the Orbitrap with a resolution of R  =  15,000 at m/z 400 . The method used allowed sequential isolation of the most intense ions  for fragmentation on the linear ion trap using collision-induced dissociation at a target value of 30,000 charges. The target ions selected for MS/MS were dynamically excluded for 60 s. Chromatographic peak apex detection triggered data dependent scans  with phase method activated and triggering window set to 30%. General MS conditions were as follows: electrospray voltage, 1.8 kV; no sheath and auxiliary gas flow. The ion selection threshold was 10,000 counts for MS/MS, and an activation Q-value of 0.22 and activation time of 30 ms were also applied.M. smegmatis mc2155 protein database available at the CMR website  or against an M. bovis BCG database . The databases were modified in-house to contain randomized sequences of all entries to control for false-positive identifications during analysis using the Andromeda search engine. The error ranges for the first and main searches were 20 ppm and 6 ppm, respectively, with 2 missed cleavages. Carbamidomethylation of cysteines was set as a fixed modification, and oxidation and protein N-terminal acetylation were selected as variable modifications for database searching. The minimum peptide length was set at 7 aa. Both peptide and protein identifications were filtered at a 1% false discovery rate and were thus not dependent on the peptide score. Enzyme specificity was set to trypsin, allowing cleavage of N-terminal proline. A ‘common contaminants’ database (incorporated in MaxQuant software) containing commonly occurring contaminations  was employed during MS runs.The raw files were processed, including peak list generation, using the MaxQuant (v1.3.0.5) computational proteomics platform and default parameters were used. The fragmentation spectra were searched using Andromeda search engine integrated into the MaxQuant platform against an Bioinformatics analysis was performed using the Perseus tool . Contaminants and random protein identification were excluded. Proteins identified by less than 2 peptides were excluded from the results, except SH, the quantification peptide. Peptide and protein identification details, including scores, are provided in For protein complex cross-linking, we selected the DNA-directed RNA polymerase, where the alpha subunit  was fused with the C-terminal GFP tag. The purification procedure was as described above, with the TEV cleavage buffer changed to a 10 mM HEPES (pH 8.0)-based buffer. The purified protein complexes eluted from the column were subjected to cross-linking. We used bis(sulfosuccinimidyl) suberate (BS3) as the cross-linker (Thermo Scientific), with an 8-carbon spacer arm (11.4 Å), according to the manufacturer’s protocol. Heavy (d4) and light (d0) versions of BS3 reagent were dissolved in DMSO and mixed at a 1∶1 ratio immediately before use. The d0/d4 mixture was used to induce stable and selective chemical cross-links between lysine (K) residues available on surfaces of purified proteins to fix potential interactions between protein partners. Next, 50 mM of the BS3 (d0/d4) mixture was added at a final concentration of 2 mM to purified proteins and incubated for 15 min at 4°C. The reaction was terminated by adding 10 μl of 3 M Tris solution (pH 8.0). The samples were precipitated with PRM, as described above. Subsequently, the proteins were digested overnight with 10 ng/ml trypsin (Promega) in 100 mM ammonium bicarbonate buffer at 37°C. The peptides were reduced in 10 mM DTT for 30 min at RT and alkylated in 55 mM iodoacetamide for 20 min at RT. Finally, trifluoroacetic acid was added at a final concentration of 0.1%.To determine protein compositions of the cross-linked samples, we used MaxQuant software (as described above). To search for the cross-linked peptides, we used pLink (pFind Studio) We used. mgf files (Mascot Generic Files generated from. raw files by Mascot Distiller) and a protein database containing proteins found in a preceding MaxQuant search. All looplinks and monolinks were excluded from our obtained results. Only inter- or intra-molecular cross-links were used for further analysis. Molecular graphics and analyses were performed with the UCSF Chimera package from the Resource for Biocomputing, Visualization and Informatics at the University of California, San Francisco (supported by NIGMS 9P41GM103311).M. smegmatis mc2155 expressing the RpoA-eGFP fusion protein was used as a model for testing GFP localization. The strain was grown in culture media described above to an OD600 of 0.6–0.8. Protein production was induced by adding 50 ng/ml tetracycline for 3 h. The cells were collected by centrifugation  and washed with PBS. As a counterstain, the nuclei were stained with 0.5 μg/ml DAPI for 10 min at RT. The cells were washed again to remove excess dye. The slides were mounted with fluorescent mounting medium (Dako). A IX81 fluorescence microscope (Olympus) fitted with a PLANAPO 100x/1.35 oil immersion objective and appropriate filter sets (Semrock) was used for bright-field and fluorescence microscopy, and images were acquired using an Orca R2 camera (Hamamatsu) and the Excellence