The authors have declared that no competing interests exist.
Conceived and designed the experiments: MJ PKW. Performed the experiments: MJ. Analyzed the data: JL MJ. Contributed reagents/materials/analysis tools: PKW PD. Wrote the paper: JL MJ PKW JH PD.
In this paper, we present a combined theoretical and experimental study of the propagation of calcium signals in multicellular structures composed of human endothelial cells. We consider multicellular structures composed of a single chain of cells as well as a chain of cells with a side branch, namely a “T” structure. In the experiments, we investigate the result of applying mechano-stimulation to induce signaling in the form of calcium waves along the chain and the effect of single and dual stimulation of the multicellular structure. The experimental results provide evidence of an effect of architecture on the propagation of calcium waves. Simulations based on a model of calcium-induced calcium release and cell-to-cell diffusion through gap junctions shows that the propagation of calcium waves is dependent upon the competition between intracellular calcium regulation and architecture-dependent intercellular diffusion.
Calcium wave signal has been found in a wide variety of cell types. Over the last years, a large number of calcium experiments have shown that calcium signal is not only an intracellular regulator but is also able to be transmitted to surrounding cells as intercellular signal. This paper focuses on the development of an approach with complementary integration of theoretical and experimental methods for studying the multi-level interactions in multicellular architectures and their effect on collective cell dynamic behavior. We describe new types of higher-order (across structure) behaviors arising from lower-order (within cells) phenomena, and make predictions concerning the mechanisms underlying the dynamics of multicellular biological systems. The theoretical approach describes numerically the dynamics of non-linear behavior of calcium-based signaling in model networks of cells. Microengineered, geometrically constrained networks of human umbilical vein endothelial cells (HUVEC) serve as platforms to arbitrate the theoretical predictions in terms of the effect of network topology on the spatiotemporal characteristics of emerging calcium signals.
Multi-level organization and dynamics is a hallmark of most biological systems. This is particularly true in tissues in which single cells are organized into multicellular structures, which are further assembled into complex tissue and organs. For example, endothelial cells are assembled into multicellular tubes (i.e. vessels) which are connected to each other to form a branched vascular tree system. Molecular signals are initiated and/or processed at the endothelial cell level yet influence overall tree behavior and vice-versa
Over the past decade, questions concerning the system behavior of cellular structures have received increasing attention. For instance, there is strong evidence that the branching architecture of the mammary gland is a major regulator of normal epithelial cell signaling and function
A particularly relevant aspect to tissue engineering is the emerging behavior of a multicellular architecture in which cell-level functions, such as intracellular communication, integrate with multicellular architectures through local cell-to-cell interactions. Central to this problem is that cellular networks inherently combine dynamical and structural complexity. Early progress on modeling coupled dynamical systems was limited to space-independent coupling or regular network topologies. Further progress to circumvent the difficulty of modeling associated with the combined complexity of the dynamics and of the architecture was achieved by taking a complementary approach where the dynamics of the network nodes is set aside and the emphasis is placed on the complexity of the network architecture
To evaluate the effects of multilevel architectures on biological signal behavior, we modeled calcium-signal propagation in networks of endothelial cells experimentally and computationally. The vasculature is an ideal system for evaluating multi-scale behavior given the relatively simple but multi-ordered organization of the cells and tissues. Here, the behavior of a calcium wave moving along branched chains of endothelial cells was simulated using experimentally observed parameters in the computation. While there are numerous stimuli that can initiate calcium waves in endothelial cells, we utilized the mechanical stimulation of a single endothelial cell as the wave initiator to minimize confounding issues related to multiple upstream and downstream effects intrinsic to diffusible (i.e. pharmacological) signals. Furthermore, mechanical forces play important roles in endothelial function in vivo
Our study is based on networks of human umbilical vein endothelial cells (HUVEC) (ATCC CRL-1730) in which intercellular calcium wave propagation is primarily dominated by gap junction
The experimental investigation of multicellular calcium ion propagation relies on organizing multiple cells into specific configurations via a surface patterning technique (
(A) Photolithography is used to form a template of the desired multicellular network. (B) PDMS is poured over the photoresist pattern to create an initial plasma shielding model. (C) PDMS mold is transformed onto a Petri Dish (polystyrene). (D) The plasma surface treatment is used to produce cell-sensitive chemical pattern on the area of PDMS mold. (E) Cell seeding. (F) Cell stimulation.
