Opinion paper

Phage “delay” towards enhancing bacterial escape from biofilms: a more comprehensive way of viewing resistance to bacteriophages

  • In exploring bacterial resistance to bacteriophages, emphasis typically is placed on those mechanisms which completely prevent phage replication. Such resistance can be detected as extensive reductions in phage ability to form plaques, that is, reduced efficiency of plating. Mechanisms include restriction-modification systems, CRISPR/Cas systems, and abortive infection systems. Alternatively, phages may be reduced in their “vigor” when infecting certain bacterial hosts, that is, with phages displaying smaller burst sizes or extended latent periods rather than being outright inactivated. It is well known, as well, that most phages poorly infect bacteria that are less metabolically active. Extracellular polymers such as biofilm matrix material also may at least slow phage penetration to bacterial surfaces. Here I suggest that such “less-robust” mechanisms of resistance to bacteriophages could serve bacteria by slowing phage propagation within bacterial biofilms, that is, delaying phage impact on multiple bacteria rather than necessarily outright preventing such impact. Related bacteria, ones that are relatively near to infected bacteria, e.g., roughly 10+ µm away, consequently may be able to escape from biofilms with greater likelihood via standard dissemination-initiating mechanisms including erosion from biofilm surfaces or seeding dispersal/central hollowing. That is, given localized areas of phage infection, so long as phage spread can be reduced in rate from initial points of contact with susceptible bacteria, then bacterial survival may be enhanced due to bacteria metaphorically “running away” to more phage-free locations. Delay mechanisms—to the extent that they are less specific in terms of what phages are targeted—collectively could represent broader bacterial strategies of phage resistance versus outright phage killing, the latter especially as require specific, evolved molecular recognition of phage presence. The potential for phage delay should be taken into account when developing protocols of phage-mediated biocontrol of biofilm bacteria, e.g., as during phage therapy of chronic bacterial infections.

    Citation: Stephen T. Abedon. Phage “delay” towards enhancing bacterial escape from biofilms: a more comprehensive way of viewing resistance to bacteriophages[J]. AIMS Microbiology, 2017, 3(2): 186-226. doi: 10.3934/microbiol.2017.2.186

    Related Papers:

    [1] Noman Zahid, Ali Hassan Sodhro, Usman Rauf Kamboh, Ahmed Alkhayyat, Lei Wang . AI-driven adaptive reliable and sustainable approach for internet of things enabled healthcare system. Mathematical Biosciences and Engineering, 2022, 19(4): 3953-3971. doi: 10.3934/mbe.2022182
    [2] Hao Yuan, Qiang Chen, Hongbing Li, Die Zeng, Tianwen Wu, Yuning Wang, Wei Zhang . Improved beluga whale optimization algorithm based cluster routing in wireless sensor networks. Mathematical Biosciences and Engineering, 2024, 21(3): 4587-4625. doi: 10.3934/mbe.2024202
    [3] Tingting Yang, Yi He . Design of intelligent robots for tourism management service based on green computing. Mathematical Biosciences and Engineering, 2023, 20(3): 4798-4815. doi: 10.3934/mbe.2023222
    [4] Angel Martin-del Rey . A novel model for malware propagation on wireless sensor networks. Mathematical Biosciences and Engineering, 2024, 21(3): 3967-3998. doi: 10.3934/mbe.2024176
    [5] Naila Naz, Muazzam A Khan, Suliman A. Alsuhibany, Muhammad Diyan, Zhiyuan Tan, Muhammad Almas Khan, Jawad Ahmad . Ensemble learning-based IDS for sensors telemetry data in IoT networks. Mathematical Biosciences and Engineering, 2022, 19(10): 10550-10580. doi: 10.3934/mbe.2022493
    [6] Haitao Huang, Min Tian, Jie Zhou, Xiang Liu . Reliable task allocation for soil moisture wireless sensor networks using differential evolution adaptive elite butterfly optimization algorithm. Mathematical Biosciences and Engineering, 2023, 20(8): 14675-14698. doi: 10.3934/mbe.2023656
    [7] B. Kiruthika, Shyamala Bharathi P . Intelligent dynamic trust secure attacker detection routing for WSN-IoT networks. Mathematical Biosciences and Engineering, 2023, 20(2): 4243-4257. doi: 10.3934/mbe.2023198
    [8] Peng-Yeng Yin, Chih-Chun Tsai, Rong-Fuh Day, Ching-Ying Tung, Bir Bhanu . Ensemble learning of model hyperparameters and spatiotemporal data for calibration of low-cost PM2.5 sensors. Mathematical Biosciences and Engineering, 2019, 16(6): 6858-6873. doi: 10.3934/mbe.2019343
    [9] Faten S. Alamri, Khalid Haseeb, Tanzila Saba, Jaime Lloret, Jose M. Jimenez . Multimedia IoT-surveillance optimization model using mobile-edge authentic computing. Mathematical Biosciences and Engineering, 2023, 20(11): 19174-19190. doi: 10.3934/mbe.2023847
    [10] Huanhai Yang, Shue Liu . A prediction model of aquaculture water quality based on multiscale decomposition. Mathematical Biosciences and Engineering, 2021, 18(6): 7561-7579. doi: 10.3934/mbe.2021374
  • In exploring bacterial resistance to bacteriophages, emphasis typically is placed on those mechanisms which completely prevent phage replication. Such resistance can be detected as extensive reductions in phage ability to form plaques, that is, reduced efficiency of plating. Mechanisms include restriction-modification systems, CRISPR/Cas systems, and abortive infection systems. Alternatively, phages may be reduced in their “vigor” when infecting certain bacterial hosts, that is, with phages displaying smaller burst sizes or extended latent periods rather than being outright inactivated. It is well known, as well, that most phages poorly infect bacteria that are less metabolically active. Extracellular polymers such as biofilm matrix material also may at least slow phage penetration to bacterial surfaces. Here I suggest that such “less-robust” mechanisms of resistance to bacteriophages could serve bacteria by slowing phage propagation within bacterial biofilms, that is, delaying phage impact on multiple bacteria rather than necessarily outright preventing such impact. Related bacteria, ones that are relatively near to infected bacteria, e.g., roughly 10+ µm away, consequently may be able to escape from biofilms with greater likelihood via standard dissemination-initiating mechanisms including erosion from biofilm surfaces or seeding dispersal/central hollowing. That is, given localized areas of phage infection, so long as phage spread can be reduced in rate from initial points of contact with susceptible bacteria, then bacterial survival may be enhanced due to bacteria metaphorically “running away” to more phage-free locations. Delay mechanisms—to the extent that they are less specific in terms of what phages are targeted—collectively could represent broader bacterial strategies of phage resistance versus outright phage killing, the latter especially as require specific, evolved molecular recognition of phage presence. The potential for phage delay should be taken into account when developing protocols of phage-mediated biocontrol of biofilm bacteria, e.g., as during phage therapy of chronic bacterial infections.


    Wireless Sensor Networks (WSNs) is a multi-hop wireless network that is formed by self-organizing the sensor nodes of large-scale deployment. By WSNs, the data information of the perceived object in the monitoring area is collected and transmitted by a coordinated manner. Since WSNs has more advantages, e.g. strong environment adaptiveness, portable and energy efficient, they are widely used to collect information from the physical world and produce large-scale sensor data sets. Obviously, the completeness and accuracy of these awareness data sets significantly affect the reliability of scientific results. If these data are lost or jumping during transmission, it will inevitably lead to the unreliable or error results. Therefore, the completeness and accuracy for scientific data are so important in decision-making. Nevertheless, in actual data collection scenario, data loss is so common. The reasons can be summarized as follows: (1) wireless channel instability and noise interference, (2) mutual interference between channels caused by tree or clustered topology, (3) congestion caused by data bursts in high-density deployments or emergencies, (4) unexpected failure due to node damage or battery problem. The mentioned cases maybe cause serious errors in receiving end and finally lead to invalidation of some scientific research and engineering calculations.