software package. The images were processed using ImageJ 1.46r and Adobe Photoshop CS4 software.The eGFP tag allows subcellular visualization of proteins of interest. M. smegmatis strains expressing eGFP fusion proteins were prepared and pre-cleared by centrifugation and the flow-through after binding to the column was diluted 1∶1 in IPP150 buffer and transferred onto a 96-well black solid plate . Cell lysate from the M. smegmatis mc2155 parent was used as a background control. Lysates were prepared from approximately the same number of cells as measured by cell pellet weight. Fluorescence counts were measured using Beckman Coulter DTX 800/880 Multimode Detector and Multimode Detection software. Excitation at 485 nm and emission at 535 nm was used, with a data integration time of 1 s. The relative binding efficiency was calculated by dividing the fluorescence intensity of flow-through by the intensity of the lysate before binding to the column, multiplied by 100%.To estimate the approximate efficiency of binding of eGFP-tagged bait proteins to the anti-GFP beads, the fluorescence intensity was measured. In brief, cell lysates derived from recombinant Affinity tags serve as selective and efficient tools for protein purification and can be used for purification of native protein complexes. Of the many available tags, we examined 4 that we selected on the basis of predicted usefulness for high-throughput purification and analysis of protein complexes in mycobacteria. To simplify the method and ensure co-purification of the majority of philological interacting partners, including weak and transient interactions, we performed single-step purification. We selected FLAG M. smegmatis. These proteins are implicated in different metabolic pathways  and fulfil varying cellular functions . All selected genes encoding selected proteins are summarized in M. smegmatis in fusion with all 4 tags, giving a total of 32 combinations.To compare efficiency and specificity of protein complex purification using the chosen tags, we selected 8 proteins from Each of the tagged genes was expressed and the resulting protein complexes were purified on a specific resin, followed by LC–MS/MS and computational analysis. Just prior to precipitation with PRM reagent, the samples were divided. Half of each sample was loaded on a Tris–glycine SDS–PAGE gel  and the LC–MS/MS experiments include high levels of contamination created mainly by non-specific interactions of proteins with the resin used for affinity purification. For complex peptide mixtures in cell lysates, co-elution may complicate biological evaluation of results. Of the most common contaminating proteins, we found chaperons, heat-shock proteins, ribosomal proteins and other proteins non-specifically bound to the purified protein complexes and the resin. To find a tag most useful in mycobacterial pull-downs and applicable for high-throughput experiments, we attempted to achieve a balance between the low number of total identified proteins (low background) without losing the real binding partners. In AP–MS studies, determining noise, false positives and false negatives is necessary to distinguish true interactions from contaminants. Sequential purification steps (e.g. tandem affinity purification) may decrease these unwanted results but at a risk of losing both weak and transient interactions. We analysed non-specifically binding proteins, commonly associated with all tested baits. We established average intensity values characteristic for each non-specifically binding protein for each of the 4 tags. The highest number of background proteins identified in all 8 proteins was observed with HA tag experiments (76 proteins) and the lowest with the eGFP tag (25 proteins). Non-specific binders for FLAG and ProtA experiments were 33 and 32, respectively . MoreoveM. smegmatis purified on specific affinity resins and were identified as dominant proteins in the respective samples . Because the structure and composition of the RNA polymerase complex is known, it is often used as a model for purifying protein complexes and thus RNA polymerase alpha subunit  was selected as the target in our study. It allows to evaluate purification and accuracy of detection of the RNA polymerase subunits.Bacterial RNA polymerase is a well-characterized enzyme composed of 5 core subunits  that bind accessory proteins such as sigma factors to form a functional holoenzyme vs. background were located in the top right-hand corner of each scatter. The abundance of RpoA was in agreement with that of SH-quant peptide, which is helpful for determining the number of RpoA molecules in each sample.The 4 core subunits of RNA polymerase co-purified with RpoA fused with all 4 tested tags. Tagged RpoA with RpoB and C subunits were detected with high signal intensity . The lowM. smegmatis is one of the best organisms to study cellular mechanisms of its pathogenic cousin M. tuberculosis. However, M. smegmatis is a non-pathogenic mycobacterium , with a genome approximately 1.7 times larger than that of M. tuberculosis. In order to use a model closer to M. tuberculosis, we tested our eGFP tag procedure in the M. bovis BCG Danish