In the current study, mechanical stimulation is used to trigger calcium release from internal stores in single cells (
(A) Force probe stimulation. The direction of stimulation is from above the cells, moving 45° to the tissue culture Petri dish surface. (B) Needle stimulation. The direction of movement is from the side, parallel to the tissue culture Petri dish surface.
Fluro-3AM was loaded into cells as a Ca2+ sensitive dye to visualize the small messenger signaling. Once loaded, esterases cleave the dye so that it cannot leave the cell and will fluoresce in the presence of Ca2+. A Nikon TE2000-U inverted phase contrast and fluorescence microscope equipped with a Cooke SensiCam was used to capture the images. Cells were first plated on patterned surfaces as described above and maintained in standard culture medium. Dye loading was initiated by adding 5 or 10 µl of a 1 mg/ml solution of Fluo-3AM (Invitrogen) dissolved in dimethyl sulfoxide (DMSO), (Fisher) and 5 or 10 µl of a 10 mg/ml solution of Pluronic F-127 (Invitrogen) dissolved in deionized water, to the three milliliters of standard culture medium contained in the patterned dish. The cells were then incubated for 15 minutes at 37°C before being gently rinsed with standard culture medium. New culture medium was added and the cells were incubated for ten minutes at 37°C. Medium was then exchanged and cells were incubated for another ten minutes at 37°C. Finally cells were rinsed with HBSS without calcium or magnesium (Fisher) and the same HBSS was added for imaging, which took place on a microscope stage heated to 37°C. Prior to stimulation, images were captured in phase contrast to visualize cell outlines and during stimulation, illumination was changed to fluorescence with a filter cube providing excitation at 460–500 nm and emission at 510–560 nm. Images were captured every 1.2 seconds and exported for later analysis. For analysis, cells were manually outlined in image sequences and analyzed using Image J, which exported integrated fluorescence versus time values for later analysis. Images and probing were obtained within ∼25 minutes of the final buffer rinse and cells were imaged at passage six or lower.
Whole cell fluorescence intensities as a function of time are obtained by integrating the intensity of every pixel over the area of each cell corrected for the integrated fluorescence of a background area and normalized by the initial intensity. In absence of a one-to-one correspondence between normalized fluorescence intensity and the level of cytosolic calcium concentration, and in light of the cell-to-cell variability in the intensity of the fluorescence, the magnitude of fluorescence is not always taken as a measure of the response of a cell. Irrespective of the magnitude of the fluorescence, a cell is considered to have responded when it exhibits a temporal fluorescence response constituted of an initial fast rising stage followed by a slower decline in fluorescence (see section “Chain Subjected to Single Stimulation: Experiments” for details). The response time of a cell is then determined as the time at which fluorescence reaches its maximum positive rate of change. For weak temporal responses that exhibit significant noise levels, the noise to signal ratio is improved by calculating the running average of the rate of change of the fluorescence. The time average is performed on four time intervals. Response times determined from the running average will therefore be associated with larger uncertainties of 1.2 s.
Since we are interested in the behavior of networks of endothelial cells composed of one-dimensional chains of cells and networks of chains of cells, a reaction/diffusion model is developed to gain insight into the architecture-dependence of calcium wave propagation. For the sake of simplicity, we only consider the dynamic of intracellular calcium and assume the intercellular Ca2+ is transported between cells by diffusion through gap junctions.
