Modeling nonviral gene delivery as a macro-to-nano communication system

Nano Communication Networks 4 (2013) 14–22

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Modeling nonviral gene delivery as a macro-to-nano communication system Beata J. Wysocki a , Timothy M. Martin b , Tadeusz A. Wysocki a,∗ , Angela K. Pannier b a

Peter Kiewit Institute, University of Nebraska-Lincoln, 1110 S. 67th Street, Omaha, NE 68182-0572, United States

b

Department of Biological Systems Engineering, University of Nebraska-Lincoln, Lincoln, NE, 68583-0726, United States

article

info

Article history: Received 9 November 2012 Accepted 13 December 2012 Available online 27 December 2012 Keywords: Genetic communication Molecular communication Protocols Communication networks Nanobioscience

abstract The principal role of any communication system is to deliver information from a source to a sink. Since gene delivery systems transport genetic information encoded as DNA to living cells, such systems can be considered as communication systems. Therefore, techniques developed for modeling conventional communication systems should be applicable to model gene delivery systems. The paper describes an approach to model nonviral gene delivery as a macro-to-nano communication system. To facilitate modeling, the gene delivery process is first described in terms of an abstractive layered communication protocol and then processing at each layer is implemented as M/M/∞ queues. To validate this approach, the model has been implemented in MATLAB/SIMULINK environment and the simulation results have been compared to experimental data from literature. © 2012 Elsevier Ltd. All rights reserved.

1. Introduction GENE delivery systems transport genetic information encoded as DNA to cells or biological systems, which then transcribe and translate that information into functional proteins produced on-demand by the genetically modified cells [1]. This process can be thought of as macroto-nano communication with the potential to directly alter endogenous gene expression and cell behavior with applications in functional genomics, tissue engineering, medical devices, and gene therapy. The macro-to-nano communication involves an experimentalist preparing and delivering such genetic information to a cell nucleus that ultimately alters operation of the cell, through transcription of the genetic code into an intermediate messenger molecule (mRNA), which in the cytoplasm is translated into a corresponding protein. While nonviral gene delivery techniques [2] are less efficient than viral systems, they

∗

Corresponding author. Tel.: +1 402 554 2164; fax: +1 402 554 2289. E-mail address: [email protected] (T.A. Wysocki).

1878-7789/$ – see front matter © 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.nancom.2012.12.001

offer the advantages of low toxicity and immunogenicity, lack of pathogenicity, and ease of production with greater control and flexibility, making these vectors attractive alternatives to viruses. In nonviral systems, plasmid DNA is typically electrostatically complexed with cationic lipids or polymers, forming a DNA complex, to facilitate gene transfer. Once formed, these complexes have to overcome extracellular and intracellular barriers to gene delivery, to achieve delivery of the DNA to the nucleus and subsequent transcription and translation of the protein encoded by the DNA—a process called transfection. A better understanding of the process of nonviral gene delivery allows for the efficacious design of the delivery system. Modeling is one approach that has been used to offer perspective and interpretation of unknown or complex cellular mechanisms involved in gene transfer. In their fundamental paper [3], Varga et al. introduced a quantitative model to analyze the process of nonviral gene delivery. Their motivation was to understand the process of nonviral gene delivery so that more efficient delivery systems could be developed. Ten years later, Jandt et al. [4] improved on the model design by providing a mechanistic

