In response to an increased concentration of inositol trisphosphate
|
|
- Ada Walker
- 5 years ago
- Views:
Transcription
1 Control of calcium oscillations by membrane fluxes J. Sneyd*, K. Tsaneva-Atanasova*, D. I. Yule, J. L. Thompson, and T. J. Shuttleworth *Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand; and Department of Pharmacology and Physiology, University of Rochester Medical Center, Rochester, NY Edited by Charles S. Peskin, New York University, New York, NY, and approved November 25, 2003 (received for review June 8, 2003) It is known that Ca 2 influx plays an important role in the modulation of inositol trisphosphate-generated Ca 2 oscillations, but controversy over the mechanisms underlying these effects exists. In addition, the effects of blocking membrane transport or reducing Ca 2 entry vary from one cell type to another; in some cell types oscillations persist in the absence of Ca 2 entry (although their frequency is affected), whereas in other cell types oscillations depend on Ca 2 entry. We present theoretical and experimental evidence that membrane transport can control oscillations by controlling the total amount of Ca 2 in the cell (the Ca 2 load). Our model predicts that the cell can be balanced at a point where small changes in the Ca 2 load can move the cell into or out of oscillatory regions, resulting in the appearance or disappearance of oscillations. Our theoretical predictions are verified by experimental results from HEK293 cells. We predict that the role of Ca 2 influx during an oscillation is to replenish the Ca 2 load of the cell. Despite this prediction, even during the peak of an oscillation the cell or the endoplasmic reticulum may not be measurably depleted of Ca 2. In response to an increased concentration of inositol trisphosphate (IP 3 ), oscillations in the concentration of free intracellular calcium (Ca 2 ) occur in many cell types and are important for the control of many cellular functions (1 4). In nonexcitable cells, such as epithelial cells, these oscillations occur as the result of Ca 2 flux into and out of the endoplasmic reticulum (ER). However, although the oscillations result from the cycling of Ca 2 between the ER and the cytoplasm, the transport of Ca 2 across the cell membrane can have a dramatic effect on these oscillations. Although Ca 2 influx is known to be important, disagreement exists, first, over the mechanisms by which Ca 2 influx is modulated during a Ca 2 oscillation, and, second, over the role played by Ca 2 influx. The capacitative entry hypothesis proposes that depletion of ER Ca 2 causes enhanced entry of Ca 2 across the plasma membrane (5 9). Often, although not necessarily, in this scenario, Ca 2 entry is necessary for the refilling of the ER, and thus oscillation frequency is controlled by the refilling time (10, 11). Although capacitative entry is certainly an important factor during the response to a maximal stimulus, other investigators have pointed to a lack of direct evidence that it plays an important role during smaller stimuli that generate oscillatory behavior (12). They maintain that Ca 2 influx, under these conditions, is controlled by a noncapacitative pathway involving arachidonic acid and that the purpose of the influx is to increase the likelihood that low levels of IP 3 will induce Ca 2 release from internal stores (13). This controversy is complicated by the fact that, in some cell types, Ca 2 oscillations persist in the absence of Ca 2 influx (14 16), whereas in other cell types, oscillations depend absolutely on influx (17, 18). Even in a single cell type, the effect of Ca 2 influx on agonist-induced oscillations varies according to the agonist (19), and the effect of removal of extracellular Ca 2 depends on when it is removed (17). Using a combination of theoretical and experimental work, we attempt to resolve this controversy by studying how Ca 2 transport across the cell membrane can affect ER-based oscillations. We conclude that small changes in Ca 2 load can have a large impact on Ca 2 oscillations. By Ca 2 load we mean the total amount of Ca 2 in the cell, including the ER, the cytoplasm, and the Ca 2 buffers. (For the purposes of the model here, we neglect mitochondrial Ca 2, but its inclusion would have no qualitative effect on our results.) The amount of Ca 2 in the ER is directly related to the Ca 2 load, and thus our model predicts that Ca 2 oscillations will also be highly sensitive to ER Ca 2 concentration. Our results are independent of the mechanism by which Ca 2 influx is controlled and thus cannot be used to distinguish between capacitative entry or noncapacitative, arachidonic aciddependent entry, but they provide a way in which seemingly contradictory experimental results can be understood. In addition, they show that direct control of Ca 2 influx by the cytosolic or ER Ca 2 concentration is not necessary for Ca 2 influx to play a crucial role in the control of oscillations. Finally, our results do not depend on the precise details of the model, but they occur in at least four different models of Ca 2 oscillations. The Model Our model for Ca 2 oscillations is based on a dynamic model of the IP 3 receptor (IPR) (20) and assumes that oscillations in [IP 3 ] are not necessary for the generation of Ca 2 oscillations. A schematic diagram of the cell is given in Fig. 1. From there we see that the conservation equations for Ca 2 are dc dt J IPR J serca J in J pm, [1] dc e dt J serca J IPR, [2] where c and c e denote [Ca 2 ] in the cytoplasm and ER, respectively, is the cytoplasmic-to-er volume ratio, and is a dimensionless parameter that controls the relative magnitudes of membrane and ER fluxes without changing the steady-state concentrations. Calcium release through the IPR is described by the model of ref. 20, slightly modified for the context of a whole-cell model. Thus, J IPR k f 0.1O 0.9A 4 g 1 c e c, [3] where g 1 models a constant background leak from the ER at zero [IP 3 ].Oand A denote the probability the IPR is in the open and activated state, respectively, and are governed by differential equations with parameters determined by fitting to experimental data from the type II hepatocyte IPR (21). Calcium pumping into the ER (J serca ) and extrusion across the plasma membrane (J pm ) are modeled by J serca V sc K s c 1 J c pm V pc 2 e, K 2 p c 2. [4] This paper was submitted directly (Track II) to the PNAS office. Abbreviations: IP 3, inositol (1,4,5)-trisphosphate; IPR, IP 3 receptor; ER, endoplasmic reticulum; HC, homoclinic bifurcation; SNP, saddle node of periodics bifurcation; CCh, carbamylcholine. To whom correspondence should be addressed. sneyd@math.auckland.ac.nz by The National Academy of Sciences of the USA PNAS February 3, 2004 vol. 101 no. 5 cgi doi pnas
2 Fig. 1. Schematic diagram of the model fluxes. These expressions are the ones used by ref. 22 and are discussed in detail there. Ca 2 entry is modeled as a linear, increasing function of [IP 3 ](p), and thus J in 1 2 p, [5] where 1 and 2 are constants. This form for J in is entirely arbitrary; we know that J in must be an increasing function of p but do not know the exact relationship. Thus, we just choose the simplest possible form. Using a more complex function for J in makes no qualitative difference to the model results. Buffering is taken into account by assuming each flux to be an effective flux, scaled by the effects of fast linear buffers. Inclusion of slower nonlinear buffers will not alter the qualitative results of our analysis. The parameter values are given in the legend to Fig. 2. Analysis of the Model Introduction of the new variable, c t c (1 )c e gives the system Fig. 2. Blue lines are the bifurcation diagram of the closed-cell model with c t as the bifurcation parameter. Parameter values of the IPR model are taken from ref. 20. Other parameter values (adapted from ref. 22) are 5.4, k f 0.96 s 1, g s 1, V s 120 M 2 s 1, K s 0.18 M, V p 28 M s 1, K p 0.42 M, M s 1, and s 1. The dotted red line is a solution of the open-cell model superimposed on the bifurcation diagram of the closed-cell model and calculated by using p 10 and ss, steady states; max osc, maximum of the oscillation. dc t dt J in J pm, [6] dc dt J IPR J serca J in J pm. [7] The new variable c t is the total number of moles of Ca 2 in the cell divided by the cytoplasmic volume. We shall call c t the Ca 2 load of the cell. When is small, c t can change only slowly, and in the limit, as 3 0, the cell becomes closed, i.e., when 0 no Ca 2 exchange occurs with the external medium. We study the model by treating c t as a bifurcation parameter and analyzing the model s behavior for a range of fixed values of c t, a procedure that was used by refs (for a general introduction, see ref. 26) in a classic study of bursting oscillations, and by refs. 27 and 28 in the context of Ca 2 oscillations