Bulletin of Mathematical Biology

, Volume 75, Issue 8, pp 1400–1416

Modeling Intercellular Transfer of Biomolecules Through Tunneling Nanotubes

Authors

  • Yasir Suhail
    • Department of Biomedical EngineeringJohns Hopkins University
    • High-Throughput Biology CenterJohns Hopkins University
  • Kshitiz
    • Department of Biomedical EngineeringJohns Hopkins University
    • Department of BioengineeringUniversity of Washington
  • Justin Lee
    • Department of BioengineeringUniversity of Washington
  • Mark Walker
    • Department of Biomedical EngineeringJohns Hopkins University
  • Deok-Ho Kim
    • Department of BioengineeringUniversity of Washington
  • Matthew D. Brennan
    • Department of Biomedical EngineeringJohns Hopkins University
  • Joel S. Bader
    • Department of Biomedical EngineeringJohns Hopkins University
    • High-Throughput Biology CenterJohns Hopkins University
    • Department of Biomedical EngineeringJohns Hopkins University
Original Article

DOI: 10.1007/s11538-013-9819-4

Cite this article as:
Suhail, Y., Kshitiz, Lee, J. et al. Bull Math Biol (2013) 75: 1400. doi:10.1007/s11538-013-9819-4

Abstract

Tunneling nanotubes (TNTs) have previosly been observed as long and thin transient structures forming between cells and intercellular protein transfer through them has been experimentally verified. It is hypothesized that this may be a physiologically important means of cell–cell communication. This paper attempts to give a simple model for the rates of transfer of molecules across these TNTs at different distances. We describe the transfer of both cytosolic and membrane bound molecules between neighboring populations of cells and argue how the lifetime of the TNT, the diffusion rate, distance between cells, and the size of the molecules may affect their transfer. The model described makes certain predictions and opens a number of questions to be explored experimentally.

1 Introduction

Cell–cell communication plays an important role in coordinating collective cell decisions. It is also critical to maintain both structural and functional homeostasis in a tissue. Since coordination between cells is an essential requirement for the successful functioning of a multicellular organism, many mechanisms have evolved to allow cells to communicate with each other bearing important outcomes in both normal functioning of the tissues and pathology. For example, high twitch muscle cells are in close proximity with blood vessels, and nerve endings, and their close interactions are essential for the correct muscle functioning (Behnke et al. 2011; Vikne et al. 2012). Cell–cell interactions between cancer cells and endothelial cells occur within solid tumor, and metastatic cancer cells extravasating the endothelium (Weis and Cheresh 2011; Qin et al. 2012; Stine et al. 2011). Extensive research has explored the mechanisms of these cell–cell interactions, resulting in extensive information on the chemical cell–cell signaling pathways occurring in autocrine (Lichtenberger et al. 2010), paracrine (Abou-Khalil et al. 2009), and juxtracrinemanner (Bosenberg and Massague 1993; Singh and Harris 2005). However, recent evidence has also suggested another form of cell–cell interaction that occurs via direct transfer of cellular components from one cell to another, thus transferring information without involvement of traditionally implicated chemical mechanisms (Niu et al. 2009; Ahmed and Xiang 2011; Li et al. 2010; Pap et al. 2009; Prochiantz 2011; Mack et al. 2000). Although the degree of such intercellular transfer of cellular components and its role in defining cell and tissue behavior in vivo remain less understood, the evidence for existence of this novel communication mechanism is overwhelming, suggesting that it could potentially have a significant effect in influencing the recipient cell phenotypes in such diverse processes as cancer progression (Ambudkar et al. 2005), immunity (Baba et al. 2001; Carlin et al. 2001; Quah et al. 2008), HIV infection (Mack et al. 2000), transfer of drug resistance (Levchenko et al. 2005), and ribosomal recruitment in neuronal axons (Twiss and Fainzilber 2009). Direct protein–protein transfer is therefore important to understand in greater detail, both experimentally and computationally.