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spatiotemporal and stochastic model describing nonviral gene delivery. Between those two papers, there were several attempts to tune the original [3] model and modify it for different types of synthetic carriers of DNA/nucleic acids [2]. However, these current models are inadequate and provide only a segmented view of gene delivery kinetics and often treat DNA complex routing as averaged or rigid events that are not biologically accurate. The main shortcoming of all those models is the fact that they do not fully capture the stochastic nature of biological processes that happen during transfection or transmission properties of transport pathways involved in delivery of genetic material to the nucleus. Hence, there is a need for new types of models that describe the complete gene delivery process with biological fitness to enable the design of more efficient systems. In [5], a layered communication approach was used to describe targeted drug delivery as a one-way macro-tonano communication. A similar approach was used in [6] to model early HIV infection as communication events among cells. However, this modeling approach has never been used to describe nonviral gene delivery. In this paper, nonviral gene delivery will be described as a type of macroto-nano communication and modeled using a standard queuing theory apparatus, commonly used in modeling communication networks. The paper is organized as follows. Section 2 provides description of in vitro nonviral gene delivery to mammalian cells as a macro-to-nano communications between the experimentalist and the cells to be modified. Section 3 introduces the model of the communication system and describes its MATLAB/SIMULINK implementation. The simulation results and their comparison to experimental data available in literature are discussed in Section 4, while Section 5 concludes the paper. 2. System description In the considered system, communication between the macro-scale and nano-scale starts when the application at the macro-scale determines that genetic modification of a cell is needed or that a cell needs to produce a certain protein to accomplish a behavior or function. In engineering terms, a series of steps must be achieved in order for successful transmission of the information: (a) encoding of information in a format understood by the destination and protecting its integrity during the transport, (b) delivery of the information carriers through the cell membrane – a process called internalization – into endosomes, (c) routing the information carriers through cytoplasm, (d) delivery of the carriers to cell nucleus, (e) reception and decoding of information by the nucleus, (f) invoking an expected application resulting in a modified cell behavior or production of the requested protein. In the following, a more detailed description of those steps is presented. To produce a protein of interest, plasmid DNA is used that encodes that information, which will be decoded within the cell nucleus. These plasmids encoding exogenous genes that are to be delivered into cells can be considered creation of message carriers or transport PDUs by

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the macro-scale host. Ionic complexation of plasmids with cationic polymers (polyplexes) [7] or lipids (lipoplexes) [8] is used to form nanoparticles called complexes. Complexation protects the DNA against degradation by nucleases and serum components [9] and enhances cellular uptake by reducing the effective size of DNA and promoting interactions between positively charged DNA complexes and the negatively charged cellular membrane [9,10]. The process of complexation can be considered as framing that is performed at the Network Layer [11], with the complexes being the Network Layer PDUs. Once formed, DNA complexes are delivered to cells in solution. The physical layer operation at macro-scale is the delivery of the solution with complexes to the media surrounding the cells. The layered protocol stack for the macro host is shown in Fig. 1 as the starting node of the communication chain involved in nonviral gene delivery. After addition of complexes into the media, complex binding to the cell can occur through receptor binding (if the cationic polymer or lipid contains a targeting ligand) or nonspecific binding, presumably mediated by the cationic nature of the complexes and the anionic cell surface heparan sulfate proteoglycans [12,13]. Upon binding to a cell, nearly all complexes enter the cell through an endocytic pathway, even in case of nonspecific binding [12,13]. Hence, an endosome can be considered the first node in the nano-scale part of the system (see Fig. 1). Operation of the physical layer of the endosome can be described as creation of an endosome around the complex that is to be internalized into the cell. This process is usually modeled as a Poisson process with intensity µi [14], similarly as packet arrival is usually modeled in case of conventional communication networks. Once internalized into the endosome, the complex can be either delivered to a lysosome for degradation or released into the cytoplasm. Hence, a form of routing is performed by endosomes. The exact nature of that routing is not well understood and can vary based on complexation agents; the available data (e.g. [3]) only provide kinetic constants for endosomal escape by particular type of complexes µee and for liposomal degradation µld . Based on those constants, the relevant probabilities of the routes can be calculated as: pee =

µee µee + µld

(1)

µld µee + µld

(2)

and pld =

where pee is probability of endosomal escape and pld is probability of lysosomal degradation. Since endosomes perform processing up to routing of complexes, their operation can be considered as implementing two layers of communication protocol, the Physical Layer and the Network Layer. The Physical Layer in endosomes is responsible for encapsulating complexes into endosomes and releasing complexes into cytoplasm or transporting them to lysosomes for degradation. Decision about the destination of the encapsulated complexes is performed by the Network Layer of endosomes.

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Fig. 1. Gene delivery process described using a four layer communication protocol.

On the path to nucleus, the cytoplasm acts as an intermediate node that routes incoming messages through two different paths to the nucleus. The first path allows for routing complexes to the nucleus, while the second path routes plasmids after unpacking them from complexes (lipids or polymers). In case of complexes being routed, the cytoplasm is the place where binding of the complexes to nuclear localization sequence (NLS)-containing cytoplasmic proteins [13,14] occurs, which then shuttle the complex into the nucleus. This operation can be considered as adding a header to a packet with the destination address, much like what happens at the Network Layer of communication protocol. For the second route, (see Fig. 1), the complexes are first unpacked (dissociation of plasmid from cationic polymer or lipid) and the same operation of binding to nuclear localization proteins (addition of network layer headers) happens. However, before binding occurs, the unpacked plasmids, being the Transport Layer PDUs, are subject to degradation. For modeling purposes, this degradation can be considered as a sort of integrity check performed at the Transport Layer of the cytoplasm. The decision of whether the complexes are routed intact to the nucleus or are first unpacked is only described in literature [3] by means of kinetic constants for complex binding µcb and complex unpacking µcu . The values of these two constants differ widely depending on the type of complexes being used, e.g. polymer, lipid, etc. [3,15]. The Transport Layer operation of the cytoplasm is also governed by two kinetic constants µpb – rate of plasmid binding to nuclear localization proteins at the Network Layer and µpd – rate of plasmid degradation at transport layer. Because plasmid binding and degradation only depend on properties of DNA, which are the same regardless of complexing agent used (polymer or lipid) the values of µpb and µpd are constant for different type of complexes. Both plasmids and complexes enter the cell nucleus through nuclear pores, which constitute an interface between the nucleus and a cytoplasm and as such can be considered the Physical Layer of the nucleus. They can also enter the nucleus through random diffusion during mitosis because of breakdown of the nuclear membrane. The nuclear pore import kinetic constants are different for plasmids µnip and for complexes µnic , as each differs in size.

Then, the unbinding of complexes and plasmids from nuclear localization proteins occurs with a kinetic constant µucp , which can be considered processing at the Network Layer of the nucleus and is an inverse operation to the binding process occurring in cytoplasm (Network Layer of cytoplasm). In the case of complexes, the complexes are unpacked with a kinetic constant µcun to release free plasmids after unbinding. On the way from being prepared at the macro-scale to successful delivery to the cell nucleus, plasmids are subject to interference and noise (i.e. biologically, degradation), which results in transmission errors. Some sort of integrity checking is performed in the nucleus and only the error free plasmids can transfect the cell. It is estimated [14] that only between 44.6% and 74.4% of plasmids arriving in the cell nucleus are error free and can be utilized for the transfection. These error free plasmids are referred to as active plasmids [14]. The integrity checking can be considered a Transport Layer operation of the cell nucleus, and in fact one can consider that a virtual transport channel exists between the macro-scale and the cell nucleus. Once an active plasmid is detected by the Application Layer of cell nucleus, the nucleus starts producing the relevant mRNA. The process of detecting active plasmids is not well understood but a method to measure transcriptional availability as an average of gene expression per plasmid has been recently described [17]. Some statistical data relating the number of active plasmids present in the cell nucleus and the probability that the cell becomes transfected are also available in literature [16]. It has been reported [16] that if 3 plasmids are present in a cell nucleus, there is a 2% chance for that cell to become transfected after 4 h, which increases to 20% after 24 h. If there are 100 plasmids in the nucleus those chances increase to 20% after 4 h and 40% after 24 h. In addition, the literature [17] suggests that after 24 h there are usually about 8000 plasmids delivered to the nucleus and that the transfection rate is ∼80%, which is heavily dependent on cell type and complexing agent [17]. Once an active plasmid is successfully detected by the Application Layer of the nucleus, the plasmid DNA is decoded through a process called transcription, producing corresponding RNA molecules. The RNA molecules, considered here as PDUs of the nuclear Application Layer, are

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then converted into mRNA that can be regarded as nuclear Transport Layer PDUs and shuttled into cytoplasm with constant rate µmRNA , as long as there are active plasmids within an intact cell nucleus. After mitosis when the cell divides into two daughter cells, the nuclear processing becomes reset and all new daughter cells must be re-transfected to start producing relevant mRNA. The transfection of the daughter cells is simplified within the context of the model presented here, as most of the plasmids present in the cell nucleus before the start of the mitosis are distributed into nuclei of the daughter cells [14]. According to [14] the plasmids are distributed normally between the nuclei of the daughter cells with a mean equal to the 50% of the number of plasmids present in the mother cell’s nucleus and a standard deviation around 25% of that number. During mitosis, however, the plasmids are susceptible to noise and interference from the cytoplasm as there is no nuclear membrane to protect them. Hence, after mitosis, the total number of active plasmids present in both daughter cells is lower than that the number of active plasmids in the mother cell’s nucleus before the start of mitosis. Once the mRNA molecules are produced in the nucleus and shuttled into the cytoplasm, they are translated by the ribosomes (located mainly on the endoplasmic reticulum) to the corresponding chain of amino acids creating an unfolded protein. Of course, as during the whole transmission chain, the mRNA molecules are subject to noise and interference, which results in certain percentage of the mRNA being degraded, before it can be translated. That degradation rate and the translation rate are denoted as µdmRNA and the translation rate by µTra , respectively. This integrity check and translation can be considered as an operation of a Transport layer protocol. The produced chain of amino acids is then folded with rate µfold into a mature protein and stays in the cell (nucleus, cytoplasm, other organelle) for a future use by a corresponding application (e.g. participation in metabolism, cell signaling, etc.), or the protein may be secreted from the cell to perform extracellular functions (see. Fig. 1). Alternatively, it can be degraded before folding with rate µdu . The process of folding and/or binding to chaperones, for example, can be considered as an operation of a Network Layer protocol as the destination address is added to the packet of information. The matured proteins are then utilized by the corresponding applications and/or finally degraded with rate µdm . That rate of degradation of matured proteins also includes degradation of those proteins that are improperly folded and cannot be repaired. This process of degradation is similar to dropping of packets where unrecoverable errors in the Network PDU headers are detected.

another time for being passed to the layer below), two separate queues have to be implemented for that layer. It should be noted here that description of the nonviral gene delivery process by means of a layered protocol stack has been done here to simplify its modeling while in telecommunication networks it is done mainly to simplify their design. The queuing theory has been very well studied with different configurations of the queues including probability distributions different than Poisson and exponential. It has been used to model different real life processes, like complex communication networks, servicing of passengers at airport terminals, etc. [18]. Therefore, the theoretical considerations are limited here to a necessary minimum. The commonly used notation to classify different queues is the so-called Kendall’s notation [19] A/B/C , where A is a letter code to describe the arrival process, B is a letter code to describe the service time distribution and C denotes the number of servers. The queue with a Poisson arrival process and an exponential service time distribution is denoted as M /M /c. Since biological processes within a cell can be considered as highly parallel, meaning that at every step in the transport pathways involved in delivery of genetic material to the nucleus, plasmids/complexes do not wait in a queue but are processed as soon as they arrive. This situation can be nicely modeled as an M /M /∞ queue [20], which results in the instantaneous service rate µ equal to (nµ), where n is the number of plasmids/complexes being serviced at the given time instant at a particular stage in the process. A significant difference between the standard data networks and transport of plasmids/complexes is that while in data networks Poisson processes can be often considered homogenous, the same cannot be said about Poisson processes used to describe what happens inside living cells. Instead, for nonviral gene delivery, all the kinetic constants available in literature for each layer represent averages taken over a large number of cells and over a certain time interval. In reality, values of those constants can vary quite significantly within certain ranges (different for each constant) depending on the complex type, cell type, condition of an individual cell, etc. Therefore, it is more convenient to use inhomogeneous Poisson processes in modeling transport of DNA to the nucleus. For an inhomogeneous Poisson process, the intensity λ(t ) is a function of time. In such a process, the expected number of events within a time interval (a, b] is:

3. System modeling

P [(N (b) − N (a)) = k] =

As described in previous section, the process of nonviral gene delivery can been divided into individual processes in a form of communication protocol layers. Each of those layers can be modeled as an individual queue, much like it can be done for a standard telecommunication system. If plasmids or complexes have to be processed by a particular layer twice (once for being passed to the upper layer and

λa,b =

b



λ(t )dt

(3)

a

and the probability of k arrivals in that time interval equals e−λa,b λka,b k!

,

k = 0, 1, 2, . . . ,

where N (t ) is the number of arrivals counted until time instant t, and e is the basis of a natural logarithm. Hence, all the protocol layers in the transmission chain are modeled as M /M /∞ queues with intensities λ(t ) and service rate µ(t ), changing randomly around the respective mean values defined by the known kinetic constants from the literature.

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Fig. 2. Block diagram of the SIMULINK model of nonviral gene delivery system.

The model has been implemented in a MATLAB/ SIMULINK environment, with all the major blocks implemented as interpreted MATLAB functions and simulation parameters set input by running a script m-file. Since SIMULINK does not allow for an easy implementation of feedback in a form of ‘algebraic loops’ such feedback has been provided through the use of global variables set before the first use to zero. The block diagram of the SIMULINK model is presented in Fig. 2. 4. Simulation results To validate telecommunications model of nonviral gene delivery, simulations were performed of an experiment, where DNA encoding green fluorescent protein (GFP) was delivered to A431 epithelial cells, using a cationic lipid R (Lipofectamine⃝ ) as described in the literature [17,23]. The parameters applied were from published literature with the full list of the numerical values of kinetic constants used in the model given in Table 1. The simulation was repeated for 300 cells with duration of the experiment set to 48 h after delivery of DNA with 0.5 s time increment. Seeds for all pseudo random number generators used to draw random variables were dependent on processor’s time and different seeds were used every time a random number was drawn. It was also assumed

Table 1 List of kinetic constants used for simulation. Kinetic constant

Description

Rate (s−1 )

Source

µi µee µld µcb µcu µnic µcun µpd µpb µnip µucp µmRNA µdmRNA µTra µdu µfold µdm

Complex internalization Endosomal escape Degradation by lysosome Complex binding Complex unpacking Nuclear pore import-complex Unpacking in nucleus Unpacked plasmids degradation Binding of unpacked plasmids Nuclear pore import-plasmids Unbinding complex/plasmid Transcription mRNA degradation Translation Unfolded protein degradation Protein maturation (folding) Degradation of matured (folded) proteins

1.4 1.7 × 10−4 8.3 × 10−5 1.7 × 10−3 1.7 × 107 5 × 10−5 1.7 × 107 8.3 × 10−5 3.3 × 10−5 1.7 × 101 1.7 × 101 5 × 10−2 2.8 × 10−5 2.8 × 10−2 9.7 × 10−6 2.8 × 10−4 1.4 × 10−4

[15] [3] [15] [15] [3] [3,15] [3,21] [3] [3,15] [3,15] [3,15] [22] [22] [22] [22] [22] [22]

that the cells were dividing at a normally distributed rate with the interdivision interval Tim having a mean of 18 h with a standard deviation of 2 h and with a mitosis lasting for 1.2 h in average with the duration being normally

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Fig. 3. Average number of plasmids in cell’s nucleus as a function of experiment time; the solid blue line represents simulated data while the red dashed line results from literature [17]. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 4. Percentage of positively transfected cells as a function of experiment time; the solid line represents simulated data and the dots represent experimentally obtained results [23].

distributed with a standard deviation of 2.4 min. While the interval for dividing time can be dependent on cell and karyotype, the time for the mitosis event is often more reproducible. The starting time of the first mitosis was chosen randomly within the first 18 h of simulation time. For a consecutive mitosis, its starting time was calculated by adding the random variable Tim to the starting time of a previous mitosis cycle. After the end of each mitosis cycle, only one daughter cell (out of 2) was considered further in simulation. The plasmids and complexes present in the mother cell before division were distributed between the daughter cells randomly with a normal distribution having a mean equal to 0.5 of the number of complexes and plasmids, respectively, and the standard deviation equal to 0.5 of the respective mean.

The simulation results are presented in Figs. 3–6. In Fig. 3, an average number of plasmids in the nuclei of cells as a function of time is presented, as compared to experimental data from literature [17]. For this simulation, cells were ‘‘exposed’’ to complexes for one hour, after which time the complexes were effectively removed and fresh medium containing no complexes was added, as described in the actual experiment [17]. In the simulation, the one hour contact of cells with complexes was implemented as a Poisson arrival of complexes for internalization with a rate equal to µi = 1.4 for the first hour and 0 for the remaining 47 h. The simulated experiment closely matches experimental data from the literature [17], with the maximum number of plasmids within the nucleus reached in both cases after about 8–10 h (7500—experimental data;

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Fig. 5. Average number of complexes in endosomes per cell; solid line—cells in contact with complexes for 2 h, dashed line—cells in contact with complexes for 1 h, only.

Fig. 6. Average number of GFP mRNA within the cell; complexes supplied for 2 h, only.

7178—simulated result), and after 48 h the results stabilize at the same value of about 1750 plasmids per cell nucleus. The discrepancies may be due to the fact that the chosen values of kinetic constants may not fully reflect the conditions of experiment reported in [17] or from differences in rate of mitosis. Results of the positive transfection rate (cells with plasmids in nucleus and GFP successfully produced, folded and active), shown in Fig. 4, nicely follow the measured results published in [23]. For this simulation (and experiment), cells were exposed to complexes for four hours, after which time the complexes were effectively removed and fresh medium containing no complexes was added, as described in the actual experiment (cite). In the

simulation, the four hour contact of cells with complexes was implemented as a Poisson arrival of complexes for internalization with a rate equal to µi = 1.4 for the first 4 h and 0 for the remaining 44 h. In both cases, the measured results are available for the first 48 h, only, and in the case of the transfection, measurements were only available for 3 different time instants: 6, 24 and 48 h [23]. Cytotoxicity could lead to reduced experimental levels in transfection as overly stressed or dying cells are incapable of maintaining adherence to the culture flask. In addition, the assay technique can often confound measured transfection levels, as can differences in mitosis rates from those used

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in the model. These reasons may explain the GFP expression variation at 24 h between the model and experimental results. In addition, with limited values available experimentally (i.e. no time point between 6 and 24 h where transfection may reach a maximum), the curves differ in shape between model and experimental results. However, these figures do demonstrate that the model is capable of illustrating nonviral gene delivery. In addition to simulating results that can be measured experimentally, the model can also be used to investigate transfection process at intermediate nodes within the nonviral gene delivery process not easily obtainable through practical experiments. To illustrate that potential, the average number of complexes being held in endosomes is shown in Fig. 5, and the average number of mRNA molecules produced by the cell nucleus but not yet converted to proteins is shown in Fig. 6. Analyzing those results can give an additional insight into the whole process of nonviral gene delivery, which can be used to improve the design of more efficient delivery systems. 5. Conclusions In the paper, we considered nonviral gene delivery to mammalian cells as a macro-to-nano communication system that for the ease of modeling was described using a layered communication protocol. This approach allowed the use of standard queuing theory approach to model the system incorporating the statistical parameters from literature. The model was implemented in a MATLAB/SIMULINK environment and tested through simulation. Simulation results show a high degree of agreement with experimental data, including internalization, nuclear accumulation, and transfection efficiency. Our novel application of queuing theory for modeling nonviral gene delivery provides an insight into the pathways and mechanisms of nonviral gene transfer, so that more efficient systems can be designed. The proposed model is flexible enough to be applied for viral gene delivery as well. References [1] D.A. Dean, B.S. Dean, S. Muller, L.C. Smith, Sequence requirements for plasmid nuclear import, Experimental Cell Research 253 (2) (1999) 713–722. [2] A. Elouahabi1, J.-M. Ruysschaert, Formation and intracellular trafficking of lipoplexes and polyplexes, Molecular Therapy 11 (2005) 336–347. [3] M.C. Garnett, Gene-delivery systems using cationic polymers, Critical Reviews in Therapeutic Drug Carrier Systems 16 (2) (1999) 147–207. [4] J.Z. Gasiorowski, D.A. Dean, Postmitotic nuclear retention of episomal plasmids is altered by DNA labeling and detection methods, Molecular Therapy 12 (3) (2005) 460–467. [5] D. Gross, Fundamentals of Queueing Theory, Wiley, New York, 1998. [6] U. Jandt1, S. Shao, M. Wirth, A.-P. Zeng, Spatiotemporal modeling and analysis of transient gene delivery, Biotechnology and Bioengineering 108 (9) (2011) 2205–2217. [7] D.G. Kendall, Stochastic processes occurring in the theory of queues and their analysis by the method of the imbedded Markov chain, Annals of Mathematical Statistics 24 (3) (1953) 338–354. [8] F.D. Ledley, Pharmaceutical approach to somatic gene therapy, Pharmaceutical Research 13 (11) (1996) 1595–1614.

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[9] W. Li, T. Ishida, R. Tachibana, M.R. Almofti, X. Wang, H. Kiwada, Cell type-specific gene expression, mediated by TFL-3, a cationic liposomal vector, is controlled by a post-transcription process of delivered plasmid DNA, International Journal of Pharmaceutics 276 (1–2) (2004) 67–74. [10] M.F. Neuts, S.-Z. Chen, The infinite-server queue with Poisson arrivals and semi-Markovian services, Operations Research 20 (2) (1972) 425–433. [11] D.W. Pack, A.S. Hoffman, S. Pun, P.S. Stayton, Design and development of polymers for gene delivery, Nature Reviews Drug Discovery 4 (2005) 581–593. [12] Z.P. Parra-Guillén, G. González-Aseguinolaza, P. Berraondo, I.F. Trocóniz, Gene therapy: a pharmacokinetic/pharmacodynamic modelling overview, Pharmaceutical Research 27 (2010) 1487–1497. [13] D. Schaffert, E. Wagner, Gene therapy progress and prospects: synthetic polymer-based systems, Gene Therapy 15 (2008) 1131–1138. [14] G. Schwake, S. Youssef, J.-T. Kuhr, S. Gude, M.P. David, E. Mendoza, E. Frey, J.O. Rädler, Predictive modeling of non-viral gene transfer, Biotechnology and Bioengineering 105 (4) (2010) 805–813. [15] T. Segura, L.D. Shea, Materials for non-viral gene delivery, Annual Review of Materials Research 31 (2001) 25–46. [16] A.T. Sharp, A.K. Pannier, B.J. Wysocki, T.A. Wysocki, A novel telecommunications-based approach to HIV modeling and simulation, Nano Communication Networks 3 (2) (2012) 129–137. [17] A.T. Sharp, S.M. Raja, B.J. Wysocki, T.A. Wysocki, Layered communication protocol for macro to nano-scale communication systems, in: Proc. IEEE ICC’2010, 23–27 May 2010, pp. 1–6. [18] W. Stallings, Data and Computer Communications, eighth ed., Prentice Hall, Upper Saddle River, 2007. [19] I. Tranchant, B. Thompson, C. Nicolazzi, N. Mignet, D. Scherman, Physicochemical optimisation of plasmid delivery by cationic lipids, The Journal of Gene Medicine 6 (2004) 24–35. [20] E.V. van Gaal, R.S. Oosting, R. van Eijk, M. Bakowska, D. Feyen, R.J. Kok, W.E. Hennink, D.J. Crommelin, E. Mastrobattista, DNA nuclear targeting sequences for non-viral gene delivery, Pharmaceutical Research 28 (7) (2011) 1707–1722. [21] C.M. Varga, K. Hong, D.A. Lauffenburger, Quantitative analysis of synthetic gene delivery vector design properties, Molecular Therapy 4 (2001) 438–446. [22] C.M. Varga, N.C. Tedford, M. Thomas, A.M. Klibanov, L.G. Griffith, D.A. Lauffenburger, Quantitative comparison of polyethylenimine formulations and adenoviral vectors in terms of intracellular gene delivery processes, Gene Therapy 12 (2005) 1023–1032. [23] C.M. Wiethoff, C.R. Middaugh, Barriers to nonviral gene delivery, Journal of Pharmaceutical Sciences 92 (2) (2003) 203–217.

Beata Joanna Wysocki, graduated from Warsaw University of Technology receiving her M.Eng. degree in Electrical Engineering in 1991. In 1994, she started her Ph.D. study in the Australian Telecommunications Research Institute at Curtin University of Technology. In March 2000, she was awarded her Ph.D. for the thesis: ‘‘Signal Formats for Code Division Multiple Access Wireless Networks’’. Since October 1999 she has been with the Telecommunications and Information Technology Research Institute at the University of Wollongong as a Research Fellow. Her research interests include: space–time signal processing, sequence design for direct sequence (DS) code division multiple access (CDMA) data networks and optimization of Ultra Wide Band (UWB) communication systems as well as modeling biological processes at nanoscale. Timothy M. Martin received a B.S. in Mechanical Engineering in 2006 and a B.S. in Biomedical Engineering in 2006 from the Rose–Hulman Institute of Technology, Terre Haute, IN, USA and a Fundamentals of Engineering certificate in 2006. A US Marine Corps combat veteran of the Iraq war, he is now a matriculate to the Ph.D. Biomedical Engineering program at the University of Nebraska–Lincoln (Lincoln, NE). Prior to continuing education, he worked for four years as a process engineer at Cook Pharmica where he provided technical

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support for protein purification operations. His current research interests include gene delivery combating heart disease, bioinformatics, and modeling. Mr. Martin is a current member of the American Institute of Chemical Engineers, UNL Graduate Student Association, and the Biomedical Engineering Society.

Dr. Wysocki was an interim Chair of the newly established Chapter of IEEE Communications Society in Western Australia in 1997 and was elected to chair that Chapter in 1998. In 2009, Dr. Wysocki was a Chair of the Nebraska Chapter of IEEE Communications Society and in 2010 and 2011 a Chair of Nebraska Chapter of IEEE Computers Society.

Tadeusz Antoni Wysocki (M’94–SM’98), received the M.Sc.Eng. degree with the highest distinction in telecommunications from the Academy of Technology and Agriculture, Bydgoszcz, Poland, in 1981. In 1984, he received his Ph.D. degree, and in 1990, was awarded a D.Sc. degree (habilitation) in telecommunications from the Warsaw University of Technology. In 1992, he moved to Perth, Western Australia to work at Edith Cowan University. He spent the whole of 1993 at the University of Hagen, Germany, within the framework of an Alexander von Humboldt Research Fellowship. In December 1998, he moved to the University of Wollongong, NSW, as an Associate Professor, within the School of Electrical, Computer and Telecommunications Engineering. Since the fall of 2007, he has been with the University of Nebraska-Lincoln as Professor of Computer and Electronics Engineering at the Peter Kiewit Institute in Omaha, NE. The main areas of his research interests include: space–time signal processing, diversity combining, indoor propagation of microwaves, and biological communications at nano-scale. He is an author or co-author of over 250 research papers.

Angela K. Pannier, received a B.S. and M.S. in Biological Systems Engineering from the University of Nebraska-Lincoln (in 2001 and 2002, respectively), and a Ph.D. in Biological Sciences from Northwestern University in Evanston, IL in 2007. She is currently an Assistant Professor in the Department of Biological Systems Engineering at the University of Nebraska-Lincoln (UNL) (since October 2007). She has also been appointed as a member of the Nebraska Center for Materials and Nanoscience at UNL and a member of the Center for Drug Delivery and Nanomedicine at the University of Nebraska Medical Center. The author of over 15 peer-reviewed articles, as well as a book chapter, her research interests including modeling nonviral gene delivery, developing novel nonviral gene delivery systems, understanding stem cell differentiation, and biomaterials for embryological and tissue engineering applications. Dr. Pannier is a member of the American Institute of Chemical Engineers, Biomedical Engineering Society, Society of Women Engineers, Institute of Biological Engineers, and the American Society of Gene and Cell Therapy.