in neurosecretory cells. If c t is constant, we replace c e by (c t c) and consider just Eq. 1. We call this the closed-cell model. The bifurcation diagram is given in Fig. 2 (blue curve). Stable oscillations exist only for an intermediate range of values of c t between the homoclinic (HC) and saddle node of periodics (SNP) bifurcations. In other words, when Ca 2 transport across the plasma membrane is blocked, oscillations can occur only if neither too much nor too little Ca 2 is inside the cell. When c t is allowed to vary, we obtain the open-cell model. A typical solution (drawn in the c, c t phase plane and superimposed on the closed-cell bifurcation diagram) is sketched in Fig. 2 (red dotted curve). Suppose that, when p 0 and 0.01, c t 12 at rest (see IPR open.ode, which is published as supporting information on the PNAS web site). Raising p to 10 will cause immediate Ca 2 oscillations, with a gradually decreasing baseline as c t decreases (Fig. 2, red dotted line). These oscillations are pseudosteady; the solution is trying to follow the oscillatory solutions of the closed-cell model, but cannot exactly, because is nonzero. Once c t gets low enough, the oscillations change their character. During the interspike intervals, the solution approximately follows the lower stable steady state. (As 3 0 the solution follows the lower stable steady state more closely. The agreement in Fig. 2 is not exact, but it is the general trend we are considering here.) Because the lower steady state is below the line where dc t dt 0, c t is increasing there. Once the solution reaches the limit point (the bend) it can no longer follow this branch, and falls off, moving toward the long period limit cycle close to the HC orbit. However, once on the other side of the dc t dt 0 line, c t starts to decrease, the solution returns to the lower stable steady state, and the cycle repeats. Thus, in response to an increase in [IP 3 ], the model cell exhibits transient pseudosteady oscillations that tend to a stable steady-state limit cycle, in which the oscillation is a degenerate bursting oscillation having only a single peak during each bursting phase. This slow modulation of the oscillations is caused by a gradual decrease in c t, and so the speed with which the model reaches the steady-state oscillation is governed by the value of, which controls the speed at which c t reaches a steady-state limit cycle. If an open cell exhibits Ca 2 oscillations, how will these oscillations be affected if membrane transport is stopped? This is most easily studied with the bifurcation diagram shown in Fig. 3. The loci of HC and SNP bifurcations as p and c t vary in the closed-cell model are shown by the red curves. Thus, for each value of p, the closed-cell model will exhibit oscillations only when c t lies between these two curves. Superimposed on this we plot bifurcation diagrams of the open-cell model (broken curves), plotting the maximum and minimum of c t over an oscillation as a function of p. For each value of p where steady oscillations exist in the open-cell model, c t moves between the appropriate broken curves. (For instance, when 0.1, the APPLIED MATHEMATICS PHYSIOLOGY Sneyd et al. PNAS February 3, 2004 vol. 101 no
3 Fig. 4. Two-parameter bifurcation diagram of the open-cell model. The lines (for three different values of ) divide the 1 p plane into regions for which oscillations do or do not exist. Fig. 3. The broken lines are the maximum (max) and minimum (min) of oscillations in the open-cell model for different values of. The curves labeled HC and SNP are two-parameter continuations of the points labeled HC and SNP in Fig. 2. Thus, for each value of, oscillations exist in the closed-cell model only for values of c t between the HC and SNP curves. broken curves are labeled max and min, and denote, respectively, the maximum and minimum values of c t over an oscillation.) It follows that oscillations can occur in both the closed-cell and open-cell models only when the broken curves lie between the solid curves. Consider the behavior at p 1 and If the open-cell model is allowed to reach its steady-state oscillation, c t will be moving between the blue short-dashed curves (over the point labeled A). If is now reduced to zero, i.e., membrane transport is shut off, c t will now be held constant at point A and will not lie between the HC and SNP curves. Hence, the closed-cell model cannot oscillate and the oscillations stop. To restore the oscillations, c t could be increased until it crosses the HC curve (point B). Alternatively, oscillations can be restored by increasing p (point C). When p 40 and 0.01, we see that stable oscillations coexist in both the open-cell and closed-cell model, but for only a relatively small region (region D). If p and c t are such that the cell sits in region D, blockage of membrane transport will not eliminate Ca 2 oscillations. When 0.001, i.e., when membrane transport in the open-cell model is very slow, the open-cell bifurcation curves (the broken lines) begin to superimpose on the HC curve of the closed-cell model, thus showing how, in the limit as 3 0, the open-cell oscillations get progressively restricted to planes of constant c t. In addition, the p interval for which stable-steady oscillations coexist in the open-cell and the closed-cell models gets wider (region E). From Fig. 2 we see that, immediately after an increase in [IP 3 ], the open-cell model exhibits oscillations with a gradually decreasing baseline and with a decreasing average c t. This finding suggests that the effects of blocking membrane transport will depend on the timing of the block. If the block occurs soon after, or before, the increase in [IP 3 ], oscillations can continue because c t has not yet fallen far enough to make oscillations impossible. However, if the block occurs later, after c t has decreased past HC, then the block will be expected to eliminate oscillations. Influx of Ca 2 from outside the cell is known to affect the frequency of Ca 2 oscillations and waves. We investigate this in the open-cell model by varying the background rate of Ca 2 influx, 1. In Fig. 4 we plot lines in the 1 p plane that separate regions where Ca 2 oscillations occur from regions where they do not. For a fixed p, an increase in Ca 2 influx will lead to oscillations or to a decrease in the oscillation period. Similarly, for a fixed 1, an increase in p will have the same effect. This occurs even when membrane transport is slow ( 0.001). Oscillations can be eliminated by a decrease in influx but can then be restored by increasing p. Physiological Interpretation of the Analysis A model cell can fire a Ca 2 spike only if its Ca 2 load (c t )is above threshold. This is because enough cytosolic Ca 2 must be present to activate the IP 3 receptor, and enough ER Ca 2 must be available to provide sufficient driving force for efflux from the ER. Once c t drops below threshold, these conditions are violated and the cell cannot fire a Ca 2 spike. At rest, the model cell has a high resting Ca 2 load (c t ). On agonist stimulation, the rise in cytosolic Ca 2 causes a net loss of Ca 2 from the cell (as it is removed by the plasma membrane pumps), even though the influx of Ca 2 has been increased. Thus, c t gradually declines, resulting in oscillations with a gradually decreasing baseline. If membrane transport is blocked during this phase of the response, c t is still high enough to maintain oscillations, which would then occur purely by recycling Ca 2 to and from the ER. Eventually, c t declines to a new steady-state average level. Now, at the peak of each oscillation, the high cytosolic concentration causes a net loss of Ca 2 from the cell. The Ca 2 load thus drops below threshold, and the cell cannot fire another spike until this Ca 2 loss is restored by Ca 2 influx. Because each oscillation involves the loss and reuptake of Ca 2 from the cell (possibly only a small amount), these oscillations depend on Ca 2 influx and will be eliminated by blockage of membrane transport. An increase in Ca 2 influx will increase oscillation frequency, as it increases the rate at which the Ca 2 lost during each spike is regained. In addition, an increase in Ca 2 influx will increase the average steady-state Ca 2 load, which will also increase oscillation frequency, even when the oscillations are not dependent on Ca 2 influx. A decrease in Ca 2 influx can eliminate oscillations, which can then be restored by an increase in [IP 3 ]. When membrane transport is slow enough, Ca 2 oscillations can persist in the absence of membrane transport, although their frequency is affected by Ca 2 influx. A closed cell needs a higher Ca 2 load to support an oscillation than does an open cell. In the closed cell, because the Ca 2 load is constant, oscillations are possible only if the Ca 2 load is cgi doi pnas Sneyd et al.