he model is based on the one-dimensional time-dependent reaction/diffusion equation:
Intracellular calcium dynamics results from the response of Ca2+ stores, primarily the endoplasmic reticulum (ER), to inositol triphosphate (IP3) and ryanodine through IP3 receptors (IP3R)
UC1 and UC2 are lower and upper thresholds of intracellular calcium concentration, respectively, which determine the value of calcium release/intake rate constant,
In the case of a spatially discrete representation of multicellular chain and considering diffusion between nearest neighbor only,
The term on the left-hand side is the concentration of Ca2+ in cell “
(A) Image of a finite single fine line of cells. Cells are labeled 1 through 9. The stimulating probe is clearly visible on the right of the stimulated cell (cell 4 labeled with a red circle). The time (in sec) at which the normalized fluorescence reaches its maximum positive rate of change is indicated for every cell. The uncertainty for each one of these times is 0.6 s. The origin of time is the time at which fluorescence in the stimulated cell attains its maximum rate of change. (B) and (C) show the normalized intensity of fluorescence of cells 4 through 9 and cells 3 through 1, respectively, as functions of time. The vertical axis is the dimensionless normalized intensity of fluorescence and the horizontal axis is the time in seconds in intervals of 1.2 s between recordings.
We investigate the behavior of several types of multicellular structures, namely single chains of endothelial cells and “T” structures subjected to either single or simultaneous double mechano-stimulation at different locations in the structures.
In this section we consider the behavior of a finite chain of endothelial cells among which a single cell in the chain is subjected to mechanical stimulation to initiate a calcium impulse, due to the intracellular increase in calcium concentration.
The observed shape of the calcium pulse is consistent with that previously reported
The cell chain in the simulation consists of 61 cells aligned in single fine line. To begin the simulation, a pulse is initiated in the middle-most cell of the chain, which is sufficiently far from the edges of the chain to avoid artifacts that could arise from boundary effects. For the ease of comparison with the experimental results, we subsequently label the cells in the chain from 26 through 34 such that the stimulated cell is labeled as cell 4. The initial calcium concentration of all but the stimulated cell is set to zero. The initial calcium concentration of the stimulated cell is
The optimum parameters are reported in
We label the stimulated cell 4 (cell 31 in the chain of 61 cells). We report the response of cells on either side of the stimulated cell as cell 5 through cell 9 and cell 1-through cell 3 to facilitate comparison with experimental results. The real time is obtained by scaling the cell-to-cell propagation time of the simulation to that of the experiment (see text for details).
Symbol | Definition | Value |
C0 | Initial concentration of calcium in stimulated cell | 2.0 |
UC1 | Calcium concentration threshold 1 | 0.3 |
UC2 | Calcium concentration threshold 2 | 3.0 |
|
Calcium release/intake rate for C<UC1 | 0.03 |
|
Calcium release/intake rate for UC1<C<UC2 | −0.025 |
|
Calcium release/intake rate for C>UC2 | 0.0045 |
|
Time interval | 0.01 |
|
Diffusion coefficient | 0.6 |
From the experimental data, the average time for propagation from one cell to the next one is 1.8 s. In the simulation, the dimensionless time for propagation from one cell position to the next one is 0.87. Thus, we obtain a conversion factor from dimensionless to real time,
Propagation is symmetric in the simulation and the response of cells 5 and 3, cells 6 and 2, cells 7 and 1 are the same. There is no variability in the magnitude of the calcium response from cell to cell in the model. The development of a calcium wave that propagates on both sides of the stimulated cell results from the competition between intracellular dynamics and intercellular diffusion. The calcium concentration of the stimulated cell initially exceeding
We now consider the behavior of a chain of cells subjected to dual mechano-stimulation. The stimulations are applied simultaneously on two cells separated by a short distance. In light of an average distance of propagation of a calcium pulse of approximately 4.7 cells, this distance is chosen so that one could expect possible overlap of the signals emanating from the two stimulated cells in the region separating them.