strain, which has an approximately 99.9% similarity to M. tuberculosis at the genetic level. Both M. bovis BCG and M. tuberculosis are member strains of the M. tuberculosis complex M. tuberculosis with only little modification. In addition, with high genetic similarity between the two, we expect little or no difference between native complexes, justifying M. bovis as a more optimal model organism to study protein–protein interactions for M. tuberculosis.Because of its fast growth rate, well-established methods for genetic manipulation and biosafety level 1 requirements, M. bovis BCG, the coding sequence of M. tuberculosis RpoA (Rv3457c) was cloned into a pKW08-eGFP vector and transformed into M. bovis BCG by electroporation. The RNA polymerase protein complex was obtained by the same method used for M. smegmatis. In this experiment, we used both C-terminal tagging and N-terminal tagging to determine their influence on the purification outcome. In addition, we prepared a strain expressing eGPF-tagged SigB , one of the less abundant subunits found in the complex, to determine if the protein will be capable of pulling down the entire complex as well. The results presented in M. smegmatis: SigA, sigma-70, sigma-F and SigB , and most of the mycobacterial components of this enzyme share high amino acid sequence similarity, we used protein cross-linking for establishing interactions between the homologous mycobacterial enzyme subunits. We employed the BS3 cross-linker that is reactive towards amine groups and is designed with a 11.4-Å spacer arm, which allows chemical cross-linking of 2 neighbouring lysine (K) residues and/or the N-terminal amino acid within reach of the spacer arm. Several cross-links were identified with pLink software (pFind Studio)  and M. smegmatis RpoA K153 and RpoB K837, homologous to E. coli RpoA E162 and RpoB T927 (separated by 16.867 Å). Our experiments also confirmed the usefulness of cross-linking in assigning real interacting partners identified initially by AP–MS. Information obtained from cross-linking may indicate the structures of multiprotein complexes Affinity purification is a standard method for analysing protein–protein interactions and topology of complexes by chemical cross-linking. Cross-linking converts non-covalent interactions between proteins surfaces into artificial covalent bonds. Cross-linking along with MS analysis can support modelling and aid in solving structures of complexes. Because the protein complex purification method based on eGFP protein fusion/resin has proven efficient with a relatively low background, we decided to test its application for cross-linking experiments. Because a 3D structure of the core RNA polymerase enzyme is available for  Studio) , and samM. tuberculosis for investigating cellular processes. It is well established that the composition of various protein complexes may differ during various growth conditions or under stress. In this study, we decided to use UvrA, a protein involved in a process of DNA damage repair system (NER) and also well conserved between the bacterial species. UvrA is known to be in complex with UvrB, where a UvrA–UvrA dimer binds UvrB to form a DNA integrity-scanning complex, UvrA2B or UvrA2B2M. tuberculosis UvrA (Rv1638), which is identical to BCG_1676 from M. bovis BCG, in BCG to determine complex formation after DNA damage induction with UV light. We observed that UvrA was in complex with UvrB in cells, as expected. We were also able to monitor complex dissociation during DNA damage repair and re-association after the repair process was completed (E. coliE. coli (20 min average) and M. bovis BCG (16–20 h). This result adds a dynamic capability to our method.Ideally, the method used in our study should translate to ompleted . PolymerM. smegmatis mc2155. All tags are a method for binding the protein to a resin with immobilized antibodies that recognize a specific epitope. We have shown that affinity tags can be used for protein purification from mycobacterial species, and interacting protein partners can be detected. The purity and background signal do vary. As described previously Affinity purification coupled with MS is used to identify proteins and their interacting partners. The first step is efficient purification of protein complexes with, ideally, no or little background. Optimizing this method to improve efficiency and breadth of interactions discovered would help in understanding the pathogen biology. Several affinity tags are now used to facilitate isolation of proteins with their partners. Based on the nature of the affinity tag and its target, we can distinguish several systems: protein-immobilized molecular ligand  In our study, the lowest background was detected in experiments using the GFP tag. In addition, one of the important features of this experimental setup is the ease of detection of tagged recombinant proteins. With the exception of GFP, all examined tags need special attention to visualize recombinant proteins within cells and to determine their subcellular localization and expression levels. Only cells expressing protein fused with eGFP can be directly used for microscopy. Our eGFP tag allows