    Although the importance of missing data in wireless sensor networks is very prominent, the research on this problem is still relatively rare. Some researchers have tried to reconstruct the missing data by using some typical interpolation algorithms [1], which always appear in the field of database [2], multimedia [2], and signal processing [3]. For example, as a classical local interpolation method, k-Nearest-Neighbor (kNN) [4] is usually used to estimate the missing data according to the nearest k neighbors around the missing data position. This scheme can achieve a good estimation performance due to high correlation between adjacent data, and is thus used in low-fidelity estimation cases. Delaunay Triangulation (DT) [5] is another typical global interpolation method. This method considers each collected data as vertices, which are connected into triangles according to the process of gradually reducing the global error, and the missing values are finally inserted into the data set. Multi-channel Singular Spectrum Analysis (MSSA) [6] is a nonparametric adaptive method, which belongs to the category of principal component analysis. This method uses embedded self-covariance matrix to insert missing values. Compressive Sensing (CS) method [7,8] was proposed in 2006, which is an advanced data recovery algorithm. If the data set is sparse, CS method can efficiently estimate the whole data set by using very little known data. Therefore, this method has attracted much research interest. On the basis of CS scheme, Kong et al. proposed an improved algorithm [9], named by Environmental Space Time Improved Compressive Sensing (ESTI-CS), which embeds customized features into the baseline CS to deal with the specific data loss patterns and then uses a multi-attribute assistant (MAA) component to perform data reconstruction. Chen et al. proposed a novel data reconstruction scheme via temporal stability guided matrix completion [10]. They formulate the data reconstruction problem as a matrix completion with structural noise and further reduce the reconstruction error by introducing a constraint about short-term stability to the matrix completion problem.

    Although the existing schemes can work for the data recovery and reconstruction, they can not completely solve the data loss in the wireless sensor network due to the following reasons:

    ● The data loss mechanism in wireless sensor networks has some special characteristics, which often do not meet the assumptions of classical interpolation algorithms.

    ● Existing schemes always reconstruct missing data by interpolation or prediction, which makes that some predicted data are not exactly consistent with the original data. Therefore, they cannot be applied in some cases that needs high data accuracy.

    ● Existing schemes can recover original data only when the missing data is small. In other words, they maybe provide an unsatisfactory accuracy when the missing data becomes large.

    Overall, existing methods always provide the estimated value for the loss data. This mechanism is usually efficient to small-scale insensitive environmental data, but for large-scale and high accuracy data, it may not work well anymore. Facing the aforementioned problems, this paper designs a data decomposition and ensemble recovery mechanism, and tries to fundamentally solve the data loss and jumping in the data transmission for wireless sensor networks. Comparing with the previous works, we make the following novel contributions.

    ● We propose a reliable data transmission scheme by designing data decomposition and ensemble recovery mechanism. We claim that proposed scheme can solve the data loss problem in WSNs, and guarantee the correctness of original data even if some data are lost or damaged in delivery.

    ● We use matrix decomposition to design data expansion mechanism, and then split the original data into multiple data shares, which are transmitted through multiple sensor nodes. Since each data share contains some data redundancy, the loss of part of the shares does not affect the recovery of original data.

    ● Ensemble recovery mechanism is designed to reconstruct the missing data. This mechanism can not only recover the missing data, but can revise the incorrect data if they occurs jumping in transmission.

    ● Comprehensive simulation experiments are performed by the WSNs including multiple sensor nodes. The experimental results demonstrate that proposed scheme can reconstruct the missing data perfectly, and significantly superior than the existing interpolation schemes.

    The rest of this paper is organized as follows. Section 2 provides the details of proposed scheme by constructing the loss model and introducing the procedure of data decomposition and ensemble reconstruction. Subsequently, a series of simulation experiments are performed to evaluate the performance of proposed scheme. The experimental results and corresponding discussions are presented in Sections 3. Finally, Section 4 concludes the paper.

    In this section, we discuss the data loss pattern in WSNs. For data unreliable transmission problem, we always intuitively think that the data is randomly lost. However, for WSNs, this problem becomes rather particular. For example, when a sensor node encounters failure, it will continuously lose data, while other nodes may not generate data loss. In general, in terms of the nature of WSNs, we can summarize two typical data loss patterns as follows.

    Data loss pattern. Since WSNs include multiple sensor nodes and each node has special function and characters, data loss pattern usually contains random loss, block random loss and continues row loss. Random loss is always caused by the noise and collision in WSNs. The missing data is evenly distributed in the data matrix. Block random loss may result from large-scale data congestion caused by unexpected events. This case usually happens in high density sensor nodes. Continues row loss presents the case that the whole data is lost from a certain location to the end of this row. This pattern may caused by battery exhausted or accidentally damaged for sensor node. The subfigures on the top of Figure 1 show the cases of data loss pattern.

    Figure 1.  The data loss and jumping pattern in wireless sensor networks. Each block represents the transmission data of one sensor node. The top subfigures present the data loss pattern and the black blocks stand for loss data, while the bottom subfigures present the data jumping pattern and the green blocks stand for the jumping data.

    Data jumping pattern. Data jumping pattern is similar to data loss pattern and also includes three case, random jumping, block random jumping and continues row jumping. In fact, data jumping pattern explains the case that when data is transmitted, single digit may be changed to another one due to signal interference. For example, 1 is changed to 0, or vice versa. The subfigures on the bottom of Figure 1 give the cases of data jumping pattern.

    Proposed data transmission scheme is comprised of three parts: data decomposition, data delivery and data ensemble recovery. In the first part, aiming at each sensor node, the original perceived data can be split into multiple data shares by matrix decomposition mechanism. These data share are sent to the the next sensor node in sequence. In the second part, each data share is delivered into complex sensor networks. They may counter noise and channel interference or sensor node fault so that some data are lost or damaged in delivery. In the third part, according to received data shares, we design ensemble mechanism to recover the original perceived data even if received data is lost a lot or contains many digital jumping. The framework of our proposed scheme is shown in Figure 2.

    Figure 2.  The framework of proposed data transmission scheme.

    In WSNs, the environmental data are perceived by sensor node and then sent to the networks in sequence. Then, multiple wireless node transmit the data by relaying, and finally deliver them to the source node. At the source node, the receiver (computer or processing center) reconstruct the original data according to a fixed order. Unfortunately, these perceived data may be attacked/damaged during transmission, such as the channel interference, network noise or sensor node fault. In this case, it is unreasonable to assume that the source node can receive the information completely and accurately. Once the data are lost, it may cause serious problems due to the incomplete of perceived data. Although researchers have tried many interpolation method, the incomplete and incorrect problem of perceived data are still difficult to solve.

    To improve the robustness of perceived data transmission in WSNs, in this section, we try to use matrix decomposition mechanism [11,12] to preprocess the perceived original data. Specifically, we are inspired by data sharing. The original perceived data are expanded and divided into multiple data shares. According to the idea of data sharing, each share only contains a small portion of valid data, partial share loss do not affect the recovery for original perceived data. The corresponding details are provided as follows.

    First, we assume that perceived data is always a decimal number or digital string. To divide the original data, they are transmitted firstly to a binary stream, and then are presented as q-ary symbol system, where q is an odd prime. We can use a simple procedure to process this presentation. For example, the binary stream are segmented into multiple pieces and each of them includes L1 bits. According to the following equation, we can convert these L1 bits to L2 q-ary digits.

    L1=L2log2q. (3.1)

    Assume that L1=4, L2=2. If we convert the original data into 5-ary notational system, we can use the following simple sample to explain this procedure.

    2ary[110101101001]5ary[231114] (3.2)

    The relationship between L1 and L2 can be represented by the following equation.

    r=1L1L2log2q (3.3)

    Obviously, if L1 and L2 are very large, we can determine that the parameter r is close to 0.

    Subsequently, we integrate all q-ary digits as a digital matrix D. The detailed data decomposition procedure can be explained by the following steps.

    Step 1: Divide D into K vectors, D = {d1,d2,,dK}, each of them can be represented as follows.

    dk={dk,1,dk,2,,dk,m} (3.4)

    where m represents that each vector contains the number of q-ary digits and k[1,K].

    Step 2: Select a1,a2,,an as a set of indices and use them to construct a q-ary Vandermonde matrix A with the size of m×n.

    A=[111a1a2ana21a22a2nam11am12am1n]modq (3.5)

    where a1,a2,,an[0,q1] are different with each other. With the core of Vandermonde matrix, m, n, and q must satisfy mnq.

    Step 3: According to the Step 1 and Step 2, each digital block dk can be divided into n shares, which are denoted as a q-ary digital vector tk.

    tk=[dk,1dk,2dk,3dk,m]A (3.6)

    where tk = [tk,1tk,2tk,3tk,n] includes n q-ary digits, and the symbol "" is the multiplication operator in q-ary notational system.