(A) Image of a finite single fine line of cells subjected to dual mechano-stimulation. The stimulating probes are visible at the top-left and bottom-right of the image. The response time of cells labeled in red was calculated from the maximum rate of change of the fluorescence intensity with uncertainties 0.6 s. The response time of cells labeled in green was calculated from a running average of the fluorescence intensity with uncertainties 1.2 s. The first response time for cell 4 (1), represents the time of the first sharp rise in fluorescence versus time. The second response time of cell 4 (2), indicates the time when the fluorescence intensity increases a second time. Cells 4 and 5 represent the region where the calcium pulses are anticipated to meet. (B) and (C) present the normalized intensity of fluorescence of individual cells as a function of time.
The time evolution of the fluorescence intensity of cells 4 and 5 is significantly different from that of the other cells and of signals observed in the case of a single chain with a single stimulation. As stated in section “Imaging”, the determination of the cell response time from signals with weak intensity is conducted on a running average of the rate of change of the intensity.
In
As described in section “Chain Subjected to Single Stimulation: Simulations”, we simulated the behavior of a long chain of cells by modeling a chain with sufficient length to avoid any edge effect during the simulation time when the dual stimulation is applied in its central region, namely cells 1 and 8. All initial calcium concentrations are set to zero except for the stimulated cells, which have an initial calcium concentration exceeding the threshold
Cell 1 and cell 8 are the stimulated cells. We report the response of cells between the stimulated cells as cell 2 through cell 7 to facilitate comparison with experimental results. The real time is obtained by scaling the cell-to-cell propagation time of the simulation to that of the experiment (see text for details).
The response of cell 1 and 8 shows a secondary peak already attributed to the discrete nature of diffusion in our model. If the calcium pulses propagating in the segment between cells 1 to 8 were able to cross one would expect a peak in calcium concentration of cell 1 resulting from the pulse originating at cell 8 at an approximate time of 16 s. The response of cell 1 does not show such a peak. The occurrence of such a peak is not possible since the computational model includes implicitly a refractory stage for CICR. The calcium waves originating from the stimulated cells merge at cells 5 and 4. There, the calcium concentration decays steadily as the rate of calcium dynamics is negative and further response of the cells is prevented. In other words, once the rate of intracellular calcium dynamics,
The growth of “T” structures formed by surface-patterning perpendicular single chains of cells does not permit the formation of cellular junctions composed of a single cell. Typically, many cells aggregate at the junction of the three branches forming a cell cluster (see
(A) Image of a T structure of cells subjected to single mechano-stimulation. The red circle indicates the location of the stimulated cell. Red labels correspond to cells exhibiting strong fluorescence with response time measured from the rate of change of the fluorescence intensity. Green labels correspond to cells exhibiting weak fluorescence and response time derived from running averages of the rate of change of the fluorescence intensity. Black labels are for cells that show very weak (within the noise level) to no fluorescence. (B–E) shows the normalized intensity of fluorescence of branch 1, cluster area, branch 2 and branch 3, respectively, as functions of time. The vertical axis is the dimensionless normalized intensity of fluorescence and the horizontal axis is the time in seconds in intervals of 1.2 s between recordings.
(A) Image of a T structure of cells subjected to single mechano-stimulation. See
In this “T” structure, a single stimulation was applied to one of the branches to determine if the calcium signal can propagate through the junction area and trigger a signal in both of the other branches. We illustrate in
In
To shed light on the experimentally observed behavior of section “T Structure-Single Stimulus: Experimental” we develop a simplified model that mimics the structural characteristics of the experimental “T” network and can capture the effect of multicellular architecture on the competition between intracellular dynamics and intercellular diffusion. The model architecture is illustrated in
(A) Schematic illustration of the model “T” structure subjected to a single stimulus. Red cell is the stimulated cell. Orange arrows represent the edge-to-edge diffusion. Green arrows represent vertex-to-vertex diffusion. Purple cells highlight the junction cell cluster. (B) Calcium concentration of cells in backbone as a function of time. (C) Calcium concentration of cells 1', 2' and cells in the side branch.
The reaction-diffusion equations for cells in the junction area are detailed in the
(A) reports the response of cells 28 to 31 in backbone as a function of time. (B) shows the calcium concentration of cells 30 to 33 in backbone as a function of time. Notice the change of scale of the vertical axis. (C) illustrates the calcium concentration of cells 31, 1' and 2' in the junction area and the side branch as a function of time. Again notice the change of scale of the concentration axis.