Previous studies have reported multiple examples of transfer of membrane proteins between cells (Levchenko et al. 2005; Guescini et al. 2012; Agnati et al. 2011; Al-Nedawi et al. 2008; Davis 2007). In addition, small cytoplasmic biochemical components have also been shown to be transferred between cells in a size-dependent manner (Niu et al. 2009). However, intercellular transfer of large cytoplasmic proteins has not been yet examined with conclusive results. Various mechanisms have been suggested for intercellular transfer of cellular components, including formation of tunneling nanotubes (TNTs) between cells (Guescini et al. 2012; Rustom et al. 2004), spontaneous secretion and integration of microvesicles (Valadi et al. 2007; Denzer et al. 2000), and transient cell–cell fusion (Driesen et al. 2005). As is frequently the case with poorly understood biological phenomena, it is not easy to discriminate between putative mechanistic details and generate most plausible models of this cell communication phenomenon. It is also possible that the mechanisms may be cell-type specific and multiple mechanisms might coexist in diverse physiological and patho-physiological contexts. However, certain findings have been suggestive of the constraints that can be placed on the mechanistic models of this process. For instance, the reports of membrane protein transfer are much more frequent and better supported than the reports of transfer of large cytosolic components, including of proteins (Agnati et al. 2011; Camussi et al. 2010). We questioned whether a reason for this discrepancy might lie in the properties of the transfer process itself. Another, potentially more revealing constraint comes from the observation that transfer of cytosolic, but not membrane components is strongly dependent on the molecular weight of the transferred molecules (Niu et al. 2009). Thus, a plausible model of the transfer process has to be able to explain these particular well-established features of the intracellular transfer of different cellular components.

Here, we propose a mathematical model to explain passive protein transfer between cells via formation of tunneling nanotubes (TNTs), which have been observed in various studies to be responsible for intercellular protein transfer (Guescini et al. 2012; Rustom et al. 2004; Bukoreshtliev et al. 2009). Our steady state model explains that while membrane protein transfer may be unrelated to the mass of the protein, cytoplasmic proteins may follow an inverse correlation with size. Though no existing report conclusively shows the transfer of cytoplasmic proteins between cells, smaller cytoplasmic components have been shown to be transferred between cells in a size-dependent manner (Niu et al. 2009), as predicted by the model. The model explains that while transfer of cytoplasmic proteins may occur between cells, it would be in relatively smaller amounts in comparison to smaller biochemical components present in the cytosol, or membrane proteins. Further, we predict that protein transfer may depend on the stabilization of TNTs for longer duration.

2 Methods

2.1 Basic Assumptions

Previous studies have revealed that proteins and other cellular components can transfer between cocultured cells (Niu et al. 2009; Li et al. 2010; Prochiantz 2011; Davis 2007). Typically donor and recipient cells are defined according to the criterion of observation for the transfer. Commonly, these observations are specific to the transferred component, e.g., by using an antibody or fluorescent tag to observe the dynamics of transfer of a biochemical molecule from one cell to another. The schematic in Fig. 1 details a typical experimental setup used to detect transfer of cellular components between cells. For simplicity, in the schematic and in the model, we assume that both membrane and cytosolic components are transferred from a donor population to a second recipient population.
https://static-content.springer.com/image/art%3A10.1007%2Fs11538-013-9819-4/MediaObjects/11538_2013_9819_Fig1_HTML.gif
Fig. 1

Schematics showing the experimental observations of molecule transfer and the TNTs. (A) Transfer of membrane and cytosolic protein transfer between cells in coculture. The donor and recipient cells are defined according to the observation criterion. After coculture, both membrane and cytosolic proteins are transferred to the recipient cells from the donor cells at a relatively slow rate in comparison to the rate of production of proteins in the donor cells. Observation post coculture depicts a small population of recipient cells that received transferred protein that can now be detected. (B) Schematic showing transfer of membrane and cytosolic components from acceptor to donor cells via tunneling nanotubes (TNTs). In this model, donor cells contains higher amount of cytosolic component (shaded), and membrane bound component (dots) than the recipient cell. Coculture results in formation of TNTs from donor cell that can transiently connect with the recipient cell, resulting in transfer of both cytosolic component, and membrane-bound component. In the model, the membrane composition of TNT remains similar to the rest of the donor cell membrane, the cytosol within the TNT shaft contains a gradient of cytosolic components till steady state is reached. Since most TNTs are transient (i.e., their lifetime is smaller than that required for the concentration of cytosolic components within the TNT shaft to attain steady state), the transfer of cytosolic components to the recipient cell is determined by the concentration of the component at the site of connection between the TNT and the recipient cell (The cytosolic component is green and the membrane proteins are red dots in the color version of the figure online)

Variables and constants used in the model are described in Table 1. We assume that cells are cultured as adherent cells in a dish. Consider a cell located at the origin of a system of coordinates superimposed onto the cell adhesion substratum. The cell can exchange proteins or other molecules with cells around it by sampling the space in some manner, by means of tunneling nanotubes (TNTs) protruding into the extracellular space (Fig. 2). The maximal length of TNTs will be limited by the physical and energetic constraints of the cell. The growth of the exploring TNT can be expected to be driven by some sort of polymeric growth, like the filopodia or actin growth. In any given direction, this growing nanotube can only expect to make a connection with the closest cell. If the cells are uniformly distributed points, and the placement of one cell is independent of another, the distance of any cell to it’s nearest cell will follow an exponential distribution. The physical limit of the TNT growth, however, limits the exponential at its tail and most of the distribution thus lies in the linear regime of the exponential. As a first-order approximation, we can thus approximate the abundance of the TNT lengths to fall linearly with length. Denoting the maximum length as l, we assume that the length r of such TNTs follows a distribution:
https://static-content.springer.com/image/art%3A10.1007%2Fs11538-013-9819-4/MediaObjects/11538_2013_9819_Equ1_HTML.gif
(1)
Hence, the probability of forming a connection to transfer protein with a part of another cell located within the infinitesimal region (rdr, ) at the polar co-ordinates (r,θ) within some time unit is
https://static-content.springer.com/image/art%3A10.1007%2Fs11538-013-9819-4/MediaObjects/11538_2013_9819_Equ2_HTML.gif
(2)
Now consider another cell of radius b located distance r away from the donor cell of interest sending out TNTs. Assuming that the region of sampling by the TNTs is much larger than the dimensions of the cells (lb and rb), the probability of forming such a connection will be p(Connection|r)∝(lr)πb2.
https://static-content.springer.com/image/art%3A10.1007%2Fs11538-013-9819-4/MediaObjects/11538_2013_9819_Fig2_HTML.gif
Fig. 2

Schematic showing the calculation of the probability of a tunneling nanotube (TNT) connection between an acceptor and donor cell. As explained in Eq. (3), consider r as the length of the TNT, and l the maximum length. For a cell located at a distance x from the boundary, there is an arc of angle 2arccos(x/r) with cells located at a distance r. This corresponds to the illustrated infinitesimal area 2arccos(x/r)rdr, which can be integrated from r=x to l for the total applicable area

Table 1

Table describing the constants and variables used in the mathematical model describing intercellular transfer of molecules through nanotubes

Description

Symbol used

Parameter value used in the analysis

Source of the parameter value

Comments

Dimensions

Radius of a cell

b

No value used, analysis done algebraically

  

Length

Maximum length of TNT

l

50 μm

Inexact estimate in the range of observations reported in (Rustom et al. 2004)

 

Length

Diffusion coefficient

D

See Table 2

  

Length2/time

Stoke’s radius

r

See Table 2

  

Length

Constant related to membrane bound molecule transfer

A

No value used, analysis done algebraically

 

Related to the area of membrane transferred on each connection, the frequency with which a cell sends out TNTs, and the active transport of the molecule to donor cell membrane

Molecules/length3

Constant related to cytosolic molecule transfer

B

No value used, analysis done algebraically

 

Related to the frequency with which a cell sends out TNTs and the concentration of the molecule in the donor cell

Molecules/length3

Cell density

ρ

No value used, analysis done algebraically

  

Cells/length2

Once such a connection is formed, we consider the cases of cytoplasmic and membrane proteins transferred from a region of donor cells to a region of acceptor cells.

2.2 Transfer of Cellular Components by TNT

We assume that when a TNT from a donor cell reaches the recipient cell, and connects with the membrane of a recipient cell, it can “donate” a small portion of the membrane to the donor cell. This process may actually occur as “exchange” of membrane portions, but here we describe only the transfer of observable membrane and cytoplasmic components present exclusively in the donor cells. Furthermore, we assume that TNTs are open to diffusive transport of donor cell components and the concentrations of the transferred components are not necessarily at the steady state in the TNTs. Due to more extensive reservoirs of the potentially transferable cytosolic vs. membrane components (e.g., cytosolic proteins) and the potential for lower diffusivity through the cytosolic vs. membrane parts of TNTs, the diffusion of the membrane components may lead to a more effective exchange vs. that of the cytosolic ones during the transient, TNT-mediated cell–cell fusion. Thus, the transfer of membrane components may be limited by the rate of their access to an individual TNT on the donor cell side, with the membrane density otherwise reaching a steady state within the TNT. On the other hand, the transfer of cytosolic components may be limited by the rate of reaching the steady state in the TNT, with transport mostly resulting in and dependent on the spatial gradient of the component within the TNT.

2.3 Transfer of Membrane Proteins

Consider an acceptor cell located at a distance x from the region of donor cells, each of radius b. There is an arc of radius r subtending an angle of θ radians from the acceptor cell that falls on the region of the donor cells where θ=2arccos(x/r). Assuming a cell density of ρ cells per unit area, the probability of our cell making a connection with any cell located in the donor region at the distance x away will thus be
$$ p(\mbox{Connection}|x) \propto \rho\pi b^{2}\int _{x}^{l}(l-r)2\arccos(x/r)r\,dr. $$
(3)
Membrane bound molecules are actively transferred to the membrane by the cellular machinery. Every time a TNT connection is formed there is a merging of the membranes of the two cells at one end of the TNT. We assume that a small amount of membrane protein is transferred to the acceptor cell due to the TNT-cell membrane contact. The total amount of membrane bound molecules (φ molecules per cell) transferred into an acceptor cell at a distance x from the region of the donor cells will be the frequency or abundance TNT connections (represented by quantity of Eq. (3)) multiplied by a constant related to the amount of molecules of interest transferred in each TNT connection:
https://static-content.springer.com/image/art%3A10.1007%2Fs11538-013-9819-4/MediaObjects/11538_2013_9819_Equ4_HTML.gif
(4)
where A is a constant with dimensions of molecules/m3 collapsing all the unknowns such as density of the protein on the donor cell membrane, efficiency of transfer across cells, etc.
With a protein degradation rate of β s−1, we have the dynamics
$$ \frac{d\phi}{dt}=\frac{d\phi}{dt\,\mathrm{Transfer}} -\beta\phi. $$
(5)
This leads to the steady state condition of
https://static-content.springer.com/image/art%3A10.1007%2Fs11538-013-9819-4/MediaObjects/11538_2013_9819_Equ6_HTML.gif
(6)
As expected, the protein is transferred up to a distance equal to the maximum length of the TNTs, l. The rate of decline of the protein levels with distance at the boundary is
$$ \biggl[\frac{d\phi(x)}{dx}\biggr]_{x\to0} = - \frac{Al^2\rho\pi b^2}{\beta}. $$
(7)

2.4 Transfer of Cytoplasmic Proteins

We consider an identical arrangement of donor and acceptor cells in this case. The chances of TNT connections formed between the donor and acceptor cells is
$$ p(\mathrm{Connection}|x)\propto \rho\pi b^2 \int _{x}^{l}(l-r)2\arccos(x/r)r\,dr. $$
(8)
Here, we assume that the diffusive transport through a TNT is the rate limiting step. According to Fick’s Law, in one-dimensional diffusion from a source of density η, the density at a distance r at time t is \(\eta\operatorname{Erfc}(r/2\sqrt{Dt})\) where D is the coefficient of diffusion and \(\operatorname{Erfc}\) is the complimentary error function. We assume that once a connection is made, the transfer of a cytosolic component occurs due to diffusion for a certain amount of time (effective connection time).
The amount of protein transfer per connection is thus proportional to \(\operatorname{Erfc}(r/2\sqrt{Dt})\). Now the rate of protein transferred will be proportional to the number of connections made per unit time and the amount of protein transferred per connection:
https://static-content.springer.com/image/art%3A10.1007%2Fs11538-013-9819-4/MediaObjects/11538_2013_9819_Equ9_HTML.gif
(9)
where B is a constant of dimension molecules/m3 (corresponding to A for the membrane bound case) incorporating the chemical unknowns and C is the mean diffusion length
$$ C=2\sqrt{Dt} $$
(10)
collapsing the diffusion coefficient and effective mean connection time of the TNT connections. The integral with the error function can be computed numerically but is analytically cumbersome.
Since we have already used the one-dimensional approximation and assumed no diffusion within the TNT before the formation of the connection, we can make one more simplifying approximation and use a linearized approximation to the error function,
https://static-content.springer.com/image/art%3A10.1007%2Fs11538-013-9819-4/MediaObjects/11538_2013_9819_Equ11_HTML.gif
(11)
Similarly, solving for the steady state with the approximation of Eq. (11), we have
https://static-content.springer.com/image/art%3A10.1007%2Fs11538-013-9819-4/MediaObjects/11538_2013_9819_Equ12_HTML.gif
(12)
Therefore, the region where the acceptor cells receive the protein is limited by both the maximum length of the TNTs and also by the mean diffusion length. The maximum protein levels evaluated from Eq. (12) seen at the boundary are
https://static-content.springer.com/image/art%3A10.1007%2Fs11538-013-9819-4/MediaObjects/11538_2013_9819_Equ13_HTML.gif
(13)
The rate of decline of protein levels with distance is also dependent on both the maximum length of the TNTs and the mean diffusion length.
https://static-content.springer.com/image/art%3A10.1007%2Fs11538-013-9819-4/MediaObjects/11538_2013_9819_Equ14_HTML.gif
(14)
Interestingly, we see that while greater mean diffusion length increases the observed levels of the transferred molecules transferred adjacent to the donor cells (Eq. (13)), it also sharpens the fall in the concentration of the molecule as we move farther from the donor cells (Eq. (14)).
To calculate the mean diffusion lengths, we assume that the diffusion coefficient follows the Einstein–Stokes equation \(D=\frac{k_{B}T}{6\pi \eta r}\), where r is the radius (or the effective Stokes radius for nonspherical particles) of the diffusing molecule; kB is the Boltzmann’s constant; T the absolute temperature, and η the viscosity of the medium. We considered a few representative molecules with varying sizes, the diffusion coefficients of which are tabulated in Table 2.
Table 2

Table detailing the diffusion coefficients of various molecules simulated by the model in Fig. 4

Molecule

Stoke’s radius

Diffusion coefficient D

Glucose

 

500 μm2/s (Groebe et al. 1994)

Dextran (3 kDa)

13 Å (Nicholson and Tao 1993)

37 μm2/s

Dextran (10 kDa)

23 Å (Nicholson and Tao 1993)

20 μm2/s

Dextran (40 kDa)

73 Å (Nicholson and Tao 1993)

6.5 μm2/s

GFP

23 Å (Nicholson and Tao 1993)

20 μm2/s

Cytochrome C

https://static-content.springer.com/image/art%3A10.1007%2Fs11538-013-9819-4/MediaObjects/11538_2013_9819_IEq5_HTML.gif, estimated from GFP

28 μm2/s

Legumainpreprotein (AEP)

https://static-content.springer.com/image/art%3A10.1007%2Fs11538-013-9819-4/MediaObjects/11538_2013_9819_IEq6_HTML.gif , estimated from GFP

17 μm2/s

According to Gregor et al. (2005), and Luby-Phelps et al. (1986), the viscosity of the cytosol is approximately 4 times of that of water, therefore, we simulated our model with the value of value of η=4.2×10−3 kg m−1 s−1.

3 Results

3.1 Range of Profusion of the Transferred Molecule

Simulating our model for protein transfer by TNT from donor to acceptor cells for membrane proteins, we observe that the membrane proteins can be transferred into the acceptor cells within the distance up to the maximum length of the TNT, l. Also, the decline of the protein levels is approximately linear with the distance from the boundary of the donor cells.

When simulated for cytoplasmic proteins, the model predicts a similar profile for the levels of transferred cytoplasmic molecules into the acceptor cells (Fig. 4). However, the amount of transferred molecules, as well as the distance over which they are effectively transferred also depends on the mean diffusion length. This can be attributed to the fact that cytoplasmic constituents, during a transient TNT formation, exist in the form of concentration gradient with the highest concentration in the location of cytoplasm before TNT was formed. The concentration of cytoplasmic constituents is lowest at the tip of the TNT in connection with the recipient cells (Fig. 3). Similar to the case of membrane-bound molecules, the fall in the levels of transferred cytoplasmic molecule is approximately linear with distance from the donor cell region boundary (Fig. 4). We then compared model predictions for a number of different biomolecules detailing the efficiency of transfer into the acceptor cells after a steady state of the transfer process is reached. For cytoplasmic molecules, both the size and the duration of stable TNT connection were found to determine the levels of transferred molecules.
https://static-content.springer.com/image/art%3A10.1007%2Fs11538-013-9819-4/MediaObjects/11538_2013_9819_Fig3_HTML.gif
Fig. 3

Simulated transfer of molecules from donor to accepted cells via TNT. (A) Transferred membrane-bound molecule levels in acceptor cells at a distance x from the boundary of the donor cells region, calculated from Eq. (6). The distances used in the plot are in units of the maximum TNT length l. The levels of transferred membrane molecules are given in units of \(\frac{Al^{3}\rho \pi b^{2}}{3\beta}\) where A is a constant related to the physics of the membrane contact and level in the donor cells, ρ the density of the donor cells, and b the radius of the cells. The level is maximal at the boundary and gradually decreases to zero at a distance equal to the maximum TNT length l, after which no TNT connection can be made between the donor and acceptor cells. (B) Transferred cytoplasmic molecule levels in acceptor cells at a distance x from the boundary of the donor cells region, calculated from Eq. (12) for various values of the mean diffusion length (C). The distances (x) used in the plot are in units of the maximum TNT length l. The level of transferred molecule levels are given in units of \(\frac{Bl^{3}\rho \pi b^{2}}{3\beta}\) where B is a constant related to the level in the donor cells, ρ the density of the donor cells, and b the radius of the cells. The values of the mean diffusion length C considered are specified as fractional multiples of the maximum TNT length l. More of the cytosolic molecule is transferred for larger mean diffusion lengths. Both the amount of molecules transferred to a particular distance and the maximal distance to which it is transferred is limited by the mean diffusion length. The mean diffusion length itself may depend on both the diffusion constant and mean time of stable TNT formations (Eq. (10)), which is explored further in Fig. 4

https://static-content.springer.com/image/art%3A10.1007%2Fs11538-013-9819-4/MediaObjects/11538_2013_9819_Fig4_HTML.gif
Fig. 4

Stability of TNT connection determines extent of cytoplasmic protein transfer in a size dependent manner. Level of transferred molecules transferred from donor to acceptor cells via TNT formation, simulated to be stabilized for mean durations of (A) 1 second, (B) 10 seconds, and (C) 100 seconds. In all cases, levels of transferred molecules in the recipient cells are plotted against the distance x from the region of donor cells, calculated from Eqs. (6) and (12). The levels of transferred molecules are given in units of \(\frac{Al^{3}\rho \pi b^{2}}{3\beta}\) for membrane bound molecules, and \(\frac{Bl^{3}\rho \pi b^{2}}{3\beta}\) for cytosolic molecules similar to Fig. 3. In all cases, size of TNT is considered to be 50 μm

3.2 Possible Mechanisms for the Regulation of TNT Molecular Transfer

A number of regulatory mechanisms for the transfer of molecules across TNTs are consistent with our model. TNT length and its stability can be modulated experimentally by stabilizing the actin cytoskeletal assembly forming the TNTs. The model predicts that the stability of TNT, and thereby connection of donor and recipient cells, will have a significant effect on the level of cytoplasmic molecules in donor cells. The length of time TNT connections are made will also influence the transfer of membrane bound molecules, with longer stable connections leading to higher membrane molecule transfer. Changes in the transport of the molecule through the Golgi apparatus, micro-vesicles, and endosomes to and from the membrane and the effect of post translational control of its binding with the membrane in the donor cells will also determine the amount of membrane-bound molecule available for transfer on the TNTs. These changes in membrane recruitment and binding could be modulated in the cells by various pathways.

3.3 Effect of the Size of the Transferred Molecules

The model predicts that small molecules are quite robust in their transfer across the TNTs while larger proteins require favorable conditions, for example, stable TNT that retract after longer durations. Our model predicts that, in general, in a typical TNT that exists for a few seconds to tens of seconds, transfer of membrane proteins will be appreciably higher than cytoplasmic molecules. Among cytoplasmic molecules, large molecules will have an extremely low transfer efficiency, with transfer occuring only within cells that are extremely close to each other (Fig. 4A). The difference of extent of transfer between small and large molecules is quite pronounced, suggesting that the size of molecules plays a significant role in cytoplasmic protein transfer between cells.

Small cytosolic molecules, for example, glucose (Groebe et al. 1994) or other metabolites, transfer at a much faster rate. Thus the model explains previous observations that dextran molecules of different sizes showed a size dependent intercellular transfer amounts between dextran containing Chinese Hamster Ovarian (CHO) cells to those without dextran (Figs. 4A, B). Since typical cytosolic proteins are much larger than smaller metabolites (e.g., green fluorescent protein used as a reporter probe in cell biology experiments, which has a Stoke’s radius of 23 Å, similar to a 10 kDa Dextran (Phillips 1997)), the extent of their transfer is expected to be much lower, suggesting a possible reason why the detection of cytosolic protein transfer has been rare, or has remained unreported.

However, as the TNT becomes more stabilized, the diffusion of cytoplasmic molecules within the TNT shaft shifts more towards a steady state, and becomes shallower. This results in higher transfer of cytoplasmic molecules (Fig. 4B). As TNTs are stabilize even further, the extent of transfer of cytoplasmic molecules approaches the transfer of membrane proteins for all distances between donor and recipient cells (Fig. 4C). The difference of transfer within cytoplasmic molecules of different sizes becomes less pronounced, suggesting that size remains a smaller factor in cytoplasmic protein transfer as TNTs stabilize (Fig. 4C).

4 Discussion

Intercellular transfer of cellular components is a fascinating phenomenon largely because it is understood so little, and does not seem to obey any known classical cell–cell communication mechanisms. This transfer also seems surprising since it suggests a phenomenon over which cells can only have partial or no active control. Even then, it has been implicated as important in various physiological and pathological contexts. For example, while heterotypic and homotypic cell–cell interactions occur frequently in various tissues, including cancer cells and blood vessels, muscles, and nerve fibers, etc., potentially allowing transfer of molecules between cells, pathological contexts present new avenues for intercellular transfer of biomolecules to play significant roles. For example, drug-resistant cancer cells could transfer small drug-resistant molecules to neighboring drug-susceptible cells causing lateral transfer of resistance. However, in spite of the importance of this passive form of intercellular communication, our present understanding about it is limited.

In spite of the relatively few reports of intercellular transfer of biomolecules, largely due to the small amounts of transfer that can frequently go undetected, a few trends stand out in the reported studies. It has been observed that the membrane bound molecules could transfer more readily from one cell to another, but cytoplasmic molecules transfer has been reported less frequently. Interestingly, while there are no reports that the efficiency of transfer of membrane-integrated molecules is dependent on the molecular weight of the transferred components, cytoplasmic molecules have been reported to transfer in a size dependent manner. In addition, there has not been any conclusive demonstration of cytoplasmic protein transfer between cells. Here, we propose a mathematical model describing intercellular transfer of biomolecules via TNTs that explains these observations and makes useful predictions.

The model makes a critical assumption about distinct characteristics of transport of membrane vs. cytosolic components through TNTs. In particular, it is assumed that large cytosolic components, such intracellular proteins, can diffuse over the length of TNT much slower that the membrane components. Thus the rate limiting step in the transfer of the membrane components is the rate of their access to TNTs on the donor cell side, whereas the rate limiting step of the transport of cytoslic components is their diffusion over TNT. As a consequence and due to the transient nature of TNTs, membrane but not cytosolic components would reach a steady state distribution over the length of a TNT, with cytoslic components forming a diffusion based gradient. Since diffusion is dependent on the size of the molecule, and consequently results in a size/mass dependent transfer of cytosolic molecules.

For both the membrane bound and cytosolic molecules, the transfer is limited by the spatial separation between an acceptor cell and the nearest donor cells. Due to the size dependence of the cytosolic molecular transfer, both the amount of the molecule transferred and the maximum separation between the cells that allows for any observable transfer becomes negligible for large proteins. A consequence of the model then is that in most physiological contexts, any signaling happening across cells in this fashion is limited to either membrane bound molecules or small cytosolic molecules. Thus, our model provides a physical basis for the observation of signaling by membrane proteins and small cytosolic molecules.

The model predictions regarding the importance of the length of the TNTs the time scale of TNT lifetimes open new avenues for of the analysis of intercellular communication through individual TNT formations. In addition, it raises the question of whether there could be specific pathways regulating the formation and behavior of such TNTs. For example, it has been reported that HIV induces the formation of TNTs in macrophages (Eugenina et al. 2009). This hypothesis can be tested by modulating the frequency of TNT formation by cells, achievable by chemical and environmental means (Lou et al. 2012). Another hypothesis generated by this model is that increased stability of TNTs could reduce the differential transfer of molecules of different sizes, and this can be tested by modulating TNT stability (Marzo et al. 2012). Recent reports of transfer of endocytotic organelles due to TNTs, which can be controlled by a number of molecular signals (Gurke et al. 2008), suggest a scope for more detailed theoretical models than the one presented here, taking into account the active and modulated TNT formation frequency and dynamics and how they affect the transfer of components in response to specific biological signals. It is plausible that TNT formation may be regulated by cells as response to various stresses or other stimuli, resulting in a controlled selection of the nature, size, and amount of the transferred components and the corresponding phenotypes.

5 Directions for experimental future studies

The model presented here, in the absence of precise values for the multitude of physical parameters involved in the process, makes a number of assumptions in order to provide some qualitative predictions. Careful experimental studies may validate or correct certain aspects of this model. These predictions and assumptions should help to tease out the role the transfer of molecules across TNTs plays physiologically.

We have a simplistic linear relation between the length of TNTs and their abundance in a uniform density of cells (Eq. (1)). Imaging a large number of cells forming TNTs could help to provide us with a better understanding of the dynamic of TNT formation and their static distribution.

Experiments measuring the profusion of cytosolic and membrane bound molecules of differing sizes can shed light on the validity of our models of diffusive transfer of cytosolic molecules and membrane transfer at the tip of the TNTs.

As mentioned earlier, experiments perturbing the frequency and stability of the TNTs provide another avenue for testing the model and at least one possible regulatory mechanism.

Once certain quantitative characteristics of the transfer of these molecules have been verified for some control molecules, any deviation from these transfer rates for physiologically important proteins opens the way for investigating the signaling pathways the cells employ for regulating this intracellular traffic.

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© Society for Mathematical Biology 2013