    We can use a simple example to explain data decomposition procedure. Assume that q=7, n=6, m=3, the original perceived data are three 7-ary digits [2 1 4], and the indices of Vandermonde matrix are fixed as [a1a2an] = [5 3 1 0 2 4]. According the Equation (3.5), the Vandermonde matrix can be built as follows.

    A=[111111531024421042] (3.7)

    We use the Equation (3.6) to calculate the expanded data vector tk = [2 6 0 2 6 0], which subsequently is sent into the WSNs by the sensor node.

    [214][111111531024421042]=[260260]modq (3.8)

    According to the data decomposition procedure, the expanded data will be sent into the WSNs. Unfortunately, since the wireless sensor nodes always face the harsh environments. If they are delivered through insecure network channel, it might encounter data loss or jumping due to diverse network faults. Following the formula of data decomposition, the source node can reconstruct the original perceived data by an ensemble mechanism only if it can receive enough expanded data.

    Assume that the source node only receive correctly a part of expanded data tk = [tk,1tk,2tk,3tk,n], mnn, and the other data is lost. In that way, as long as the loss number for original data vector tk is not more than nm, the source node can reconstruct original perceived data by the following equation.

    [dk,1dk,2dk,3dk,m]=[tk,1tk,2tk,3tk,m](A)1 (3.9)

    where tk,1, tk,2, tk,3, , tk,m are m received digits selecting randomly from the remaining digits (Here, we suppose the remaining digits do not contain the jumping case). In addition, A is a m×m Vandermonde matrix built by the indices a1, a2, , am that correspond to one-to-one with the tk,1, tk,2, tk,3, , tk,m. A1 is the inversion matrix of A in q-ary notational system and we can find the derivation process of the inversion matrix in [12].

    Obviously, the case for data loss can be also explained by a simple example. Following the actual example shown in Section 3.2. Assume that the received expanded data are [2 6 2 0] (the complete expanded data [2 6 0 2 3 0]). We randomly select 3 digits [2 6 2] and their corresponding indices is [5 3 0] (the complete indices [5 3 1 0 2 4]). Accordingly, we can build easily the Vandermonde matrix A by Equation (3.5) and also calculate the inversion matrix easily based on the derivation in [12].

    A=[111530420]modq(A)1=[065021161]modq (3.10)

    The original perceived data can be calculated easily by Equation (3.11).

    [262][065021161]=[214]modq (3.11)

    Similarly, we also assume that the source node receive a part of expanded data tk = [tk,1tk,2tk,3tk,n], mnn. The received data may suffer some jumping (more or less), but we can not determine which data are changed. Although the jumping number for tk is not determined, the source node can also recover original perceived data by ensemble mechanism, which is explained detailed in Algorithm 1. Actually, the data jumping case that we discuss here includes the data loss case.

    Algorithm 1: Ensemble Recovery for Data Jumping
    Input: tk = [tk,1tk,2tk,3tk,n], the corresponding indices a1, a2, , an for tk, multi-ary parameter q, ensemble rounds R.
    Output: Original data vector dk={dk,1,dk,2,,dk,m}.
    1 for i 1 to R do
    6 end
    7 dk = MajorityVoting(d1,d2,d3,,dR).

    In order to understand the ensemble mechanism easily, we also use the actual example proposed in Section 3.3.1. According to the complete expanded data [2 6 0 2 6 0], we assume that the last digit is lost and the second digit is jumping in transmission (take '6' to '4' as an example). Thus, the received data are [2 4 0 2 6]. Since the source node does not know which digits are jumping, the ensemble mechanism with majority voting is used to decide the correct original data. An actual ensemble example is shown in Figure 3.

    Figure 3.  An example for data ensemble recovery processing. In this example, we use five rounds ensemble in 7-ary notational system (R=5 in Algorithm 1). The complete expanded digits are [2 6 0 2 6 0] and the received digits are [2 4 0 2 6]. Since m=3 and n=6, each experiment can randomly select 3 digits from the received digits.

    We would like to remind readers that if we only consider the case of data loss in WSNs, we can provide an effective solution by the description in Section 3.3.1. However, if the received data contains both cases, data loss and data jumping, then we must use the ensemble reconstruction mechanism. In practice, we always use ensemble mechanism to handle all situations because we can't confirm whether the received data contains data jumping.

    According to the data decomposition mechanism, we can easily expand m q-ary digits to n q-ary digits. In other words, n q-ary digits contain nm redundancy digits and the redundancy rate, named as Re in this paper, can be calculated easily by Equation (3.12). Obviously, two parameters m and n have an important impact for redundancy rate. If the data lost rate is more than Re, the original data will be hard to recover. If the data lost rate is less than Re (assume that the number of received data are n), we can randomly select m digits from n to recover the original data.

    Re=1mn. (3.12)

    In addition, we would like to stress that the proposed ensemble reconstruction mechanism will be used more generally to recover the original perceived data, because we do not know whether the received data contain the jumping digits even if there is not any data loss. Nevertheless, we also remind that ensemble reconstruction mechanism only make an accurate decision with greater probability and can not thus guarantee that the original data is recovered perfectly. Similar to data loss pattern, if the data jumping rate is more than Re, ensemble mechanism does not work.

    In fact, we can calculate data recovery probability theoretically. Assume that we transmit n digits through WSNs, and in the receiving end, p1 digits are lost and p2 digits are jumping. The recovery probability T1 can be calculated as following when the ensemble mechanism is not used.

    T1=Cmnp1p2Cmnp1 (3.13)

    When the ensemble mechanism is used, the recovery probability T2 is

    T2=1[(1Cmnp1p2Cmnp1)R+RCmnp1p2Cmnp1(1Cmnp1p2Cmnp1)R1] (3.14)

    where R is the ensemble rounds (corresponding to the parameter R in Algorithm 1). In all the ensemble results, the result with the maximum number of occurrences will be decided as the correct original data.

    In this section, we validate the proposed scheme by simulating a wireless sensor network, which include 30 sensor nodes and one source node. We assume that the original data sent by each node is already decomposition data*. These data are delivered by multiple sensor nodes to source node and some of them may be lost in this procedure, our goal is to reconstruct original data.

    * In fact, to ease comparison, we can set a fixed decomposition matrix in all sensor nodes.

    To simulate the proposed scheme, we distribute 30 wireless sensor nodes in a 100m×100m area. The 30 wireless sensor nodes and source node are intergraded to form a wireless network with star topology, which is shown in Figure 1. We design a series of experiments by randomly select sensor node as sending end. The selected node sends the decomposition data to source node through multiple nodes' delivery. Some data may be lost in this transmission, then the source node will reconstruct the original data by proposed algorithm if the loss rate is not more than its limitation.

    In this paper, the actual network protocol in the wireless sensor networks is not considered. To ease understand, we use a simple self-organizing protocol and secure scheme [15] to simulate wireless network scenario.

    We repeat each experiment 100 times to obtain an average result, which is considered as the overall performance evaluation. Each time, we select a different sensor node as the sending end, which maybe send different original data.

    In this section, we analyze the reliability of proposed data transmission scheme. According to the idea of proposed scheme, the Vandermonde matrix is used to expand m original data to n shares, that is also to say, n expanded data carry m original data. Actually, it is similar to the data sharing mechanism. In this mechanism, each expanded data contains nmn redundancy data and the redundancy rate Re can be also calculated by Equation (3.12).

    Apparently, the redundancy rate Re depends on the parameters m and n and can be up very high if there is an extreme gap between m and n. Table 1 shows the relationship between redundancy rate Re and parameters m and n. By fixing parameter m, the redundancy rate Re will gradually raise with n increasing. This conclusion has been reflected theoretically by Figure 2.

    Table 1.  The relationship between parameters (m,n) and redundancy rate Re.
    m n q Re
    5 7 11 28.57%
    5 11 13 54.55%
    5 31 37 83.87%
    5 101 103 95.05%
    5 991 997 99.50%

     | Show Table
    DownLoad: CSV

    In this section, we test the recovery performance of proposed scheme for data loss pattern. Since data completeness is very easy to be checked by the source node (we suppose that the decomposition matrix is known by source node.), when source node receives all the data shares, it can check quickly whether the lost data exceeds the redundancy rate Re. Table 2 provides the original data recoverability for different expanded parameters m and n. In this table, we set m=5 and q=37. The data loss rates are fixed to five levels, which are 10%, 30%, 50%, 70%, 80%. As can be seen from the table, when data loss is not more than the redundancy rate Re, the original data can be reconstructed perfectly by source node. On the contrary, the original data can not be recovered once the received data rate is less than m/n. Actually, this conclusion can be also validated theoretically by the reliability analysis in Section 4.1.