measurement of the binding efficiency of the tagged protein to the respective affinity resin .The eGFP tag is a full-length enhanced green fluorescent protein, which may impact structure or solubility of the tagged protein within cells. It is often detectable during overexpression of recombinant proteins when missfolded proteins aggregate and form inclusion bodies Additional advantages of the eGFP tag included the ability to quickly and accurately control expression of the protein fused to eGFP, the high recovery ratio from the anti-GFP resin and the very low cost of purification. Cost is a critical parameter when an affinity tag and appropriate resin is selected, particularly for high-throughput experiments. We compared the price of purification for different affinity resins. In-house preparation of the anti-GFP affinity resin, as was done for this work, markedly decreases expenses .Mycobacterium. To aid this quest, we compared 4 different affinity tags commonly used for affinity purification and evaluated their potential use in high-throughput experiments in mycobacterial model. Although, two-hybrid and three-hybrid systems have been used successfully M. smegmatis subunits that mapped to the E. coli model Deciphering the protein–protein interactions may be very helpful for improving our understanding of the biology and pathogenesis of M. bovis BCG  and a DNA helicase II, annotated as UvrD2. However, additional studies will have to be conducted to understand the underlying mechanisms of such interactions. One possibility would be that the DNA integrity-scanning complex requires TopoI and DNA helicase II to respectively relax and unwind the DNA during scanning. In eukaryotes, it was shown that down modulation of topoisomerase I using antisense RNA inhibits repair of UV-induced lesions. The experiments show that TopoI is actively recruited onto genomic DNA following DNA damage by UV light, possibly acting during pre- or post-DNA damage processing Mycobacteria and possibly other prokaryotes. A previous study demonstrated the interaction between UvrA, UvrB and UvrD in E. coli using immunoprecipitation Using the nucleotide excision repair protein UvrA in Table S1List of primers used in this study.(PDF)Click here for additional data file.Table S2Peptide identification details for AP-MS experiments.(XLSX)Click here for additional data file.Table S3Protein identification details for AP-MS experiments.(XLSX)Click here for additional data file.Table S4MaxQuant based semi-quantitative analysis of preys purified in AP-MS experiments.(XLSX)Click here for additional data file.Table S5List of prey proteins identified as common contaminants.(XLSX)Click here for additional data file.Table S6Cross-links between the subunits of RNA polymerase identified by pLINK software.(XLSX)Click here for additional data file.Table S7Comparison of expense of protein binding resins used in this study.(PDF)Click here for additional data file.


Protein structures are better conserved than protein sequences, and consequently more functional information is available in structures than in sequences. However, proteins generally interact with other proteins and molecules via their surface regions and a backbone-only analysis of protein structures may miss many of the functional and evolutionary features. Surface information can help better elucidate proteins' functions and their interactions with other proteins. Computational analysis and comparison of protein surfaces is an important challenge to overcome to enable efficient and accurate functional characterization of proteins.In this study we present a new method for representation and comparison of protein surface features. Our method is based on mapping the 3-D protein surfaces onto 2-D maps using various dimension reduction methods. We have proposed area and neighbor based metrics in order to evaluate the accuracy of this surface representation. In order to capture functionally relevant information, we encode geometric and biochemical features of the protein, such as hydrophobicity, electrostatic potential, and curvature, into separate color channels in the 2-D map. The resulting images can then be compared using efficient 2-D image registration methods to identify surface regions and features shared by proteins.We demonstrate the utility of our method and characterize its performance using both synthetic and real data. Among the dimension reduction methods investigated, SNE, LandmarkIsomap, Isomap, and Sammon's mapping provide the best performance in preserving the area and neighborhood properties of the original 3-D surface. The enriched 2-D representation is shown to be useful in characterizing the functional site of chymotrypsin and able to detect structural similarities in heat shock proteins. A texture mapping using the 2-D representation is also proposed as an interesting application to structure visualization. The advent of new technologies has resulted in a massive expansion of the protein sequence and structure databases. This enables the characterization of the similarities of sequences and structures and identification of the location of functional sites. High throughput sequencing