4 always over threshold. In the open cell this constraint is relaxed. For a large part of the oscillatory cycle, the Ca 2 load can be below threshold. It is only when Ca 2 influx from the outside drives the Ca 2 load over threshold that a spike occurs. Some of the Ca 2 released from the ER is then pumped out of the cell, the Ca 2 load drops below threshold, and the cycle repeats. Thus, when averaged over one cycle, the Ca 2 load is lower for the open cell than for the closed cell. For open-cell oscillations, Ca 2 influx serves to increase the Ca 2 load to a level where another oscillation can occur, and an increase in Ca 2 influx increases the oscillation frequency. However, although it is cell refilling that is governing the oscillation period, the amount of Ca 2 actually lost from the cell during each oscillation can be small and not easily detectable. From our analysis we predict the following: Prediction 1. Blocking membrane transport can eliminate Ca 2 oscillations. An increase in the Ca 2 load of the cell will restore oscillations that have been eliminated by the block. Prediction 2. The effects of blocking membrane transport will depend on the timing of the block. If the block occurs soon after, or before, the increase of [IP 3 ], it will not eliminate oscillations, whereas if it occurs after the cell has reached a steady-state oscillation, it will eliminate the oscillations. Experimental Verification We tested our predictions experimentally in the following way. HEK293 cells were stably transfected with the m3 human muscarinic receptor and loaded with fluo-4. They were imaged on a TILL Photonics system with a monochromator (TILL Photonics, Planegg, Germany) and a progressive line-scan digital camera (Imago, Scientific Instruments, Madison, WI). The cells were stimulated with 0.5 M carbamylcholine (CCh) to induce Ca 2 oscillations, then 1 mm La 3 was added to block both Ca 2 entry and the plasma membrane Ca 2 pump (29 33). Fig. 5 shows the effects of the addition of La 3 at two different times: after steady oscillations had appeared (Upper) and immediately before the addition of CCh (Lower). As predicted, oscillations were eliminated in the first case but not in the second (20 cells in four separate experiments). In the first case, the effect of La 3 was reversible. This result is similar to previous results showing that removal of extracellular Ca 2 before application of CCh to pancreatic acinar cells did not prevent oscillations, whereas removal of extracellular Ca 2 from a cell exhibiting Ca 2 oscillations terminated oscillations (17). In a second set of experiments, the cells were also loaded with caged Ca 2. Then, after the addition of La 3, intracellular Ca 2 was increased by uncaging the Ca 2 with the strobe mode on the TILL flash unit. This mode releases Ca 2 by brief low-energy flashes of UV light at 12 Hz. This strobing typically lasted for min (Fig. 6). Then the La 3 was washed out, still in the presence of 0.5 M CCh. A typical result (from seven cells in three separate experiments) is shown in Fig. 6. On addition of CCh, the cell exhibited Ca 2 oscillations, which terminated on blockage of membrane transport, even though the Ca 2 load of the cell remained unchanged by the addition of La 3. Thus, it is not the Ca 2 load alone that is controlling the oscillations, it is the combination of the Ca 2 load and the transport across the plasma membrane. An increase in c t by the strobe then leads to the resumption of Ca 2 oscillations, which persist even when the strobe is turned off. Thus, once c t is increased sufficiently, Ca 2 oscillations persist even in the absence of membrane transport, as predicted by the model. When membrane transport is restored by the removal of La 3, the oscillations continue. Application of the strobe in the absence of CCh, but the presence of La 3, resulted in a small increase in resting [Ca 2 ] (Fig. 6, red line). On removal of the strobe, [Ca 2 ] remained Fig. 5. Addition of La 3 to HEK293 cells after addition of CCh eliminates oscillations (Upper), whereas addition of La 3 before CCh does not prevent oscillations (Lower). unchanged, because the La 3 prevented it from leaving the cell; on removal of the La 3, [Ca 2 ] returned to baseline. Application of the strobe in the absence of caged Ca 2 has no effect on oscillations (34). Discussion Our results suggest that membrane transport of Ca 2 controls oscillations by controlling the Ca 2 load of the cell. It is already well known that Ca 2 influx affects oscillation frequency in many cell types (10, 13, 35 37). In Xenopus oocytes, which have a very small surface-to-volume ratio and thus a small, Ca 2 oscillations persist in the absence of external Ca 2, as found in the Fig. 6. Addition of CCh initiates oscillations that terminate on addition of La 3. Increasing c t by strobed photorelease of cytosolic Ca 2 restores oscillations even during continued blockage of membrane transport (blue lines). This is equivalent to moving from point A to point B in Fig. 3. The red lines show the effect of the strobe in the presence of La 3 alone (done in a separate experiment, but plotted here on the same graph for ease of comparison). Note how, when the strobe is removed, [Ca 2 ] does not decline until the La 3 is removed. APPLIED MATHEMATICS PHYSIOLOGY Sneyd et al. PNAS February 3, 2004 vol. 101 no
5 model. Nevertheless, an increase in Ca 2 influx increases oscillation frequency and wave speed (16, 35). In pancreatic acinar cells application of acetylcholine gives rise to Ca 2 oscillations, which disappear on reduction of external Ca 2. However, these oscillations reappear when the concentration of acetylcholine is increased (38), as expected from the results in Fig. 4. The effects of Ca 2 load on oscillations and waves have also been well characterized in cardiac cells (39 41). Our model is also consistent with the results of ref. 42, which showed that blockage of Ca 2 influx during the interspike period eliminated further spikes, whereas, if the block occurred during a spike, the spike occurred as usual. According to our model, this is because only a small amount of Ca 2 influx during the interspike period is needed to push the Ca 2 load of the cell over threshold, whereas the majority of the Ca 2 in a spike is released from the ER. We