    Table 2.  Data recoverability for different redundancy rate Re. Data loss rates are fixed to five levels, which are 10%, 30%, 50%, 70%, 80%, and the parameters m and q are fixed as 5 and 37, respectively.
    n Re Data loss rate
    10% 30% 50% 70% 80%
    9 44.44% Yes Yes No NoNo
    14 64.29% Yes Yes Yes No No
    19 73.68% Yes Yes Yes Yes No
    24 79.17% Yes Yes Yes Yes No
    29 82.76% Yes Yes Yes Yes Yes

     | Show Table
    DownLoad: CSV

    In addition, we also test the data recoverability only for data loss by comparing proposed scheme with the k-NearestNeighbor (kNN) scheme, which is also illustrated as classical traditional reconstruction method for data loss pattern. For any loss data, kNN scheme uses the k nearest neighbors to estimate it, and always replace the loss data with the majority of the k nearest neighbors. Note that the direct comparison is rather hard, because most of traditional data reconstruction schemes only provide a estimated value for the lost data, that is also to say, there is a slight gap between reconstruction value and actual value for kNN scheme, while proposed scheme can definitely give an exact value if the loss rate is not more than Re. Therefore, we need to build a fair comparison between proposed scheme and kNN scheme by setting a recovery error α in our following experiment. When the absolute of recovery error falls into a certain range (0,α), the reconstruction data is considered to be valid. Thus, the data recoverability (DR) can be calculated as follows.

    DR=NumberofcorrectdataTotalnumberofdata (4.1)

    To gain more insight, we imitate four seasons to simulate the real sensor network, and set the sensor nodes to perceive the environment temperature, Spring (1022℃), Summer (2237℃), Autumn (1022℃), and Winter (010℃). For kNN scheme, the parameter k is set to k=3 and five distance measures are used to give the comparison results. Moreover, the recovery error parameter α is fixed as 0.5 and 1.0, respectively. This indicates that the error ranges are set to [0.5,0.5] and [1,1]. Each experiment, we repeat 100 times to give the average DR value. The experimental results are shown in Figure 3 and Figure 4. In these figures, the x-axis represents data lost rate, while the y-axis denotes the data recoverability DR. It is easy to observe that for proposed scheme, when the data loss rate is lower than the theoretical redundancy rate Re, the overall DR values can reach 100%. However, when the data loss rate is more than the theoretical redundancy rate Re=73.68% (m=5, n=19, q=37), proposed scheme will not work well. In addition, for kNN method, the overall DR values are tending towards decreasing slowly with an increasing data loss rate. This is because there is a data estimation processing for kNN scheme, if the data loss rate becomes high, the valid data might be rather sparse so that the gap between reconstruction value and actual value becomes bigger and bigger, because it is very difficult to find k nearest neighbors with similar value.

    Figure 4.  The topology of sensors networks in our simulation experiments.

    Moreover, we also test the data recoverability for kNN scheme with different error ranges [α,α]{[0.5,0.5],[1.0,1.0],[2.0,2.0],[3.0,3.0]}. In this experiment, kNN scheme uses five distance measures, Euclidean, Manhattan, Chebyshev, Angle cosine and Hamming, to give the comparison results, which are shown in Table 3. We can see that when the recovery error range [α,α] becomes big, the data recoverability is slightly stronger. In fact, this phenomenon is explained easily. When α has a large range, more estimation data may be involved in valid data, leading to a higher data recovery rate. Also, we can also observe that proposed scheme consistently provide a perfect recoverability as long as the data loss rate is lower than Re, but, when the data loss rate is more than theoretical redundancy rate Re, e.g. 80%, proposed scheme does not work.

    Table 3.  Data recoverability for proposed scheme and kNN scheme using five measure methods. Four error ranges [α,α], [-0.5, 0.5], [-1.0, 1.0], [-2.0, 2.0], [-3.0, 3.0], are tested in this experiment. Data loss rates are fixed to five levels, which are 10%, 30%, 50%, 70%, 80%, and the parameters m and q are fixed as 5 and 37 (corresponding to Re=73.68%), respectively.
    Scheme Measure [α,α] Data loss rate
    10% 30% 50% 70% 80%
    kNN Euclidean [-0.5, 0.5] 0.878 0.756 0.556 0.400 0.322
    [-1.0, 1.0] 0.967 0.878 0.767 0.789 0.711
    [-2.0, 2.0] 0.978 0.967 0.944 0.944 0.944
    [-3.0, 3.0] 1.000 1.000 1.000 1.000 1.000
    Manhattan [-0.5, 0.5] 0.900 0.756 0.622 0.444 0.411
    [-1.0, 1.0] 0.956 0.900 0.789 0.778 0.744
    [-2.0, 2.0] 0.978 0.967 0.944 0.944 0.944
    [-3.0, 3.0] 1.000 1.000 1.000 1.000 1.000
    Chebyshev [-0.5, 0.5] 0.911 0.733 0.600 0.467 0.400
    [-1.0, 1.0] 0.967 0.933 0.811 0.800 0.722
    [-2.0, 2.0] 0.978 0.967 0.944 0.944 0.944
    [-3.0, 3.0] 1.000 1.000 1.000 1.000 1.000
    Angle cosine [-0.5, 0.5] 0.878 0.733 0.611 0.489 0.422
    [-1.0, 1.0] 0.944 0.900 0.722 0.711 0.656
    [-2.0, 2.0] 1.000 0.956 0.956 0.922 0.900
    [-3.0, 3.0] 1.000 0.989 0.978 0.967 0.978
    Hamming [-0.5, 0.5] 0.867 0.744 0.600 0.389 0.311
    [-1.0, 1.0] 0.911 0.811 0.611 0.589 0.578
    [-2.0, 2.0] 0.956 0.800 0.722 0.700 0.622
    [-3.0, 3.0] 0.978 0.911 0.856 0.800 0.778
    Proposed - - 1.000 1.000 1.000 1.000 0

     | Show Table
    DownLoad: CSV

    In this section, we discuss the data jumping pattern for unreliable transmission in WSNs. Essentially, the data jumping pattern should consider the combination of data loss and data jumping, because the network transmission always include these two cases, and the source node in WSNs is hard to identify the data jumping, but is easy to detect the data loss.

    We show the advantages of proposed by simulating a sensor network and test data recoverability in the context of ensemble reconstruction (R>1) and single reconstruction (R = 1). We use the 30 sensor nodes and one source node to build the simulation scenario. The decomposition matrix is calculated through fixing three parameters m=7, n=30, and q=37, and five jumping rates, 10%, 20%, 30%, 40%, and 50%, are considered in this experiment. In order to build a fair comparison, we fix data loss rate as 10% for each experiment, and give the comparison experimental results by using ensemble recovery and single recovery. The experiments are repeated 100 time.

    Table 4 shows the corresponding comparison results. As can be seen in this table, the overall data recoverability for the case using ensemble recovery is always higher than the case using single recovery, no matter what the data jumping rate is. We can explain this phenomenon as follows. For source node, when the data loss rate is less than theoretical redundancy rate Re, it is believed that the original data can be reconstructed perfectly. Actually, the source node can not identify the jumping data, e.g. decimal digit 6 ('110' for binary) changing to decimal digit 4 ('100' for binary). If the source node use single recovery to reconstruct data, it may select a data share including jumping digits. Finally, it results in an error recovery. On the contrary, ensemble mechanism can largely avoid this problem. As long as the jumping rate is less than theoretical redundancy rate Re, the recovery results calculating from all received data shares contain at least two identical results, which is likely to be the original data.

    Table 4.  Data recoverability for single recovery and ensemble recovery. The data loss rate is set to 10% and the jumping rates are respectively 10%, 20%, 30%, 40%, and 50%.
    Scheme Round R Data jumping rate
    10% 20% 30% 40% 50%
    Single Recovery R=1 46% 16% 5% 2% 0%
    Ensemble Recovery R=5 100% 99% 95% 78% 0%
    R=50 100% 100% 100% 87% 51%
    R=100 100% 100% 100% 98% 99%
    R=1000 100% 100% 100% 100% 99%
    R=5000 100% 100% 100% 100% 100%

     | Show Table
    DownLoad: CSV

    Notably, we need to stress that the jumping rate must be less than, not equal to, theoretical redundancy rate Re. This is because if the jumping rate is equal to the redundancy rate Re, the recovery results calculating from all received data shares may be different from each other. This makes that the source node can not decide which result is the original data, leading to a wrong reconstruction result.