data analysis has opened up new applications and facilitated the study of proteins. The alignment of protein sequences and structures has been able to investigate convergent and divergent protein relationships; this has been facilitated by the exponentially increasing size of the available data. Traditionally, sequence analysis has been largely based on pairwise and multiple sequence alignments, which are algorithmically based on dynamic programming ,2. HeuriUnlike protein sequences, protein structure analysis has not yet enjoyed a widely accepted comparison or search method. The Protein Databank (PDB) is a repository of 3-D protein and nucleic acids structures . As of FUnlike sequence alignment, structure alignment captures information not detectable in a protein's sequence due to the nature of protein folding: two amino acids that are far away from each other in a protein sequence may be brought close together when the protein folds. Although three dimensional protein structures are determined by primary sequences, even large sequence variations (due to mutation) usually only cause minor and unimportant structural variations. Thus, evolutionary relationships are best detected at the structural level.The computation of protein structure alignment is a computationally hard problem, due to the number of possible combinations of residue associations that can be used to generate corresponding translation and rotation matrices, and it is usually solved by heuristic approaches -9. DespiProtein structure uncovers more distant evolutionary relationships than protein sequence. However, we cannot neglect the fact that two different proteins' surface characteristics may converge through evolution and result in similar functions . Two proIn addition to advancing the general body of functional knowledge for proteins, protein surfaces can also play a role in rational drug design. The analysis of protein surfaces could identify protein binding pockets so that the requirements for a given pharmaceutical compound's size and binding orientation can be determined . FurtherIn this paper, we introduce a new method for the analysis and comparison of protein surfaces. We utilize a two dimensional representation that enables efficient computational storage and comparison. The reduced representation is optimized using dimension reduction methods, such that the geometric relationship of the atoms in 3-D is preserved in the 2-D representation. We demonstrate that this reduced representation captures biologically important information by characterizing an enriched 2-D map of a chymotrypsin protein and by comparing enriched image representations of heat shock proteins.First, we consider the problem of map generation as an error minimization problem, and utilize dimension reduction methods to perform this mapping. While the accuracy of earlier studies is limited by how close the shape of protein is to a sphere or ellipse, our approach attempts to address more complex shapes, as are present in almost all proteins. Secondly, we enrich the surface map with bio-chemical and geometrical properties, such as electrostatic potential, hydrophobicity and curvature, in order to facilitate functional analysis. While other surface features can also be mapped in a similar fashion as the method described here, we leave an exhaustive feature mapping to a future endeavor. Image registration is then applied on these feature-enriched images. Thirdly, we utilize the 3D-2D mapping to perform texture-mapping of arbitrary images back on the 3-D surface, to complement the existing graphical visualization options.Figure A number of different representations have been developed to describe the protein surface  . Unlike Starting from Connolly's work, numerous methods have been proposed for surface representation, Sanner  introducProtein surfaces generated by these methods have found use in a variety of visualization and analysis applications. Almost all popular macromolecular visualization programs now contain routines for the generation and visualization of different types of surface representations ,20.The difficulty of dealing with surfaces is apparent, in comparison to the more widely utilized primary sequence or backbone conformation, which possess numerous alignment methods. Due to the complexity of the surfaces and the lack of established methods for general-purpose analysis, most studies have focused on certain surface features, such as active or functional sites and structural motifs . These sApproaches that have attempted to represent and analyze the entire surface have been geared toward extracting generic shape parameters that are not amenable to detailed characterization of surfaces. 3-D Spherical harmonics and Zernike descriptors have been used as feature vectors for protein structure comparison and similarity-based retrieval . GeometrOur approach to study the protein surfaces is based on finding an accurate representation of the protein surface in 2-D. Representing 3-D surfaces in 2-D is an old problem, most known in geography, where some terrain or the entire globe is shown on a map. This process has been coined "molecular cartography" for macromolecular structures ,27. ThesThe studies by both Fanning et al.  and PawlOur approach is based on the method of representing the surface of a three dimensional object on several planar grids. A dimension reduction method (DRM) is a geometric technique that maps higher dimensional data into a lower dimensional space while preserving some geometrical properties of the higher dimensional data, such as the variance or inter-point distances. There are many different dimension reduction methods, but they generally fall into three categories: linear methods, global nonlinear methods, and local nonlinear methods.Principal Components Analysis (PCA) is one of the classic linear dimension reduction methods. It attempts to find a linear mapping between high dimensional and low dimensional data using the principal eigenvectors of the covariance matrix of data  PCA is aMultidimensional Scaling (MDS) is a global nonlinear dimension reduction method. MDS constructs a dissimilarity matrix in high dimensional data points using Euclidean distance and tries to maintain the minimum distance errors. The stress function of choice is often Kruskal's stress or Sammon's stress measures . Other gLocally-Linear Embedding (LLE) involves finding the nearest neighbors of each point and then determining weights for each point in order to express the point as a linear combination of its neighbors. The weiWhile visual inspection of the 2-D mappings can provide insights into the maps generated by different methods, a more quantitative evaluation is needed for comparison. For a given dataset of protein structures, we evaluate each dimension reduction method based on its accuracy and speed in mapping the surface. The accuracy of a dimension reduction method is evaluated by its ability to preserve the spatial features and relationships among the points. We have defined two assessment criteria for area and neighbor preservation. The area score (ranging from -1 to 1) is calculated as the Pearson's correlation coefficient between the areas of the surface triangles in 3-D and in 2-D, and it measures the level of distortions induced by the mapping procedure. The higher the correlation value of a method, the better the method preserves the relative spatial distributions of the points. The neighbor score (ranging from 0 to 1) evaluates the ability of a method to preserve the neighborhood relationships among the points, and is calculated using the Tanimoto similarity coefficient of the connectivity matrices of all points in 2-D and 3-D. In 3-D, the connectivity matrix is obtained using the geodesic distances of the k-nearest neighbors of each point. In 2-D, the connectivity matrix is obtained using the Euclidean distance of the k-nearest neighbors of each point (we used k = 3). These connectivity matrices are then represented as linear bit vectors  X and Y. The Tanimoto coefficient  of two bThe higher the Tanimoto coefficient, the better the method is at preserving the neighbors of the points.Dimension reduction provides a mapping on to the 2-D space, and implicitly captures only the geometric properties of the original surface points. While the area and neighborhood properties of the points are preserved as much as possible under the constraints of the 2-D space, other geometric properties are mostly ignored. Note however, that we can enrich the mapped points with color channels representing additional information. Specifically, we associate a color channel for curvature information, thus capture additional 3-D geometric properties.Even though geometric features of the protein surface are important functional determinants, the biochemical properties of the surface points are as important in determining binding interactions and enzymatic activity. We have investigated two biochemical features: electrostatic potential and hydrophobicity. The electrostatic potential plays an important role in indicating molecular interactions and protein folding. We have used the Poisson-Boltzman formulation to calculate the electrostatic potential at each surface point . The hydThere are many registration methods available, and they can be classified in different ways such as feature-based and intensity-based methods. Feature-based methods use the common features to find the correspondence between two images. These features can be based on points, curves, or surfaces, each with a corresponding distance metric to facilitate the identification of feature associations between two images. The feature-based methods work well if the images contain salient patterns, such as corners or contours. Intensity-based methods rely on pixel intensities and have several different metrics, such as Normalized Cross Correlation of the pixel intensities, Mutual Information, and the Sum of Squared Differences .In order to evaluate our approach and characterize the performance of different methods and parameter choices, we used both synthetic and real data. The synthetic data consisted of an idealized sphere with 162 equi-distant points triangulated into 320 triangles. The real data consisted of 8198 surface points generated from protein 1kaz which were triangulated into 16160 triangles.Mapping of an idealized spherical surface using PCA and sinusoidal cartography  is illusIn order to evaluate the performance of various dimension reduction methods, we mapped a triangulated hemisphere with equally distributed points. Table 1kaz[Protein structures have naturally evolved to have more complex shapes, with pockets and protrusions. In order to evaluate the performance of the dimension reduction methods on real proteins, we performed the same experiment describe above for an idealized hemisphere, to a heat shock protein ATPase domain (PDB ID: 1kaz), The prAs expected from the more complex structure of the protein, the dimension reduction methods result in lower area and neighbor scores compared to the simpler hemisphere experiment above. 18 of the methods have an area score between 0.66 and 0.70. Among these, SNE, Isomap, and LandmarkIsomap have a neighbor score better than 0.23. The protein surface contained 50 times more points than the hemisphere, which significantly increased the running time for most of the methods.2ea3) [A visual inspection of the 2-D surface maps confirmed that the methods SNE, Isomap, LandmarkIsomap, and Sammon produced comparable maps that were superior to those generated by other methods (results not shown). We have used the 2-D maps produced by Sammon mapping for the downstream analysis described below. In order to evaluate the ability of our 2-D representation to capture the biologically important information, we conducted an experiment on a bacterial chymotrypsin (PDB ID: 2ea3)  Chymotry1bup[1kaz[In order to evaluate whether the 2-D representation of protein surfaces can be used for surface comparison, we conducted an experiment with two heat shock proteins (PDB IDs: 1bup and 1kaz1bup[1kaz). These 1bup[1kaz,44 and mThe hydrophobicity map reveals that the active site lies on a blue hydrophobic belt-shaped area. The electrostatic potential image shows the active site to lie in a red region of negative charge, and the curvature image shows it to be a concave valley enclosed by a bulged "mountain" structure. These observations conform to the relevant theory and also prove the accuracy of the feature enrichment as a descriptive guide for characterization of the active site.Once the hydrophobicity, electrostatic potential and curvature models are generated, two (or more) protein surfaces can be compared. Note that the proteins are likely to be in different spatial orientations in the model database, thus an image registration needs to be performed to reorient and superpose them before similarities can be highlighted. We have left an investigation of automated image registration methods for a future study and have resorted to a manual image registration at present to ensure accuracy.The claim that our representation can capture structural similarity can best be demonstrated using the 2-D curvature maps of proteins. Figure The 2-D mapping presented in here lends itself to an interesting visualization application. Specifically, the 2-D map of a surface can be overlaid with an arbitrary image to associate each map point with a pixel value from the image. Figure 1kaz), where an image of a color wheel is texture-mapped on the protein  by obviating complex structural analysis in favor of surface features, which have greater functional relevance.Thus, surface comparison attempts to identify protein functional sites which are better predictors of protein function than sequence or structural features. We achieve surface comparison by mapping 3-D protein surfaces into 2-D through dimension reduction methods and enriching the 2-D representation with biochemical and geometrical features. Various dimension reduction methods are evaluated for their ability to accurately represent the protein surface and their computational efficiency. The alignment of pairs of protein models obtained by these methods is obtained through a manual image registration process. An automated registration process which quantifies the similarity of proteins and localizes the active site will be presented separately. Furthermore, the 3-D to 2-D mapping of surface points enables novel visualizations of protein structure and properties, including texture mapping in which the 2-D protein map is overlaid onto an arbitrary image. Future work, including the automatic implementation of the entire workflow described above, provides a clear path toward a protein function prediction system in which a query protein is ranked against a database of existing protein surface maps. Prediction of protein-protein interaction partners and interaction sites is possible through a similar system in which a query protein would be searched against a pre-built database of interaction sites, and their correlation used in making predictions.The authors declare that they have no competing interests.AS conceived of the study and coordinated the project. HY was the primary developer, who implemented the method and performed the experiments. RQ contributed to the design and test of the method. All authors participated in the analysis of the results. HY and RQ contributed to the writing of the manuscript. All authors read and approved of the final draft.