Cells in the junction area and the side branch exhibit very low levels of calcium.
In section “Single Chain-Dual Stimulation: Experiments” we have demonstrated that two calcium waves cannot cross when propagating toward each other in a chain of endothelial cells. We consider, here, the dual-stimulation of a “T” structure with stimulations located in two separate branches. We address the question of the interaction of the two calcium pulses in the junction area.
To facilitate comparison between dual and single stimulation, two separate mechano-stimulations are applied on cells close to the junction in order to ensure that calcium waves would propagate well beyond the junction and into the side branches. Two calcium signals were generated from each stimulated cell. They propagate in two opposite directions. For instance, the calcium signal induced in cell 19 propagates upward toward the junction and downward along the chain of cells that constitute branch 1. Two of the pulses, generated from cell 2 and cell 19 respectively, meet in the junction area. The other pulse terminates at the ends of branches 1 and 3 (see
(A) Image of a T structure of cells subjected to double mechano-stimulation. The red circle identifies the stimulated cells. Red labels indicate the response time individual cells. All the cells exhibited strong fluorescence with response times calculated from the rate of change of the fluorescence intensity. Black labels show cells exhibiting only noise level fluorescence. (B–E) show the normalized intensity of fluorescence of branch 1, cluster area, branch 2 and branch 3, respectively, as functions of time. The vertical axis is the dimensionless normalized intensity of fluorescence and the horizontal axis is the time in seconds in intervals of 1.2 s between recordings.
(A) Schematic representation of “T” structure of cells subjected to dual stimulation. Red cells are the stimulated cells. See
We consider the case of
In this paper, we study experimentally the propagation of calcium waves in different multicellular structures composed of human umbilical vein endothelial cells (HUVEC). The fabrication of cell-chain based multicellular chain structures relies on organizing multiple cells into specific configurations via selective plasma surface functionalization, which guides cellular attachment. Calcium waves are actuated via mechano-stimulation of selected cells. Calcium wave propagation is characterized by time-resolved fluorescence microscopy. The experimental observations are complemented by modeling and simulation of calcium wave propagation using a diffusion/reaction model. The model of intracellular calcium dynamics is non-linear and mimics the IP3-induced calcium release and calcium induced calcium release (CICR). In order to capture the essence of cross-level interactions in calcium signal propagation in multicellular architectures, we only consider a single component model of CICR. This model is different from previous CICR models, which consisted of multiple coupled non-linear differential equations describing the kinetics of IP3/Ca2+ pumping, release and activation
Cell-to-cell interactions are described in this paper via intercellular diffusion through gap junctions. Experimental observation of calcium waves induced by a single mechano-stimulation and propagating along a chain of endothelial cells is used to calibrate the model. Experiments and simulations of chains of cells subjected to dual stimulation (i.e. simultaneous stimulation of two different cells) show that two calcium waves cannot cross each other due to the refractory stage of endothelial cells. The study of more complex multicellular structures utilized “T” structures, which are composed of three side branches joining at a junction. The junction is comprised of cell clusters. In this case, we observe experimentally that when a single cell in one of the side braches is stimulated, the calcium signal does not propagate beyond the junction area. However, when two mechano-stimulations are simultaneously applied on separate branches the calcium signal can propagate through the junction area and beyond well into the third unstimulated side branch of the “T” structure. A computational model of a “T” structure, which includes a cell cluster at the junction, shows the importance of intracellular calcium dynamics and intercellular diffusion in determining the propagation behavior of calcium waves. In particular, the organization of cells in the junction determines the existence of multiple paths for intercellular diffusion, which may affect the accumulation of cytosolic calcium and subsequently the ability of cells to undergo CICR.
In summary, this work demonstrates that the propagation of calcium waves is dependent upon the architecture of multicellular structures. This dependence is due to the competition between intracellular calcium reaction and diffusion, which is affected by the topology through cell connectivity via gap junctions.
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