    In this subsection, we compare the proposed ensemble scheme with several existing interpolation methods, 'Zero interpolation' [10], 'Slinear interpolation' [13], and 'Quadratic interpolation' [14]. Proposed scheme first uses data decomposition to expand the original data to multiple data shares and then deliver them by wireless sensor networks. Even though the source node do not receive all data shares, it can still reconstruct original data by using ensemble recovery mechanism. Note that the direct comparison is also difficult, because existing typical interpolation methods usually estimate the original data so that the exact values are hard to be obtained, whereas our proposed scheme definitely gets the exact original data as long as data loss rate is lower than theoretical redundancy rate Re. According to above consideration, we need to build a fair comparison between the proposed scheme and several interpolation methods as follows.

    All simulation experiments are implemented in the same wireless sensor network, which contains 30 sensor nodes and one source node. For every data reconstruction scheme, we divide the same original data (also named as original valid data) and set different data loss rates. The data recoverability performance can be measured by counting how much original valid data the recipient can finally receive. The experiments are repeated 100 times. In addition,

    ● For the proposed scheme, we decompose the original data to multiple data shares. All shares are integrated and sent by the sensor nodes randomly. In this experiment, the ensemble rounds are set to R=101 and the decomposition parameters are fixed as m=7, n=30, and q=37, respectively. Thus, the original data will be expanded to nm=4.3 times. The Equation (4.1) is used to calculate the overall recovery accuracy rate, which represents the data recoverability of proposed scheme.

    ● For the other interpolation schemes, original valid data are directly transmitted over sensor network. Since the estimation values always have some errors comparison with the actual values, we therefore set the error ratio (ER) to show the difference between actual value x(i) and estimation value ˆx(i), which is calculated by Equation (4.2).

    ER=i,j(x(i,j)ˆx(i,j))2i,j(x(i,j))2 (4.2)

    We carry out a serial of experiments to compare the proposed scheme and existing works. The average recovery error ratio is used to measure the performance of different methods. It indicates the proportion of error times for the total number of experimental times. Figure 5 shows the results of average error ratio for several schemes. Since proposed scheme either obtains the exact original data, or gets the complete wrong original data, in our experiments the average error ratio will be set directly to 100% once the data damaged rate (including data loss and data jumping) is more than theoretical redundancy rate Re.

    Figure 5.  The relationship between redundancy rate Re and two parameters (m,n). We test four different values, m=3, m=7, m=13, m=19 with the condition mnq.

    We can observe that proposed scheme achieves low average recovery error ratio with high data loss rate, e.g. Figure 5. In fact, this conclusion has been explained in detail by Section 3.4. Also, we note that proposed ensemble scheme has significantly effective for the case of combination data loss and data jumping, e.g. Figure 6. When we fix data loss rate to 12.5%, average recovery error ratio for ensemble recovery is even approximate zero when data jumping rate is up to 20%, the effect, however, does not work well for single recovery. This demonstrates that proposed ensemble scheme can efficiently improve the accuracy of data recovery. We also explain this interesting phenomenon as follows. The interpolation methods are usually very hard to provide the exact value for each original data. This makes that the recovery data may be decided as wrong value once the recovery error α is out of the range, and finally leads to a high average recovery error ratio. Moreover, for existing interpolation methods, we can also observe that zero interpolation method gives an inferior performance than other several schemes. This is mainly because zero interpolation always employs the nearest neighbors to estimate the original data. If data is continuously lost, The estimation value that provided by zero interpolation method may deviate significantly from the exact value, leading to an inferior performance.

    Figure 6.  Correlation between data recoverability (DR) and different data lost rate (%) by comparing kNN with five distance measures (Euclidean, Manhattan, Chebyshev, Angle cosine and Hamming) and proposed scheme. The recovery error is α=0.5. For kNN method, the parameter k is set to k=3.
    Figure 7.  Correlation between data recoverability (DR) and different data lost rate (%) by comparing kNN with five distance measures (Euclidean, Manhattan, Chebyshev, Angle cosine and Hamming) and proposed scheme. The recovery error is α=1.0. For kNN method, the parameter k is set to k=3.
    Figure 8.  The variation tendency for average reconstruction error rate when only data loss pattern is considered. In this test, the ensemble recovery mechanism is used and the ensemble rounds is set to R=101.
    Figure 9.  The variation tendency for average reconstruction error rate when only data loss pattern is considered. In this test, the ensemble recovery mechanism is used and the ensemble rounds is set to R=101.

    In this paper, we addressed the reliable data transmission problem in WSNs and proposed a new scheme based on data decomposition and ensemble recovery mechanism, which is significantly different from the traditional interpolation schemes. We design matrix decomposition mechanism to split the original data into multiple data shares, and then transmit them through wireless networks, which including multiple sensor nodes. In order to reconstruct the original data completely, ensemble recovery mechanism is designed to ensure the correct recovery for missing data. This mechanism can not only recover the missing data, but can revise the incorrect data if they occurs jumping in transmission. We compared our scheme with several existing interpolation schemes. The results show proposed scheme has better performance and herein shows a valuable attempt for data recovery in wireless sensor networks.

    In addition, we should note that the proposed scheme can circumvent the problem of data loss in network transmission. However, its disadvantage are also obvious due to the following two aspects: (1) Since the original data are expanded and divided into multiple shares by data decomposition mechanism, the sensor nodes need to spend more time sending these data. It may cause energy waste. As we known, the energy is very important for individual sensor node. (2) Unlike the interpolation scheme, proposed scheme requires the individual sensor node to pre-process the original data, that is, calculate the expanded data by decomposition matrix. This increases the computational requirements for individual sensor node. Overall, proposed method may be more suitable for the high-precision data recovery.

    In the future, we plan to carry our work forward in two directions. First, we should further optimize the data decomposition mechanism and find a fast computation method. Second, we should try to combine the estimation method and data decomposition mechanism. This will be considered as part of the future effort.

    This work was supported by Natural Science Foundation of China under Grants (61602295, U1736120, 61672337) and Natural Science Foundation of Shanghai (16ZR1413100).

    All authors declare no conflicts of interest in this paper.