have shown that it is not the Ca 2 load per se that is the controlling factor, but it is rather the interplay between Ca 2 load and membrane transport. In HEK293 cells, addition of CCh stimulates Ca 2 oscillations with a gradually decreasing baseline (Fig. 6). If membrane transport is then blocked, the oscillations terminate, even though the cell s Ca 2 load remains unchanged. A subsequent increase in the Ca 2 load restores oscillations (Fig. 6), even though membrane transport of Ca 2 still does not occur. Furthermore, the effects of blocking membrane transport depend on the timing of the block. If the block occurs while the Ca 2 load is high, i.e., before application of agonist, an increase in [IP 3 ] will cause oscillations, whereas if the block occurs later, after the Ca 2 load has declined, agonist-induced oscillations will be eliminated (Fig. 5). Thus, our model can also explain previous puzzling results of ref. 17, which showed that removal of extracellular Ca 2 before the application of CCh did not eliminate oscillations, whereas, if Ca 2 oscillations had already developed, they were eliminated by the removal of extracellular Ca 2. That small changes in Ca 2 load can have large effects on oscillations suggests a possible resolution of the controversy over the role of Ca 2 entry. Since experimental data have been unable to show conclusively that the ER is significantly depleted during an oscillation (43), it has been argued that ER depletion, and hence capacitative Ca 2 entry, does not play a significant role (12). In contrast, our model shows that cell depletion (i.e., a decrease in cytosolic and ER Ca 2 ) can play a crucial role, even when depletion is so small as to be unmeasurable. Our analysis also provides a consistent framework for understanding why removal of extracellular Ca 2 has such different effects, depending on the cell type, and it can explain why the timing of removal is so important (17, 42). The same qualitative behavior occurs in at least three other models of Ca 2 oscillations: the Li Rinzel model (44), and modified versions of the Atri model (45) and the LeBeau model (38) (computations not shown), all of which have different models for the IP 3 receptor and Ca 2 pumps. This finding suggests that our predictions do not depend on the precise model details, but they are instead a generic feature of models that have the structure shown in Fig. 1. We hypothesize that every model to follow this basic structure will exhibit the same behavior, no matter what the exact details are of the various pumps and release processes. We thank Robert T. Dirksen and Vivien Kirk for helpful discussions. J.S. and K.T.-A. were supported by the Marsden Fund of the Royal Society of New Zealand. D.I.Y. was supported by National Institutes of Health Grants DE14756 and DK T.J.S. was supported by National Institutes of Health Grant GM Sanderson, M. J., Charles, A. C., Boitano, S. & Dirksen, E. R. (1994) Mol. Cell. Endocrinol. 98, Clapham, D. (1995) Cell 80, Thomas, A. P., Bird, G. S. J., Hajnóczky, G., Robb-Gaspers, L. D. & Putney, J. W. J. (1996) FASEB J. 10, Berridge, M. J. (1997) J. Physiol. 499, Putney, J. W., Jr. (1990) Cell Calcium 11, Putney, J. W., Jr., Broad, L. M., Braun, F. J., Lievremont, J. P. & Bird, G. S. (2001) J. Cell Sci. 114, Hoth, M. & Penner, R. (1992) Nature 355, Hoth, M. & Penner, R. (1993) J. Physiol. 465, Berridge M. J. (1995) Biochem. J. 312, Kawanishi T., Blank, L. M., Harootunian, A. T., Smith, M. T. & Tsien, R. Y. (1989) J. Biol. Chem. 264, Berridge, M. J. (1993) Nature 361, Shuttleworth, T. J. (1999) Cell Calcium 25, Shuttleworth, T. J. & Thompson, J. L. (1996) Biochem. J. 313, Rooney, T. A., Sass, E. J. & Thomas, A. P. (1989) J. Biol. Chem. 264, Lechleiter, J. D. & Clapham, D. E. (1992) Cell 69, Girard, S. & Clapham, D. (1993) Science 260, Yule, D. I. & Gallacher, D. V. (1988) FEBS Lett. 239, Martin, S. C. & Shuttleworth, T. J. (1994) FEBS Lett. 352, Yule, D. I., Lawrie, A. M. & Gallacher, D. V. (1991) Cell Calcium 12, Sneyd, J. & Dufour, J. F. (2002) Proc. Natl. Acad. Sci. USA 99, Dufour, J.-F., Arias, I. M. & Turner, T. J. (1997) J. Biol. Chem. 272, Sneyd, J., Tsaneva-Atanasova, K., Bruce, J. I., Straub, S. V., Giovannucci, D. R. & Yule, D. I. (2003) Biophys. J. 85, Rinzel, J. (1985) in Ordinary and Partial Differential Equations, eds. Sleeman, B. D. & Jarvis, R. J. (Springer, New York). 24. Rinzel, J. & Lee, Y. S. (1986) in Nonlinear Oscillations in Biology and Chemistry. Lecture Notes in Biomathematics, ed. Othmer, H. G. (Springer, New York), Vol Rinzel, J. (1987) in Mathematical Topics in Population Biology, Morphogenesis, and Neurosciences. Lecture Notes in Biomathematics, eds. Teramoto, E. & Yamaguti, M. (Springer, Berlin), Vol Keener, J. P. & Sneyd, J. (1998) Mathematical Physiology (Springer, New York). 27. Li,Y.-X., Stojilković, S. S., Keizer, J. & Rinzel, J. (1997) Biophys. J. 72, Sherman A. S., Li, Y.-X. & Keizer, J. E. (2002) in Computational Cell Biology, eds. Fall, C. P., Marland, E. S., Wagner, J. M. & Tyson, J. J. (Springer, New York). 29. Pandol, S. J., Schoeffield, M. S., Fimmel, C. J. & Muallem, S. (1987) J. Biol. Chem. 262, Kwan, C. Y., Takemura, H., Obie, J. F., Thastrup, O. & Putney, J. W., Jr. (1990) Am. J. Physiol. 258, C1006 C Shimizu, H., Borin, M. L. & Blaustein, M. P. (1997) Cell Calcium 21, Herscher, C. J. & Rega, A. F. (1997) Ann. N. Y. Acad. Sci. 834, Mignen, O. & Shuttleworth, T. J. (2000) J. Biol. Chem. 275, Wagner L. E., II, Li, W. H. & Yule, D. I. (2003) J. Biol. Chem., / jbc.m Yao, Y. & Parker, I. (1994) J. Physiol. 476, Bootman, M. D., Young, K. W., Young, J. M., Moreton, R. B. & Berridge, M. J. (1996) Biochem. J. 314, Liu X., Liao, D. & Ambudkar, I. S. (2001) J. Membr. Biol. 181, LeBeau, A. P., Yule, D. I., Groblewski, G. E. & Sneyd, J. (1999) J. Gen. Physiol. 113, Cheng, H., Lederer, M. R., Lederer, W. J. & Cannell, M. B. (1996) Am. J. Physiol. 270, C148 C Satoh, H., Blatter, L. A. & Bers, D. M. (1997) Am. J. Physiol. 272, H657 H Bers, D. M., Li, L., Satoh, H. & McCall, E. (1998) Ann. N.Y. Acad. Sci. 853, Thorn, P. (1995) J. Physiol. 482, Park, M. K., Petersen, O. H. & Tepikin, A. V. (2000) EMBO J. 19, Li, Y.-X. & Rinzel, J. (1994) J. Theor. Biol. 166, Atri, A., Amundson, J., Clapham, D. & Sneyd, J. (1993) Biophys. J. 65, cgi doi pnas Sneyd et al.
Oscillations and waves in the concentration of free intracellular
A dynamic model of the type-2 inositol trisphosphate receptor James Sneyd* and Jean-François Dufour *Institute of Information and Mathematical Sciences Massey University Albany Campus Private Bag 102-904
More informationAn Application of Reverse Quasi Steady State Approximation
IOSR Journal of Mathematics (IOSR-JM) ISSN: 78-578. Volume 4, Issue (Nov. - Dec. ), PP 37-43 An Application of Reverse Quasi Steady State Approximation over SCA Prashant Dwivedi Department of Mathematics,
More informationCalcium Oscillations in a Triplet of Pancreatic Acinar Cells
Biophysical Journal Volume 88 March 2005 1535 1551 1535 Calcium Oscillations in a Triplet of Pancreatic Acinar Cells K. Tsaneva-Atanasova,* D. I. Yule, y and J. Sneyd z *Department of Mathematics, University
More informationModelling the transition from simple to complex Ca 2+ oscillations in pancreatic acinar cells
Modelling the transition from simple to complex Ca 2+ oscillations in pancreatic acinar cells NEERAJ MANHAS 1, *, JAMES SNEYD 2 and KR PARDASANI 1 1 Department of Mathematics, Maulana Azad National Institute
More informationCalcium dynamics, 7. Calcium pumps. Well mixed concentrations
Calcium dynamics, 7 Calcium is an important ion in the biochemistry of cells Is used a signal carrier, i.e. causes contraction of muscle cells Is toxic at high levels The concentration is regulated through
More informationIntroduction to Physiology IV - Calcium Dynamics
Introduction to Physiology IV - Calcium Dynamics J. P. Keener Mathematics Department Introduction to Physiology IV - Calcium Dynamics p.1/26 Introduction Previous lectures emphasized the role of sodium
More informationMathematical Analysis of Bursting Electrical Activity in Nerve and Endocrine Cells
Mathematical Analysis of Bursting Electrical Activity in Nerve and Endocrine Cells Richard Bertram Department of Mathematics and Programs in Neuroscience and Molecular Biophysics Florida State University
More information26 Robustness in a model for calcium signal transduction dynamics
26 Robustness in a model for calcium signal transduction dynamics U. Kummer 1,G.Baier 2 and L.F. Olsen 3 1 European Media Laboratory, Villa Bosch, Schloss-Wolfsbrunnenweg 33, 69118 Heidelberg, Germany
More informationStochastic effects in intercellular calcium spiking in hepatocytes
Stochastic effects in intercellular calcium spiking in hepatocytes M. E. Gracheva, R. Toral, J. D. Gunton Department of Physics, Lehigh University, Bethlehem, PA 805 Instituto Mediterraneo de Estudios
More informationFinite Volume Model to Study Calcium Diffusion in Neuron Involving J RYR, J SERCA and J LEAK
JOURNAL OF COMPUTING, VOLUME 3, ISSUE 11, NOVEMB 011, ISSN 151-9617 WWW.JOURNALOFCOMPUTING.ORG 41 Finite Volume Model to Study lcium Diffusion in Neuron Involving J RYR, J SCA and J LEAK Amrita Tripathi
More informationA Mathematical Study of Electrical Bursting in Pituitary Cells
A Mathematical Study of Electrical Bursting in Pituitary Cells Richard Bertram Department of Mathematics and Programs in Neuroscience and Molecular Biophysics Florida State University Collaborators on
More informationTHE ROLE OF IP3R CLUSTERING IN Ca 2 + SIGNALING
THE ROLE OF IP3R CLUSTERING IN Ca 2 + SIGNALING ALEXANDER SKUPIN alexander.skupinbmi.de MARTIN FALCKE falckebmi. de Max-Delbriick-Center for Molecular Medince, Departement of Mathematical Cell Physiology,
More informationHysteresis and bistability in a realistic model for IP 3 -driven Ca 2+ oscillations
EUROPHYSICS LETTERS 1 September 2001 Europhys. Lett., 55 (5), pp. 746 752 (2001) Hysteresis and bistability in a realistic model for IP -driven Ca 2+ oscillations J. J. Torres 1 ( ),P.H.G.M.Willems 2,
More informationdynamic processes in cells (a systems approach to biology)
dynamic processes in cells (a systems approach to biology) jeremy gunawardena department of systems biology harvard medical school lecture 12 11 october 2016 = vasopressin CCh = carbachol GnRH = gonadotropin
More informationA spatial Monte Carlo model of IP 3 -dependent calcium. oscillations. Evan Molinelli. Advisor: Gregry D. Smith. Department of Applied Science
A spatial Monte Carlo model of IP 3 -dependent calcium oscillations Evan Molinelli Advisor: Gregry D. Smith Department of Applied Science The College of William and Mary Williamsburg, VA 23187 4/14/06
More informationCalcium Domains around Single and Clustered IP 3 Receptors and Their Modulation by Buffers
Biophysical Journal Volume 99 July 200 3 2 3 Calcium Domains around Single and Clustered IP 3 Receptors and Their Modulation by Buffers S. Rüdiger, Ch. Nagaiah, G. Warnecke, and J. W. Shuai { * Institute
More informationWave bifurcation and propagation failure in a model of Ca2+ release
Loughborough University Institutional Repository Wave bifurcation and propagation failure in a model of Ca2+ release This item was submitted to Loughborough University's Institutional Repository by the/an
More informationComputational Cell Biology
Computational Cell Biology Course book: Fall, Marland, Wagner, Tyson: Computational Cell Biology, 2002 Springer, ISBN 0-387-95369-8 (can be found in the main library, prize at amazon.com $59.95). Synopsis:
More informationFigure 1: Ca2+ wave in a Xenopus oocyte following fertilization. Time goes from top left to bottom right. From Fall et al., 2002.
1 Traveling Fronts Richard Bertram Department of Mathematics and Programs in Neuroscience and Molecular Biophysics Florida State University Tallahassee, Florida 32306 2 When mature Xenopus oocytes (frog
More informationStochastic E4ects in Intercellular Calcium Spiking in Hepatocytes
J. theor. Biol. (2001) 212, 111}125 doi:10.1006/jtbi.2001.2362, available online at http://www.idealibrary.com on Stochastic E4ects in Intercellular Calcium Spiking in Hepatocytes M. E. GRACHEVA*?, R.
More informationStabilizing Role of Calcium Store-Dependent Plasma Membrane Calcium Channels in Action-Potential Firing and Intracellular Calcium Oscillations
Biophysical Journal Volume 89 December 2005 3741 3756 3741 Stabilizing Role of Calcium Store-Dependent Plasma Membrane Calcium Channels in Action-Potential Firing and Intracellular Calcium Oscillations
More informationSpatiotemporal multiple coherence resonances and calcium waves in a coupled hepatocyte system
Vol 18 No 3, March 2009 c 2009 Chin. Phys. Soc. 1674-1056/2009/18(03)/0872-09 Chinese Physics B and IOP Publishing Ltd Spatiotemporal multiple coherence resonances and calcium waves in a coupled hepatocyte
More informationRegulation of calcium entry in exocrine gland cells and other epithelial cells
362 MINI-REVIEW Regulation of calcium entry in exocrine gland cells and other epithelial cells James W Putney and Gary S Bird Laboratory of Signal Transduction, National Institute of Environmental Health
More informationLIMIT CYCLE OSCILLATORS
MCB 137 EXCITABLE & OSCILLATORY SYSTEMS WINTER 2008 LIMIT CYCLE OSCILLATORS The Fitzhugh-Nagumo Equations The best example of an excitable phenomenon is the firing of a nerve: according to the Hodgkin
More informationdynamic processes in cells (a systems approach to biology)
dynamic processes in cells (a systems approach to biology) jeremy gunawardena department of systems biology harvard medical school lecture 11 6 october 2016 Hill functions are GRFs Hill functions fitted
More informationLaw of Mass Action, Detailed Balance, and the Modeling of Calcium Puffs
PRL 105, 048103 (2010) P H Y S I C A L R E V I E W L E T T E R S week ending 23 JULY 2010 Law of Mass Action, Detailed Balance, and the Modeling of Calcium Puffs S. Rüdiger, 1 J. W. Shuai, 2, * and I.
More informationComputer Science Department Technical Report. University of California. Los Angeles, CA
Computer Science Department Technical Report University of California Los Angeles, CA 995-1596 COMPUTER SIMULATION OF THE JAFRI-WINSLOW ACTION POTENTIAL MODEL Sergey Y. Chernyavskiy November 1998 Boris
More informationA minimalist model of calcium-voltage coupling in GnRH cells
Journal of Physics: Conference Series A minimalist model of calcium-voltage coupling in GnRH cells To cite this article: Martin Rennie et al 2011 J. Phys.: Conf. Ser. 285 012040 View the article online
More informationModeling 3-D Calcium Waves from Stochastic Calcium sparks in a Sarcomere Using COMSOL
Modeling 3-D Calcium Waves from Stochastic Calcium sparks in a Sarcomere Using COMSOL Zana Coulibaly 1, Leighton T. Izu 2 and Bradford E. Peercy 1 1 University of Maryland, Baltimore County 2 University
More informationSimulation of the Fertilization Ca 2 Wave in Xenopus laevis Eggs
2088 Biophysical Journal Volume 75 October 1998 2088 2097 Simulation of the Fertilization Ca 2 Wave in Xenopus laevis Eggs John Wagner,* Yue-Xian Li,* John Pearson, and Joel Keizer* # *Institute of Theoretical
More informationdynamic processes in cells (a systems approach to biology)
dynamic processes in cells (a systems approach to biology) jeremy gunawardena department of systems biology harvard medical school lecture 11 13 october 2015 the long road to molecular understanding P&M
More informationTranslating intracellular calcium signaling into models
Translating intracellular calcium signaling into models Rüdiger Thul * School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, United Kingdom Abstract The rich experimental data
More information2013 NSF-CMACS Workshop on Atrial Fibrillation
2013 NSF-CMACS Workshop on A Atrial Fibrillation Flavio H. Fenton School of Physics Georgia Institute of Technology, Atlanta, GA and Max Planck Institute for Dynamics and Self-organization, Goettingen,
More informationReaction-Diffusion in the NEURON Simulator
Reaction-Diffusion in the NEURON Simulator Robert A. McDougal Yale School of Medicine 16 October 2015 Getting Started When should I use the reaction-diffusion module? What is a reaction-diffusion system?
More informationDynamical Systems in Neuroscience: Elementary Bifurcations
Dynamical Systems in Neuroscience: Elementary Bifurcations Foris Kuang May 2017 1 Contents 1 Introduction 3 2 Definitions 3 3 Hodgkin-Huxley Model 3 4 Morris-Lecar Model 4 5 Stability 5 5.1 Linear ODE..............................................
More informationStochastic Properties of Ca 2 Release of Inositol 1,4,5-Trisphosphate Receptor Clusters
Biophysical Journal Volume 83 July 2002 87 97 87 Stochastic Properties of Ca 2 Release of Inositol 1,4,5-Trisphosphate Receptor Clusters Jian-Wei Shuai and Peter Jung Department of Physics and Astronomy
More information4.3 Intracellular calcium dynamics
coupled equations: dv dv 2 dv 3 dv 4 = i + I e A + g,2 (V 2 V ) = i 2 + g 2,3 (V 3 V 2 )+g 2, (V V 2 )+g 2,4 (V 4 V 2 ) = i 3 + g 3,2 (V 2 V 3 ) = i 4 + g 4,2 (V 2 V 4 ) This can be written in matrix/vector
More informationSpace State Approach to Study the Effect of. Sodium over Cytosolic Calcium Profile
Applied Mathematical Sciences, Vol. 3, 2009, no. 35, 1745-1754 Space State Approach to Study the Effect of Sodium over Cytosolic lcium Profile Shivendra Tewari Department of Mathematics Maulana Azad National
More informationA role of the endoplasmic reticulum in a mathematical model of corticotroph action potentials
A role of the endoplasmic reticulum in a mathematical model of corticotroph action potentials Paul R. Shorten, Andrew P. LeBeau A. Bruce Robson, Alan E. McKinnon, and David J.N. Wall Biomathematics Research
More informationCOMPUTER SIMULATION OF DIFFERENTIAL KINETICS OF MAPK ACTIVATION UPON EGF RECEPTOR OVEREXPRESSION
COMPUTER SIMULATION OF DIFFERENTIAL KINETICS OF MAPK ACTIVATION UPON EGF RECEPTOR OVEREXPRESSION I. Aksan 1, M. Sen 2, M. K. Araz 3, and M. L. Kurnaz 3 1 School of Biological Sciences, University of Manchester,
More informationBuffer kinetics shape the spatiotemporal patterns of IP 3 -evoked Ca 2+ signals
J Physiol (2003), 553.3, pp. 775 788 DOI: 10.1113/jphysiol.2003.054247 The Physiological Society 2003 www.jphysiol.org Buffer kinetics shape the spatiotemporal patterns of IP 3 -evoked Ca 2+ signals Sheila
More informationFinite Difference Model to Study the Effects of Na + Influx on Cytosolic Ca 2+ Diffusion
World Academy of Science, Engineering and Technology 5 008 Finite Difference Model to Study the Effects of + Influx on Cytosolic Ca + Diffusion Shivendra Tewari and K. R. Pardasani Abstract Cytosolic Ca
More informationSr2+ can Pass through Ca2+ Entry Pathway Activated by Ca2+ Depletion, but can be Hardly Taken up by the Ca2+ Stores in the Rat Salivary Acinar Cells
Tohoku J. Exp. Med., 1995, 176, 83-97 Sr2+ can Pass through Ca2+ Entry Pathway Activated by Ca2+ Depletion, but can be Hardly Taken up by the Ca2+ Stores in the Rat Salivary Acinar Cells YASUE FUKUSHI,
More informationLocal and global calcium signals and fluid and electrolyte secretion in mouse submandibular acinar cells
Am J Physiol Gastrointest Liver Physiol 288: G118 G124, 2005. First published August 12, 2004; doi:10.1152/ajpgi.00096.2004. Local and global calcium signals and fluid and electrolyte secretion in mouse
More informationA model of slow plateau-like oscillations based upon the fast Na current in a window mode
Neurocomputing 38}40 (2001) 159}166 A model of slow plateau-like oscillations based upon the fast Na current in a window mode G.S. Cymbalyuk*, R.L. Calabrese Biology Department, Emory University, 1510
More information6.3.4 Action potential
I ion C m C m dφ dt Figure 6.8: Electrical circuit model of the cell membrane. Normally, cells are net negative inside the cell which results in a non-zero resting membrane potential. The membrane potential
More informationMathematical modeling of intracellular and intercellular calcium signaling
Mathematical modeling of intracellular and intercellular calcium signaling Jian-Wei Shuai, a Suhita Nadkarni, a Peter Jung, a, * Ann Cornell-Bell b and Vickery Trinkaus-Randall c a Department of Physics
More informationDynamical Systems for Biology - Excitability
Dynamical Systems for Biology - Excitability J. P. Keener Mathematics Department Dynamical Systems for Biology p.1/25 Examples of Excitable Media B-Z reagent CICR (Calcium Induced Calcium Release) Nerve
More informationFluid secretion in secretory epithelial cells requires polarized
Local uncaging of caged Ca 2 reveals distribution of Ca 2 -activated Cl channels in pancreatic acinar cells Myoung Kyu Park*, Richard B. Lomax, Alexei V. Tepikin, and Ole H. Petersen Medical Research Council
More informationCorrelation of NADH and Ca 2+ signals in mouse pancreatic acinar cells
Journal of Physiology (2002), 539.1, pp. 41 52 DOI: 10.1013/jphysiol.2001.013134 The Physiological Society 2002 www.jphysiol.org Correlation of NADH and Ca 2+ signals in mouse pancreatic acinar cells S.
More informationCoupled dynamics of voltage and calcium in paced cardiac cells
Coupled dynamics of voltage and calcium in paced cardiac cells Yohannes Shiferaw, 1,2 Daisuke Sato, 1 and Alain Karma 1 1 Department of Physics and Center for Interdisciplinary Research on Complex Systems,
More informationThe Development of a Comprehensive Mechanism for Intracellular Calcium Oscillations: A Theoretical Approach and an Experimental Validation
Salve Regina University Digital Commons @ Salve Regina Pell Scholars and Senior Theses Salve's Dissertations and Theses 5-1-2010 The Development of a Comprehensive Mechanism for Intracellular Calcium Oscillations:
More informationModel for Receptor-Controlled Cytosolic Calcium Oscillations and for External Influences on the Signal Pathway
Biophysical Journal Volume 65 November 1993 2047-2058 Model for Receptor-Controlled Cytosolic Calcium Oscillations and for External Influences on the Signal Pathway 2047 C. Eichwald and F. Kaiser Institute
More informationCELL BIOLOGY - CLUTCH CH. 9 - TRANSPORT ACROSS MEMBRANES.
!! www.clutchprep.com K + K + K + K + CELL BIOLOGY - CLUTCH CONCEPT: PRINCIPLES OF TRANSMEMBRANE TRANSPORT Membranes and Gradients Cells must be able to communicate across their membrane barriers to materials
More informationLESSON 2.2 WORKBOOK How do our axons transmit electrical signals?
LESSON 2.2 WORKBOOK How do our axons transmit electrical signals? This lesson introduces you to the action potential, which is the process by which axons signal electrically. In this lesson you will learn
More informationPeripheral Nerve II. Amelyn Ramos Rafael, MD. Anatomical considerations
Peripheral Nerve II Amelyn Ramos Rafael, MD Anatomical considerations 1 Physiologic properties of the nerve Irritability of the nerve A stimulus applied on the nerve causes the production of a nerve impulse,
More informationMultimodal Information Encoding in Astrocytes
Multimodal Information Encoding in Astrocytes Helen Saad BGGN 260: NeuroDynamics UCSD Winter 2010 Abstract Astrocytes encode information about external stimuli through complex intracellular calcium dynamics.
More informationChannels can be activated by ligand-binding (chemical), voltage change, or mechanical changes such as stretch.
1. Describe the basic structure of an ion channel. Name 3 ways a channel can be "activated," and describe what occurs upon activation. What are some ways a channel can decide what is allowed to pass through?
More informationElectrophysiology of the neuron
School of Mathematical Sciences G4TNS Theoretical Neuroscience Electrophysiology of the neuron Electrophysiology is the study of ionic currents and electrical activity in cells and tissues. The work of
More informationTopics in Neurophysics
Topics in Neurophysics Alex Loebel, Martin Stemmler and Anderas Herz Exercise 2 Solution (1) The Hodgkin Huxley Model The goal of this exercise is to simulate the action potential according to the model
More informationSupporting Online Material for
www.sciencemag.org/cgi/content/full/319/5869/1543/dc1 Supporting Online Material for Synaptic Theory of Working Memory Gianluigi Mongillo, Omri Barak, Misha Tsodyks* *To whom correspondence should be addressed.
More informationSpike-Frequency Adaptation: Phenomenological Model and Experimental Tests
Spike-Frequency Adaptation: Phenomenological Model and Experimental Tests J. Benda, M. Bethge, M. Hennig, K. Pawelzik & A.V.M. Herz February, 7 Abstract Spike-frequency adaptation is a common feature of
More informationHybrid stochastic and deterministic simulations of calcium blips
Biophys J BioFAST, published on May 11, 2007 as doi:10.1529/biophysj.106.099879 This un-edited manuscript has been accepted for publication in Biophysical Journal and is freely available on BioFast at
More informationA Model Based Analysis of Steady-State versus Dynamic Elements in the Relationship between Calcium and Force
A Model Based Analysis of Steady-State versus Dynamic Elements in the Relationship between Calcium and Force Casey L. Overby, Sanjeev G. Shroff BACKGROUND Cardiac contraction and calcium. Intracellular
More informationThe Simplification of Biological Models using Voronoi Tiling of the Phase Plane
The Simplification of Biological Models using Voronoi Tiling of the Phase Plane Supervisors: James Hetherington (Dept. of Anatomy and Developmental Biology) Sachie Yamaji (Dept. of Anatomy and Developmental
More informationRahaf Nasser mohammad khatatbeh
7 7... Hiba Abu Hayyeh... Rahaf Nasser mohammad khatatbeh Mohammad khatatbeh Brief introduction about membrane potential The term membrane potential refers to a separation of opposite charges across the
More informationKinetic model of the inositol trisphosphate receptor that shows both steadystate and quantal patterns of Ca 2 release from intracellular stores
Biochem. J. (2003) 370, 621 629 (Printed in Great Britain) 621 Kinetic model of the inositol trisphosphate receptor that shows both steadystate and quantal patterns of Ca 2 release from intracellular stores
More informationMEMBRANE POTENTIALS AND ACTION POTENTIALS:
University of Jordan Faculty of Medicine Department of Physiology & Biochemistry Medical students, 2017/2018 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ Review: Membrane physiology
More informationLecture Notes 8C120 Inleiding Meten en Modelleren. Cellular electrophysiology: modeling and simulation. Nico Kuijpers
Lecture Notes 8C2 Inleiding Meten en Modelleren Cellular electrophysiology: modeling and simulation Nico Kuijpers nico.kuijpers@bf.unimaas.nl February 9, 2 2 8C2 Inleiding Meten en Modelleren Extracellular
More informationCommentary Functional Interactions in Ca 2 Signaling over Different Time and Distance Scales
Commentary Functional Interactions in Ca 2 Signaling over Different Time and Distance Scales Jonathan S. Marchant and Ian Parker From the Department of Neurobiology and Behavior, Laboratory of Cellular
More informationReaction-Diffusion in the NEURON Simulator
Robert A. McDougal Anna Bulanova Yale School of Medicine 26 July 2014 What is a reaction-diffusion system? Reaction diffusion systems are mathematical models which explain how the concentration of one
More informationElectrodiffusion Model of Electrical Conduction in Neuronal Processes
i. ISMS OF CONDlTlONlff PLASTICITY ditecl by Charks B. Woody, Daniel L. Alk~n, and James b. McGauyh (Plenum Publishing Corporation, 19 23 Electrodiffusion Model of Electrical Conduction in Neuronal Processes
More informationAndrew P. LeBeau, 1 Fredrick Van Goor, 2 Stanko S. Stojilkovic, 2 and Arthur Sherman 1
The Journal of Neuroscience, December 15, 2000, 20(24):9290 9297 Modeling of Membrane Excitability in Gonadotropin-Releasing Hormone-Secreting Hypothalamic Neurons Regulated by Ca 2 - Mobilizing and Adenylyl
More informationOne of the pathways for intracellular signaling involves Ca 2
From calcium blips to calcium puffs: Theoretical analysis of the requirements for interchannel communication Stéphane Swillens*, Geneviève Dupont, Laurent Combettes, and Philippe Champeil *Institut de
More informationModeling A Multi-Compartments Biological System with Membrane Computing
Journal of Computer Science 6 (10): 1177-1184, 2010 ISSN 1549-3636 2010 Science Publications Modeling A Multi-Compartments Biological System with Membrane Computing 1 Ravie Chandren Muniyandi and 2 Abdullah
More informationA model for diffusion waves of calcium ions in a heart cell is given by a system of coupled, time-dependent reaction-diffusion equations
Long-Time Simulation of Calcium Waves in a Heart Cell to Study the Effects of Calcium Release Flux Density and of Coefficients in the Pump and Leak Mechanisms on Self-Organizing Wave Behavior Zana Coulibaly,
More informationSUPPLEMENTARY INFORMATION
Cell viability rate 0.8 0.6 0 0.05 0.1 0.2 0.3 0.4 0.5 0.7 1 Exposure duration (s) Supplementary Figure 1. Femtosecond laser could disrupt and turn off GFP without photons at 473 nm and keep cells alive.
More informationCaffeine-induced Ca 2C oscillations in type I horizontal cell of carp retina: A mathematical model
Channels 8:6, 509--518; November/December 2014; Published with license by Taylor & Francis Group, LLC RESEARCH PAPER Caffeine-induced Ca 2C oscillations in type I horizontal cell of carp retina: A mathematical
More informationMuscle regulation and Actin Topics: Tropomyosin and Troponin, Actin Assembly, Actin-dependent Movement
1 Muscle regulation and Actin Topics: Tropomyosin and Troponin, Actin Assembly, Actin-dependent Movement In the last lecture, we saw that a repeating alternation between chemical (ATP hydrolysis) and vectorial
More informationPhysiology Unit 2. MEMBRANE POTENTIALS and SYNAPSES
Physiology Unit 2 MEMBRANE POTENTIALS and SYNAPSES In Physiology Today Ohm s Law I = V/R Ohm s law: the current through a conductor between two points is directly proportional to the voltage across the
More informationChapter 8 Calcium-Induced Calcium Release
Chapter 8 Calcium-Induced Calcium Release We started in Chap. 2 by assuming that the concentrations of the junctional sarcoplasmic reticulum (JSR) and the network sarcoplasmic reticulum (NSR) are identical
More informationChapter 24 BIFURCATIONS
Chapter 24 BIFURCATIONS Abstract Keywords: Phase Portrait Fixed Point Saddle-Node Bifurcation Diagram Codimension-1 Hysteresis Hopf Bifurcation SNIC Page 1 24.1 Introduction In linear systems, responses
More informationSimulation of calcium waves in ascidian eggs: insights into the origin of the pacemaker sites and the possible nature of the sperm factor
JCS epress online publication date 3 August 24 Research Article 4313 Simulation of calcium waves in ascidian eggs: insights into the origin of the pacemaker sites and the possible nature of the sperm factor
More informationStochastic Oscillator Death in Globally Coupled Neural Systems
Journal of the Korean Physical Society, Vol. 52, No. 6, June 2008, pp. 19131917 Stochastic Oscillator Death in Globally Coupled Neural Systems Woochang Lim and Sang-Yoon Kim y Department of Physics, Kangwon
More informationBifurcation structure of a model of bursting pancreatic cells
BioSystems 63 (2001) 3 13 www.elsevier.com/locate/biosystems Bifurcation structure of a model of bursting pancreatic cells Erik Mosekilde a, *, Brian Lading a, Sergiy Yanchuk b, Yuri Maistrenko b a Department
More informationCa influx in resting rat sensory neurones that regulates and is regulated by ryanodine-sensitive Ca stores
9070 Journal of Physiology (1999), 519.1, pp. 115 130 115 Ca influx in resting rat sensory neurones that regulates and is regulated by ryanodine-sensitive Ca stores Yuriy M. Usachev and Stanley A. Thayer
More informationModeling action potential generation and propagation in NRK fibroblasts
Am J Physiol Cell Physiol 287: C851 C865, 2004. First published May 12, 2004; 10.1152/ajpcell.00220.2003. Modeling action potential generation and propagation in NRK fibroblasts J. J. Torres, 1,2 L. N.
More informationThis script will produce a series of pulses of amplitude 40 na, duration 1ms, recurring every 50 ms.
9.16 Problem Set #4 In the final problem set you will combine the pieces of knowledge gained in the previous assignments to build a full-blown model of a plastic synapse. You will investigate the effects
More information2.6 The Membrane Potential
2.6: The Membrane Potential 51 tracellular potassium, so that the energy stored in the electrochemical gradients can be extracted. Indeed, when this is the case experimentally, ATP is synthesized from
More informationEquality of average and steady-state levels in some nonlinear models of biological oscillations
Theory Biosci. (28) 127:1 14 DOI 1.17/s1264-7-18-4 ORIGINAL PAPER Equality of average and steady-state levels in some nonlinear models of biological oscillations Beate Knoke Æ Marko Marhl Æ Matjaž Perc
More informationNonlinear Gap Junctions Enable Long-Distance Propagation of Pulsating Calcium Waves in Astrocyte Networks
Nonlinear Gap Junctions Enable Long-Distance Propagation of Pulsating Calcium Waves in Astrocyte Networks Mati Goldberg 1, Maurizio De Pittà 1, Vladislav Volman 2,3, Hugues Berry 4 *,Eshel Ben-Jacob 1,2
More informationInvariant Manifold Reductions for Markovian Ion Channel Dynamics
Invariant Manifold Reductions for Markovian Ion Channel Dynamics James P. Keener Department of Mathematics, University of Utah, Salt Lake City, UT 84112 June 4, 2008 Abstract We show that many Markov models
More informationMixed mode oscillations as a mechanism for pseudo-plateau bursting
J Comput Neurosci (2010) 28:443 458 DOI 10.1007/s10827-010-0226-7 Mixed mode oscillations as a mechanism for pseudo-plateau bursting Theodore Vo Richard Bertram Joel Tabak Martin Wechselberger Received:
More informationAn algorithm for detecting oscillatory behavior in discretized data: the damped-oscillator oscillator detector
An algorithm for detecting oscillatory behavior in discretized data: the damped-oscillator oscillator detector David Hsu, Murielle Hsu, He Huang and Erwin B. Montgomery, Jr Department of Neurology University
More informationsix lectures on systems biology
six lectures on systems biology jeremy gunawardena department of systems biology harvard medical school lecture 3 5 april 2011 part 2 seminar room, department of genetics a rather provisional syllabus
More informationDirect stochastic simulation of Ca 2+ motion in Xenopus eggs
Direct stochastic simulation of Ca 2+ motion in Xenopus eggs Y.-B. Yi, 1 H. Wang, 1 A. M. Sastry, 1,2, * and C. M. Lastoskie 2,3 1 Department of Mechanical Engineering, University of Michigan, Ann Arbor,
More informationagonist-stimulated oscillations in Ca2+ concentration
Proc. Natl. Acad. Sci. USA Vol. 89, pp. 9895-9899, October 1992 iophysics A single-pool inositol 1,4,5-trisphosphate-receptor-based model for agonist-stimulated oscillations in Ca2+ concentration GARY
More informationNeural Modeling and Computational Neuroscience. Claudio Gallicchio
Neural Modeling and Computational Neuroscience Claudio Gallicchio 1 Neuroscience modeling 2 Introduction to basic aspects of brain computation Introduction to neurophysiology Neural modeling: Elements
More informationTheory of selective excitation in stimulated Raman scattering
Theory of selective excitation in stimulated Raman scattering S. A. Malinovskaya, P. H. Bucksbaum, and P. R. Berman Michigan Center for Theoretical Physics, FOCUS Center, and Department of Physics, University
More informationLinearization of F-I Curves by Adaptation
LETTER Communicated by Laurence Abbott Linearization of F-I Curves by Adaptation Bard Ermentrout Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, U.S.A. We show that negative
More information