    [1] Whitman WB, Coleman DC, Wiebe WJ (1998) Prokaryotes: The unseen majority. Proc Natl Acad Sci USA 95: 6578–6583.
    [2] Flemming HC, Wingender J (2010) The biofilm matrix. Nat Rev Microbiol 8: 623–633.
    [3] Hall MR, McGillicuddy E, Kaplan LJ (2014) Biofilm: basic principles, pathophysiology, and implications for clinicians. Surg Infect (Larchmt ) 15: 1–7.
    [4] Hyman P, Abedon ST (2012) Smaller fleas: viruses of microorganisms. Scientifica 2012: 734023.
    [5] Wommack KE, Colwell RR (2000) Virioplankton: viruses in aquatic ecosystems. Microbiol Mol Biol Rev 64: 69–114.
    [6] Weinbauer MG (2004) Ecology of prokaryotic viruses. FEMS Microbiol Rev 28: 127–181.
    [7] Abedon ST (2015) Ecology of anti-biofilm agents I. antibiotics versus bacteriophages. Pharmaceuticals 8: 525–558.
    [8] Abedon ST (2015) Ecology of anti-biofilm agents II. bacteriophage exploitation and biocontrol of biofilm bacteria. Pharmaceuticals 8: 559–589.
    [9] Briandet R, Lacroix-Gueu P, Renault M, et al. (2008) Fluorescence correlation spectroscopy to study diffusion and reaction of bacteriophages inside biofilms. Appl Environ Microbiol 74: 2135–2143.
    [10] Fukuyo M, Sasaki A, Kobayashi I (2012) Success of a suicidal defense strategy against infection in a structured habitat. Sci Rep 2: 238.
    [11] Hyman P, Abedon ST (2010) Bacteriophage host range and bacterial resistance. Adv Appl Microbiol 70: 217–248.
    [12] Labrie SJ, Samson JE, Moineau S (2010) Bacteriophage resistance mechanisms. Nat Rev Microbiol 8: 317–327.
    [13] Dy RL, Richter C, Salmond GP, et al. (2014) Remarkable mechanisms in microbes to resist phage infections. Annu Rev Virol 1: 307–331.
    [14] Seed KD (2015) Battling phages: How bacteria defend against viral attack. PLoS Path 11: e1004847.
    [15] Parma DH, Snyder M, Sobolevski S, et al. (1992) The rex system of bacteriophage l: tolerance and altruistic cell death. Genes Dev 6: 497–510.
    [16] Shub DS (1994) Bacterial viruses. Bacterial altruism? Curr Biol 4: 555–556.
    [17] Dy RL, Przybilski R, Semeijn K, et al. (2014) A widespread bacteriophage abortive infection system functions through a Type IV toxin-antitoxin mechanism. Nucl Acids Res 42: 4590–4605.
    [18] Iranzo J, Lobkovsky AE, Wolf YI, et al. (2015) Immunity, suicide or both? Ecological determinants for the combined evolution of anti-pathogen defense systems. BMC Evol Biol 15: 43.
    [19] Dennehy JJ, Abedon ST, Turner PE (2007) Host density impacts relative fitness of bacteriophage f6 genotypes in structured habitats. Evolution 61: 2516–2527.
    [20] Abedon ST, Yin J (2008) Impact of spatial structure on phage population growth, In: Abedon, S.T. Editor, Bacteriophage Ecology, Cambridge, UK: Cambridge University Press, 94–113.
    [21] Abedon ST (2011) Bacteriophages and biofilms: ecology, phage therapy, plaques, Hauppauge, New York: Nova Science Publishers.
    [22] Abedon ST (2016) Bacteriophage exploitation of bacterial biofilms: phage preference for less mature targets? FEMS Microbiol Lett 363: fnv246.
    [23] Abedon ST (2012) Spatial vulnerability: bacterial arrangements, microcolonies, and biofilms as responses to low rather than high phage densities. Viruses 4: 663–687.
    [24] Abedon ST (2012) Thinking about microcolonies as phage targets. Bacteriophage 2: 200–204.
    [25] Abedon ST (2008) Phage population growth: constraints, games, adaptation, In: Abedon, S.T. Editor, Bacteriophage Ecology, Cambridge, UK: Cambridge University Press, 64–93.
    [26] Abedon ST (2009) Impact of phage properties on bacterial survival, In: Adams, H.T. Editor, Contemporary Trends in Bacteriophage Research, Hauppauge, New York: Nova Science Publishers, 217–235.
    [27] Payne RJH, Jansen VAA (2001) Understanding bacteriophage therapy as a density-dependent kinetic process. J Theor Biol 208: 37–48.
    [28] Abedon ST, Thomas-Abedon C (2010) Phage therapy pharmacology. Curr Pharm Biotechnol 11: 28–47.
    [29] Hamilton WD (1964) The genetical evolution of social behaviour. I. J Theor Biol 7: 1–16.
    [30] West SA, Gardner A (2010) Altruism, spite, and greenbeards. Science 327: 1341–1344.
    [31] Iranzo J, Lobkovsky AE, Wolf YI, et al. (2014) Virus-host arms race at the joint origin of multicellularity and programmed cell death. Cell Cycle 13: 3083–3088.
    [32] West SA, Griffin AS, Gardner A, et al. (2006) Social evolution theory for microorganisms. Nat Rev Microbiol 4: 597–607.
    [33] Ewald PW (1994) Evolution of Infectious Disease, New York: Oxford University Press.
    [34] Michod RE, Nedelcu AM, Roze D (2003) Cooperation and conflict in the evolution of individuality. IV. Conflict mediation and evolvability in Volvox carteri. Bio Systems 69: 95–114.
    [35] van Gestel J, Vlamakis H, Kolter R (2015) Division of labor in biofilms: the ecology of cell differentiation. Microbiol Spectr 3: MB-0002-2014.
    [36] Andrews JH (1998) Bacteria as modular organisms. Ann Rev Microbiol 52: 105–126.
    [37] Kaplan JB (2010) Biofilm dispersal: mechanisms, clinical implications, and potential therapeutic uses. J Dent Res 89: 205–218.
    [38] McDougald D, Rice SA, Barraud N, et al. (2012) Should we stay or should we go: mechanisms and ecological consequences for biofilm dispersal. Nat Rev Microbiol 10: 39–50.
    [39] Davies DG (2011) Biofilm disperson, In: Flemming, H.C., Wingender, J., Szewzyk, U. Editors, Biofilm Highlights, Berlin: Springer, 1–28.
    [40] Barraud N, Kjelleberg S, Rice SA (2015) Dispersal from microbial biofilms. Microbiol Spectr 3: MB-0015-2014.
    [41] Petrova OE, Sauer K (2016) Escaping the biofilm in more than one way: desorption, detachment or dispersion. Curr Opin Microbiol 30: 67–78.
    [42] Kim SK, Lee JH (2016) Biofilm dispersion in Pseudomonas aeruginosa. J Microbiol 54: 71–85.
    [43] Ronce O (2007) How does it feel to be like a rolling stone? Ten questions about dispersal evolution. Ann Rev Ecol Evol Syst 38: 231–253.
    [44] Korber DR, Lawrence JR, Lappin-Scott HM, et al. (1995) Growth of microorganisms on surfaces, In: Costerton, J.W., Lappin-Scott, H. Editors, Microbial biofilms, Cambridge, UK: Cambridge University Press, 15–45.
    [45] Bjarnsholt T (2013) The role of bacterial biofilms in chronic infections. Apmis 121: 1–51.
    [46] Battin TJ, Besemer K, Bengtsson MM, et al. (2016) The ecology and biogeochemistry of stream biofilms. Nat Rev Microbiol 14: 251–263.
    [47] Costerton JW, Lappin-Scott H (1995) Introduction to microbial biofilms, In: Costerton, J.W., Lappin-Scott, H. Editors, Microbial biofilms, Cambridge, UK: Cambridge University Press, 1–11.
    [48] Costerton JW, Marrie TJ, Cheng KJ (1985) Phenomena of bacterial adhesion, In: Savage, D.C., Fletcher, M. Editors, Bacterial Adhesion: Mechanisms and Physiological Significance, New York: Plenum Press, 3–43.
    [49] Somerville DA, Noble WC (1973) Microcolony size of microbes on human skin. J Med Microbiol 6: 323–328.
    [50] Mitarai N, Brown S, Sneppen K (2016) Population dynamics of phage and bacteria in spatially structured habitats using phage l and Escherichia coli. J Bacteriol 198: 1783–1793.
    [51] Kreft JU (2004) Biofilms promote altruism. Microbiology 150: 2751–2760.
    [52] Nadell CD, Bassler BL (2011) A fitness trade-off between local competition and dispersal in Vibrio cholerae biofilms. Proc Natl Acad Sci USA 108: 14181–14185.
    [53] Bryers JD (1988) Modeling biofilm accumulation, In: Brazin, M.J., Prosser, J.I. Editors, Physiological Models in Microbiology, Eds., FL: CRC Press, 109–144.
    [54] Garny K, Horn H, Neu TR (2008) Interaction between biofilm development, structure and detachment in rotating annular reactors. Bioprocess Biosyst Eng 31: 619–629.
    [55] Brading MG, Jass J, Lappin-Scott HM (1995) Dynamics of bacterial biofilm formation, In: Costerton, J.W., Lappin-Scott, H. Editors, Microbial biofilms, Cambridge, UK: Cambridge University Press, 46–63.
    [56] Vanysacker L, Boerjan B, Declerck P, et al. (2014) Biofouling ecology as a means to better understand membrane biofouling. Appl Microbiol Biotechnol 98: 8047–8072.
    [57] Bester E, Wolfaardt G, Joubert L, et al. (2005) Planktonic-cell yield of a pseudomonad biofilm. Appl Environ Microbiol 71: 7792–7798.
    [58] Knowles B, Silveira CB, Bailey BA, et al. (2016) Lytic to temperate switching of viral communities. Nature 531: 466–470.
    [59] Gonzalez S, Fernandez L, Campelo AB, et al. (2017) The behavior of Staphylococcus aureus dual-species biofilms treated with bacteriophage phiIPLA-RODI depends on the accompanying microorganism. Appl Environ Microbiol 83: AEM-02821-16.
    [60] Sutherland IW, Hughes KA, Skillman LC, et al. (2004) The interaction of phage and biofilms. FEMS Microbiol Lett 232: 1–6.
    [61] Nale JY, Chutia M, Carr P, et al. (2016) "Get in early"; biofilm and wax moth (Galleria mellonella) models reveal new insights into the therapeutic potential of Clostridium difficile bacteriophages. Front Microbiol 7: 1383.
    [62] Doolittle MM, Cooney JJ, Caldwell DE (1996) Tracing the interaction of bacteriophage with bacterial biofilms using fluorescent and chromogenic probes. J Indust Microbiol 16: 331–341.
    [63] Abedon ST (1992) Lysis of lysis inhibited bacteriophage T4-infected cells. J Bacteriol 174: 8073–8080.
    [64] Abedon ST (1989) Selection for bacteriophage latent period length by bacterial density: A theoretical examination. Microb Ecol 18: 79–88.
    [65] Wang IN, Dykhuizen DE, Slobodkin LB (1996) The evolution of phage lysis timing. Evol Ecol 10: 545–558.
    [66] Hadas H, Einav M, Fishov I, et al. (1997) Bacteriophage T4 development depends on the physiology of its host Escherichia coli. Microbiology 143: 179–185.
    [67] Abedon ST (2012) Bacterial "immunity" against bacteriophages. Bacteriophage 2: 50–54.
    [68] Koonin EV, Zhang F (2017) Coupling immunity and programmed cell suicide in prokaryotes: Life-or-death choices. BioEssays 39: 1–9.
    [69] Hoyland-Kroghsbo NM, Paczkowski J, Mukherjee S, et al. (2017) Quorum sensing controls the Pseudomonas aeruginosa CRISPR-Cas adaptive immune system. Proc Natl Acad Sci USA 114: 131–135.
    [70] Goldfarb T, Sberro H, Weinstock E, et al. (2015) BREX is a novel phage resistance system widespread in microbial genomes. EMBO J 34: 169–183.
    [71] Abedon ST (2015) Bacteriophage secondary infection. Virol Sin 30: 3–10.
    [72] McLean RJ, Corbin BD, Balzer GJ, et al. (2001) Phenotype characterization of genetically defined microorganisms and growth of bacteriophage in biofilms. Meth Enzymol 336: 163–174.
    [73] Azeredo J, Sutherland IW (2008) The use of phages for the removal of infectious biofilms. Curr Pharm Biotechnol 9: 261–266.
    [74] Sillankorva S, Azeredo J (2014) The use of bacteriophages and bacteriophage-derived enzymes for clinically relevant biofilm control, In: Borysowski, J., Miedzybrodzki, R., Górski, A. Editors, Phage Therapy: Current Research and Applications, Norfolk, UK: Caister Academic Press, 305–325.
    [75] Kutter E, Kellenberger E, Carlson K, et al. (1994) Effects of bacterial growth conditions and physiology on T4 infection, In: Karam, J.D., Kutter, E., Carlson, K., Guttman, B. Editors, The Molecular Biology of Bacteriophage T4, Washington, DC: ASM Press, 406–418.
    [76] Miller RV, Day M (2008) Contribution of lysogeny, pseudolysogeny, and starvation to phage ecology, In: Abedon, S.T. Editor, Bacteriophage Ecology, Cambridge, UK: Cambridge University Press, 114–143.
    [77] Pearl S, Gabay C, Kishony R, et al. (2008) Nongenetic individuality in the host-phage interaction. PLoS Biol 6: e120.
    [78] Abedon ST (2009) Disambiguating bacteriophage pseudolysogeny: an historical analysis of lysogeny, pseudolysogeny, and the phage carrier state, In: Adams, H.T. Editor, Contemporary Trends in Bacteriophage Research, Hauppauge, New York: Nova Science Publishers, 285–307.
    [79] Los M, Wegrzyn G (2012) Pseudolysogeny. Adv Virus Res 82: 339–349.
    [80] Golec P, Karczewska-Golec J, Los M, et al. (2014) Bacteriophage T4 can produce progeny virions in extremely slowly growing Escherichia coli host: comparison of a mathematical model with the experimental data. FEMS Microbiol Lett 351: 156–161.
    [81] Harper DR, Parracho HMR, Walker J, et al. (2014) Bacteriophages and biofilms. Antibiotics 3: 270–284.
    [82] Bryan D, el-Shibiny A, Hobbs Z, et al. (2016) Bacteriophage T4 infection of stationary phase E. coli: life after log from a phage perspective. Front Microbiol 7: 1391.
    [83] Yin J (1991) A quantifiable phenotype of viral propagation. Biochem Biophys Res Com 174: 1009–1014.
    [84] Filippini M, Buesing N, Bettarel Y, et al. (2006) Infection paradox: high abundance but low impact of freshwater benthic viruses. Appl Environ Microbiol 72: 4893–4898.
    [85] Wilkinson JF (1958) The extracellualr polysaccharides of bacteria. Bacteriol Rev 22: 46–73.
    [86] van Benthum WAJ, van Loosdrecht MCM, Tijhuis L, et al. (1995) Solids retention time in heterotrophic and nitrifying biofilms in a biofilm airlift suspension reactor. Water Sci Technol 32: 35–43.
    [87] Reichert P, Wanner O (1997) Movement of solids in biofilms-significance of liquid phase transport. Water Sci Technol 36: 321–328.
    [88] Davey ME, O'Toole GA (2000) Microbial biofilms: from ecology to molecular genetics. Microbiol Mol Biol Rev 64: 847–867.
    [89] Hanlon GW, Denyer SP, Olliff CJ, et al. (2001) Reduction in exopolysaccharide viscosity as an aid to bacteriophage penetration through Pseudomonas aeruginosa biofilms. Appl Environ Microbiol 67: 2746–2753.
    [90] Resch A, Fehrenbacher B, Eisele K, et al. (2005) Phage release from biofilm and planktonic Staphylococcus aureus cells. FEMS Microbiol Lett 252: 89–96.
    [91] Forde A, Fitzgerald GF (2003) Molecular organization of exopolysaccharide (EPS) encoding genes on the lactococcal bacteriophage adsorption blocking plasmid, pCI658. Plasmid 49: 130–142.
    [92] Flood JA, Ashbolt NJ (2000) Virus-sized particles can be entrapped and concentrated one hundred fold within wetland biofilms. Adv Environ Res 3: 403–411.
    [93] Storey MV, Ashbolt NJ (2001) Persistence of two model enteric viruses (B40-8 and MS-2 bacteriophages) in water distribution pipe biofilms. Water Sci Technol 43: 133–138.
    [94] Lacroix-Gueu P, Briandet R, Lévêque-Fort S, et al. (2005) In situ measurements of viral particles diffusion inside mucoid biofilms. C R Biol 328: 1065–1072.
    [95] Brüssow H (2013) Bacteriophage-host interaction: from splendid isolation into a messy reality. Curr Opin Microbiol 16: 500–506.
    [96] Fan X, Li W, Zheng F, et al. (2013) Bacteriophage inspired antibiotics discovery against infection involved biofilm. Crit Rev Eukaryot Gene Expr 23: 317–326.
    [97] Parasion S, Kwiatek M, Gryko R, et al. (2014) Bacteriophages as an alternative strategy for fighting biofilm development. Pol J Microbiol 63: 137–145.
    [98] Chan BK, Abedon ST (2015) Bacteriophages and their enzymes in biofilm control. Curr Pharm Des 21: 85–99.
    [99] Gutierrez D, Rodriguez-Rubio L, Martinez B, et al. (2016) Bacteriophages as weapons against bacterial biofilms in the food industry. Front Microbiol 7: 825.
    [100] Khalifa L, Shlezinger M, Beyth S, et al. (2016) Phage therapy against Enterococcus faecalis in dental root canals. J Oral Microbiol 8: 32157.
    [101] Motlagh AM, Bhattacharjee AS, Goel R (2016) Biofilm control with natural and genetically-modified phages. World J Microbiol Biotechnol 32: 67.
    [102] Abedon ST (2014) Phage therapy: eco-physiological pharmacology. Scientifica 2014: 581639.
    [103] Arber W, Linn S (1969) DNA modification and restriction. Annu Rev Biochem 38: 467–500.
    [104] Korona R, Levin BR (1993) Phage-mediated selection and the evolution and maintenance of restriction-modification. Evolution 47: 556–575.
    [105] Chao L, Levin BR, Stewart FM (1977) A complex community in a simple habitat: an experimental study with bacteria and phage. Ecology 58: 369–378.
    [106] Bohannan BJM, Travisano M, Lenski RE (1999) Epistatic interactions can lower the cost of resistance to multiple consumers. Evolution 53: 292–295.
    [107] Hill C (1993) Bacteriophage and bacteriophage resistance in lactic acid bacteria. FEMS Microbiol Rev 12: 87–108.
    [108] Nissen SB, Magidson T, Gross K, et al. (2016) Publication bias and the canonization of false facts. eLife 5: e21451.
    [109] Costerton JW, Cheng JJ, Geesey GG, et al. (1987) Bacterial biofilms in nature and disease. Ann Rev Microbiol 41: 435–464.
    [110] Oh YJ, Jo W, Yang Y, et al. (2007) Influence of culture conditions on Escherichia coli O157:H7 biofilm formation by atomic force microscopy. Ultramicroscopy 107: 869–874.
    [111] Cheng KJ, Costerton JW (1980) The formation of microcolonies by rumen bacteria. Can J Microbiol 26: 1104–1113.
    [112] Lacqua A, Wanner O, Colangelo T, et al. (2006) Emergence of biofilm-forming subpopulations upon exposure of Escherichia coli to environmental bacteriophages. Appl Environ Microbiol 72: 956–959.
    [113] Shen Y, Mitchell MS, Donovan DM, et al. (2012) Phage-based enzybiotics, In: Hyman, P., Abedon, S.T. Editors, Bacteriophages in Health and Disease, Wallingford, UK: CABI Press, 217–239.
    [114] Yan J, Mao J, Xie J (2014) Bacteriophage polysaccharide depolymerases and biomedical applications. BioDrugs 28: 265–274.
    [115] Gutiérrez D, Briers Y, Rodríguez-Rubio L, et al. (2015) Role of the pre-neck appendage protein (Dpo7) from phage vB_SepiS-phiIPLA7 as an anti-biofilm agent in staphylococcal species. Front Microbiol 6: 1315.
    [116] Pires DP, Oliveira H, Melo LD, et al. (2016) Bacteriophage-encoded depolymerases: their diversity and biotechnological applications. Appl Microbiol Biotechnol 100: 2141–2151.
    [117] Westra ER, van HS, Oyesiku-Blakemore S, et al. (2015) Parasite exposure drives selective evolution of constitutive versus inducible defense. Curr Biol 25: 1043–1049.
    [118] Berngruber TW, Lion S, Gandon S (2013) Evolution of suicide as a defence strategy against pathogens in a spatially structured environment. Ecol Lett 16: 446–453.
    [119] Refardt D, Kummerli R (2013) Defying bacteriophages: contrasting altruistic with individual-based resistance mechanisms in Escherichia coli. Commun Integr Biol 6: e25159.
    [120] Heilmann S, Sneppen K, Krishna S (2012) Coexistence of phage and bacteria on the boundary of self-organized refuges. Proc Natl Acad Sci USA 109: 12828–12833.
    [121] Abedon ST, Kuhl SJ, Blasdel BG, et al. (2011) Phage treatment of human infections. Bacteriophage 1: 66–85.
    [122] Borysowski J, Miedzybrodzki R, Górski A (2014) Phage Therapy: Current Research and Applications, Norfolk, UK: Caister Academic Press.
    [123] Scali C, Kunimoto B (2013) An update on chronic wounds and the role of biofilms. J Cutan Med Surg 17: 371–376.
    [124] Cooper RA, Bjarnsholt T, Alhede M (2014) Biofilms in wounds: a review of present knowledge. J Wound Care 23: 570–580.
    [125] Macia MD, Rojo-Molinero E, Oliver A (2014) Antimicrobial susceptibility testing in biofilm-growing bacteria. Clin Microbiol Infect 20: 981–990.
    [126] Abedon ST (2015) Phage therapy of pulmonary infections. Bacteriophage 5: e1020260.
    [127] Fish R, Kutter E, Wheat G, et al. (2016) Bacteriophage treatment of intransigent diabetic toe ulcers: a case series. J Wound Care 25: S27–S33.
    [128] Abedon ST (2017) Bacteriophage clinical use as antibactertial "drugs": utility precident. Microbiol Spectr.
    [129] Stewart PS, Franklin MJ (2008) Physiological heterogeneity in biofilms. Nat Rev Microbiol 6: 199–210.
    [130] Davis KM, Mohammadi S, Isberg RR (2015) Community behavior and spatial regulation within a bacterial microcolony in deep tissue sites serves to protect against host attack. Cell Host Microbe 17: 21–31.
    [131] Harmsen M, Yang L, Pamp SJ, et al. (2010) An update on Pseudomonas aeruginosa biofilm formation, tolerance, and dispersal. FEMS Immunol Med Microbiol 59: 253–268.
    [132] Purevdorj-Gage B, Costerton WJ, Stoodley P (2005) Phenotypic differentiation and seeding dispersal in non-mucoid and mucoid Pseudomonas aeruginosa biofilms. Microbiology 151: 1569–1576.
    [133] Hamilton WA (1987) Biofilms: microbial interactions and metabolic activities, In: Fletcher, M., Gray, T.R.G., Jones, J.G. Editors, Ecology of Microbial Communities, Cambridge: Cambridge University Press, 361–385.
    [134] Abedon ST, Herschler TD, Stopar D (2001) Bacteriophage latent-period evolution as a response to resource availability. Appl Environ Microbiol 67: 4233–4241.
    [135] Levin BR, Bull JJ (2004) Population and evolutionary dynamics of phage therapy. Nat Rev Microbiol 2: 166–173.
    [136] Gill JJ (2008) Modeling of bacteriophage therapy, In: Abedon, S.T. Editor, Bacteriophage Ecology, Cambridge, UK: Cambridge University Press, 439–464.
    [137] Stent GS (1963) Molecular Biology of Bacterial Viruses, San Francisco, CA: WH Freeman and Co.
    [138] Gallet R, Shao Y, Wang IN (2009) High adsorption rate is detrimental to bacteriophage fitness in a biofilm-like environment. BMC Evol Biol 9: 241.
    [139] Yin J, McCaskill JS (1992) Replication of viruses in a growing plaque: a reaction-diffusion model. Biophys J 61: 1540–1549.
    [140] Abedon ST, Culler RR (2007) Bacteriophage evolution given spatial constraint. J Theor Biol 248: 111–119.
    [141] Hewson I, Fuhrman JA (2003) Viriobenthos production and virioplankton sorptive scavenging. Microb Ecol 46: 337–347.
    [142] Hoyland-Kroghsbo NM, Maerkedahl RB, Svenningsen SL (2013) A quorum-sensing-induced bacteriophage defense mechanism. MBio 4: e00362.
    [143] Boots M, Mealor M (2007) Local interactions select for lower pathogen infectivity. Science 315: 1284–1286.
    [144] Abedon ST (2016) Commentary: phage therapy of staphylococcal chronic osteomyelitis in experimental animal model. Front Microbiol 7: 1251.
    [145] Kutter E, De Vos D, Gvasalia G, et al. (2010) Phage therapy in clinical practice: treatment of human infections. Curr Pharm Biotechnol 11: 69–86.
    [146] Hyman P, Abedon ST (2009) Practical methods for determining phage growth parameters. Meth Mol Biol 501: 175–202.
    [147] Mirzaei MK, Nilsson AS (2015) Isolation of phages for phage therapy: a comparison of spot tests and efficiency of plating analyses for determination of host range and efficacy. PLoS One 10: e0118557.
    [148] Abedon ST (2014) Bacteriophages as drugs: the pharmacology of phage therapy, In: Borysowski, J., Miedzybrodzki, R., Górski, A. Editors, Phage Therapy: Current Research and Applications, Norfolk, UK: Caister Academic Press, 69–100.
  • This article has been cited by:

    1. Fengyong Li, Meng Sun, EMLP: short-term gas load forecasting based on ensemble multilayer perceptron with adaptive weight correction, 2021, 18, 1551-0018, 1590, 10.3934/mbe.2021082
    2. Noman Zahid, Ali Hassan Sodhro, Usman Rauf Kamboh, Ahmed Alkhayyat, Lei Wang, AI-driven adaptive reliable and sustainable approach for internet of things enabled healthcare system, 2022, 19, 1551-0018, 3953, 10.3934/mbe.2022182
    3. Seema J. Kampli, D. Ramesh, K. B. Shivakumar, Markov model based dynamic chain routing protocol for grid WSN, 2022, 13, 0975-6809, 2261, 10.1007/s13198-022-01634-0
  • Reader Comments
  • © 2017 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(11055) PDF downloads(1450) Cited by(60)

Figures and Tables

Figures(6)

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog