English

# Presence of PI-rich vesicles is required for the PLC ζ activation according to mathematical modeling

## Introduction

During mammalian fertilization, sperm induces a series of calcium oscillations in the egg that induce egg activation and early embryonic development
[
1
##### Essential Role of Sperm-Specific PLC-Zeta in Egg Activation and Male Factor Infertility: An Update

A. Saleh, J. Kashir, A. Thanassoulas, B. Safieh-Garabedian, F. Lai, M. Nomikos

Frontiers in Cell and Developmental Biology. 2020, 8, None

]
. Phospholipase C (PLC) ζ is a sperm-specific protein capable of causing Ca2+ release
[
2
##### Broad, ectopic expression of the sperm protein PLCZ1 induces parthenogenesis and ovarian tumours in mice

N. Yoshida, M. Amanai, T. Fukui, E. Kajikawa, M. Brahmajosyula, A. Iwahori, Y. Nakano, S. Shoji, J. Diebold, H. Hessel, R. Huss, A. Perry

Development. 2007, 134, 3941-3952

]
. PLCζ is an enzyme that catalyzes the reaction of phosphatidylinositol-4,5-phosphate (PIP2) hydrolysis into inositol-3-phosphate (IP3) and diacylglycerol (DAG). It is present in the sperm cell acrosome and cytosol but doesn’t significantly affect its metabolism. However, after the fusion of sperm and egg cell, its activity increases as PLC ζ begins to bind membranes of the egg cell and generate IP3
. PLC ζ can also initiate calcium oscillations in oocytes without the sperm cell if its expression in the oocyte is artificially enabled
[
2
##### Broad, ectopic expression of the sperm protein PLCZ1 induces parthenogenesis and ovarian tumours in mice

N. Yoshida, M. Amanai, T. Fukui, E. Kajikawa, M. Brahmajosyula, A. Iwahori, Y. Nakano, S. Shoji, J. Diebold, H. Hessel, R. Huss, A. Perry

Development. 2007, 134, 3941-3952

]
. Some eggs fertilized by PLCζ-null sperm can develop, albeit at greatly reduced efficiency, and after a significant time-delay
.
One of the main questions about PLC ζ is the reason for the absence of its activity in sperm cells, as well as in other cell types like Chinese hamster ovary cells (CHO)
. Several hypotheses are explaining the cause of exclusive PLC ζ activity in the oocyte (Fig. 1). One of them assumes that there is an unknown cofactor that activates PLC ζ (Fig. 1A). This cofactor is located in oocyte cytosol
. The alternative explanation suggests that in sperm PLC ζ is bound to some kind of inhibitor (Fig. 1B), and after fusion with the oocyte, the complex with inhibitor dissolves. This hypothesis partially contradicts data from
, which demonstrated that when expressed in Chinese hamster ovary cells PLC ζ shows no significant impact on calcium concentration. None of these hypotheses are supported by direct evidence.
The alternative hypothesis is based on PIP2-rich vesicles in oocytes (Fig. 1C, D). These vesicles have much higher relative surface space than the membrane, and it was demonstrated that a large part of PLC ζ bounds to these vesicles
[
5,
##### Divergent effect of mammalian PLCζ in generating Ca2+ oscillations in somatic cells compared with eggs

S. Phillips, Y. Yu, A. Rossbach, M. Nomikos, V. Vassilakopoulou, E. Livaniou, B. Cumbes, F. Lai, C. George, K. Swann

Biochemical Journal. 2011, 438, 545-553

]
.
The modelling approach has been successfully used to study the calcium activation mechanism in both the sperm and egg cells
, but no work exists on the PLC ζ activity regulation. In this work, we utilize the modelling approach to clarify the mechanisms regulating the PLC ζ activity in sperm and egg cells.
Figure 1. Major hypotheses explaining PLC ζ activity in the oocyte. (А) The first hypothesis is that the PLC ζ acquires the ability to cleave the oocyte membrane PIP2 (〖PIP2〗_m) and produce IP3 upon activation by an unspecified PLC ζ activator A present in oocytes. (B) The second hypothesis is the presence of an unspecified PLC ζ inhibitor in all cell types but eggs (C, D). The third hypothesis suggests that mammalian oocytes contain vesicles higher in PIP2 (〖PIP2〗_v) content, and PLC ζ is targeted on the vesicle surface.

## Materials and methods

### Computational model construction and integration

To study the PLCζ activity in mammalian eggs, a computer model was developed. First, the ordinary differential equations were constructed based on laws of chemical kinetics (either mass action law, Henry-Michaelis-Menten kinetics, or Hill functions). Kinetic equation parameters were either taken from the literature or estimated based on existing experimental data. The final model consisted of 18 equations with two unknown parameters. The model was solved using the LSODA method.

## Results and discussion

### Mathematical model of PLCζ activity

Before checking the hypotheses described above, an accurate mathematical model of PLCζ activity that can describe the existing experimental data
[
5,
##### Divergent effect of mammalian PLCζ in generating Ca2+ oscillations in somatic cells compared with eggs

S. Phillips, Y. Yu, A. Rossbach, M. Nomikos, V. Vassilakopoulou, E. Livaniou, B. Cumbes, F. Lai, C. George, K. Swann

Biochemical Journal. 2011, 438, 545-553

8
##### A Model for the Acrosome Reaction in Mammalian Sperm

J. Simons, L. Fauci

Bulletin of Mathematical Biology. 2018, 80, 2481-2501

]
was developed. According to multiple authors (
[
5,
##### Divergent effect of mammalian PLCζ in generating Ca2+ oscillations in somatic cells compared with eggs

S. Phillips, Y. Yu, A. Rossbach, M. Nomikos, V. Vassilakopoulou, E. Livaniou, B. Cumbes, F. Lai, C. George, K. Swann

Biochemical Journal. 2011, 438, 545-553

8
##### A Model for the Acrosome Reaction in Mammalian Sperm

J. Simons, L. Fauci

Bulletin of Mathematical Biology. 2018, 80, 2481-2501

]
) the unique feature of PLCζ is its high cooperativity for Ca2+ binding, which is performed by its four EF-hand domains. Its Hill coefficient varies from 3.8 to 4.3 (
[
8,
##### A Model for the Acrosome Reaction in Mammalian Sperm

J. Simons, L. Fauci

Bulletin of Mathematical Biology. 2018, 80, 2481-2501

9,
##### Human PLC  exhibits superior fertilization potency over mouse PLC  in triggering the Ca2+ oscillations required for mammalian oocyte activation

M. Nomikos, M. Theodoridou, K. Elgmati, D. Parthimos, B. Calver, L. Buntwal, G. Nounesis, K. Swann, F. Lai

Molecular Human Reproduction. 2014, 20, 489-498

10
##### Recombinant Phospholipase Cζ Has High Ca2+ Sensitivity and Induces Ca2+ Oscillations in Mouse Eggs

Z. Kouchi, K. Fukami, T. Shikano, S. Oda, Y. Nakamura, T. Takenawa, S. Miyazaki

Journal of Biological Chemistry. 2004, 279, 10408-10412

]
) according to different sources. However, as it was shown below, such a high value for Hill coefficient is incompatible with the data demonstrated in these articles. Therefore, the Hill coefficient was calculated using two different methods. It was shown that its value, according to the data from
[
9
##### Human PLC  exhibits superior fertilization potency over mouse PLC  in triggering the Ca2+ oscillations required for mammalian oocyte activation

M. Nomikos, M. Theodoridou, K. Elgmati, D. Parthimos, B. Calver, L. Buntwal, G. Nounesis, K. Swann, F. Lai

Molecular Human Reproduction. 2014, 20, 489-498

]
, is close to 1.1.
A simple mathematical model which could predict calcium dependence of PLCζ activity in physiologically relevant concentrations of calcium $$\left(10^{-8}-10^{-6} M\right)$$ was created. It was based on Klotz equation (1) and a hypothesis that every next calcium ion binds with equilibrium coefficient equal to previous one multiplied on cooperativity constant  (2-5) $$B=\frac{\left[P L C z_{-} C a\right]+2 *\left[P L C z_{-} 2 C a\right]+3 *\left[P L C z_{-} 3 C a\right]+4 *\left[P L C z_{-} 4 C a\right]}{P L Ctotal} = \\ = \frac{K e q *[C a]+2 * a * K e q^{2} *[C a]^{2}+3 * a^{3} * K e q^{3} *[C a]^{3}+4 * a^{6} * K e q^{4} *[C a]^{4}}{1+K e q *[C a]+a * K e q^{2} *[C a]^{2}+a^{3} * K e q^{3} *[C a]^{3}+a^{6} * K e q^{4} *[C a]^{4}}\tag{1}$$

$$K 2=K 1 * a\tag{2}$$ $$K 3=K 1 * a^{2}\tag{3}$$ $$K 4=K 1 * a^{3}\tag{4}$$ $$K r=K 1 / K e q\tag{5}$$

Here K1 is the constant for the first calcium ion binding, K2 – for the second calcium ion binding, K3 – for the third, K4 – for the fourth, Keq is the equilibrium constant for the first calcium ion binding reaction, Kr is the calcium unbinding constant for every step, a is cooperativity constant, $$\left[P L C z_{-} C a\right]$$ is the concentration of PLCζ bound with one Ca ion in the steady-state, $$\left[P L C z_{-} 2 C a\right]$$ is the concentration of PLCζ bound with two Ca2+ ions in the steady-state, $$\left[P L C z_{-} 3 C a\right]$$ with three, $$\left[P L C z_{-} 4 C a\right]$$with four. $$\text { PLCtotal }$$is the total concentration of all forms of PLCζ summarized. B is a parameter in the Klotz equation, representing the molar ratio of total PLCζ and calcium bound with it.
Using equations 2-5, a mathematical model based on mass action law was developed. Calcium concentration in this model was fixed, while variables represent dynamics of PLCζ bound with different amount of calcium ions: $$\frac{d[P L C z]}{d t}=-K 1 *[\mathrm{Ca}] *[P L C z]+K r *\left[P L C z_{-} \mathrm{Ca}\right]\tag{6}$$

$$\frac{d\left[P L C z_{-} C a\right]}{d t}=K 1 *[C a] *[P L C z]-K r *\left[P L C z_{-} C a\right] - \\ - K 2 *[C a] *\left[P L C z_{-} C a\right] +K r *\left[P L C z_{-} 2 C a\right]\tag{7}$$

$$\frac{d[PLCz_{-} 2Ca]}{dt} = K2 * [Ca] * [PLCz_{-}Ca] - K r * [PLCz_{-}2Ca] - \\ - K3 * [Ca] * [PLCz_{-}2Ca] + K r * [PLCz_{-}3Ca]\tag{8}$$

$$\frac{d[PLCz_{-} 3Ca]}{dt} = K3 * [Ca] * [PLCz_{-}2Ca] - K r * [PLCz_{-}3Ca] - \\ - K4 * [Ca] * [PLCz_{-}3Ca] + K r * [PLCz_{-}4Ca]\tag{9}$$

$$\frac{d[PLCz_{-}4Ca]}{dt} = K4 * [Ca] * [PLCz_{-}3Ca] - K r * [PLCz_{-}4Ca]\tag{10}$$

Here, K1 is constant for the first calcium ion binding, K2 – for the second, K3 – for third, K4 – for fourth, Keq is the equilibrium constant for the first calcium ion binding reaction, Kr is calcium unbinding constant for every step, a is cooperativity constant, $$[P L C z]$$. The concentration of PLCζ, $$\left[P L C z_{-} C a\right]$$ is the concentration of PLCζ bound with one Ca ion in the steady-state, $$\left[P L C z_{-} 2 C a\right]$$ is the concentration of PLCζ bound with two Ca2+ ions in the steady-state, $$\left[P L C z_{-} 3 C a\right]$$ - with three, $$\left[P L C z_{-} 4 C a\right]$$ - with four.
We have investigated the steady-state of the model. The details are given in S1.
The model $$\% \text { of activity }$$was calculated as follows: $$\frac{0.03 * [PLCz_{-}2Ca] + 0.22 * [PLCz_{-}3Ca] + [PLCz_{-}4Ca]}{PLCtotal} = \% \ of\ activity\tag{11}$$
This parameter depends on the concentrations of PLCζ forms associated with two, three or four calcium ions. The coefficients for recalculating the activity of the concentrations of these forms are taken from the data on the maximum activity of PLCζ with the deletion of one or two EF-hands
[
12
##### The Role of EF-hand Domains and C2 Domain in Regulation of Enzymatic Activity of Phospholipase Cζ

Z. Kouchi, T. Shikano, Y. Nakamura, H. Shirakawa, K. Fukami, S. Miyazaki

Journal of Biological Chemistry. 2005, 280, 21015-21021

]
. For PLCζ bound to three calcium ions, the data on PLCζ with one EF-hand deletion was used (in this case, activity was 22% of the native enzyme form activity). For PLCζ bound to two calcium ions, the data on PLCζ with two EF-hand deletion was used (in this case, activity was 3% of the native enzyme form activity).
Parameter optimization was performed using a genetic algorithm. The experimental enzyme activity in relation to the maximal $$\text { (%of activity) }$$ was obtained from the literature data.
The model predicted equilibrium constant Keq = $$8.3 * 10^{8}$$ M-1 and cooperativity constant a = 0.33. Using these values, a dependency of PLCζ activity on calcium concentration was built (Fig. 2A).

### Hill approximation of PLCζ activity

As an alternative approach to describing PLCζ activity, we used the Hill equation. The Hill equation for an enzyme has the following form: $$\frac{E}{Emax} = \frac{[Ca]^n}{[EC50]^n + [Ca]^n}\tag{12}$$
E is PLCζ activity, $$\text { Emax }$$ is on PLCζ maximum activity, EC50 is calcium concentration required for 50% activity, [Ca] is calcium concentration, n is Hill coefficient.
If we take the Hill coefficient from
[
10
##### Recombinant Phospholipase Cζ Has High Ca2+ Sensitivity and Induces Ca2+ Oscillations in Mouse Eggs

Z. Kouchi, K. Fukami, T. Shikano, S. Oda, Y. Nakamura, T. Takenawa, S. Miyazaki

Journal of Biological Chemistry. 2004, 279, 10408-10412

]
, (n=4.3), we will receive calcium dependency, which can be observed on Fig. 2B. It approximates the experimental data with much higher standard deviation than our model described in (6)-(10). The same stands true for the Hill coefficient obtained from
[
11
##### Role of Phospholipase C-ζ Domains in Ca2+-dependent Phosphatidylinositol 4,5-Bisphosphate Hydrolysis and Cytoplasmic Ca2+ Oscillations

M. Nomikos, L. Blayney, M. Larman, K. Campbell, A. Rossbach, C. Saunders, K. Swann, F. Lai

Journal of Biological Chemistry. 2005, 280, 31011-31018

]
(n=0.9).
Hill coefficient could be estimated from data on calcium concentration at different activities (EC90 and EC10 – 90% and 10% of maximum activity accordingly). $$n=\frac{\log 10(81)}{\log 10(E C 90 / E C 10)}\tag{13}$$
For PLCζ activity predicted by our model, EC90 is $$2.7 * 10^{-7} M$$, while EC10 is $$5.3 * 10^{-9} M$$. By using equation (13), we can find that Hill coefficient for PLCζ is equal to 1.12.
The same procedure was repeated for data from
[
10
##### Recombinant Phospholipase Cζ Has High Ca2+ Sensitivity and Induces Ca2+ Oscillations in Mouse Eggs

Z. Kouchi, K. Fukami, T. Shikano, S. Oda, Y. Nakamura, T. Takenawa, S. Miyazaki

Journal of Biological Chemistry. 2004, 279, 10408-10412

]
. For PLCζ, EC90 is $$4.3 * 10^{-7} M$$, and EC10 is $$8 * 10^{-9} M$$. By using the same equation (13), we can find that the actual experimental Hill coefficient for PLCζ is approximately equal to 1.1, which corresponds well with the predictions of our model.
Figure 2. Validation of the models. (A) Validation of our calcium-binding model with experimental data from [9]. (B) Comparison of Hill equation for n=4.3 with experimental data from [9]. (C) Comparison of Hill equation for n=0.9 with experimental data from [9]. (D) Comparison of Hill equation for n=1.1 with experimental data from [9].

### The complete model of phospholipase C activity in mammalian spermatozoa and egg cells

The complete model of PLCζ activity on egg (Fig. 3A) and sperm membranes (Fig. 3B) was developed. In the sperm and the egg, two similar reaction schemes were used. PLCζ could bind calcium and the available plasmatic membranes independently, but only the form that was bound both to the membrane and four calcium ions could produce IP3. IP3 was removed from the system with a constant rate. The differences between two models were as follows: the egg contains vesicles rich in phosphoinositides, while sperm does not. All reactions occurring on the vesicle membrane duplicate the reactions occurring on the plasmalemma. The reaction constants between schemes did not differ, except for the presence of a separate constant for PLC binding to vesicles in the oocyte model and the rate constant for inositol-3-phosphate degradation.
Using the schemes described above, two models were created: model for PLCζ activity in the oocyte (Fig.3, A) and sperm cell (Fig.3, B). The model equations are described in S2. The details of the model parameters are given in Table S1.
Figure 3. Scheme of the full model. (A) Reactions in the oocyte, PLCζ – calcium-free PLCζ , PLCζ_Ca – PLCζ, bound with one calcium ion, PLCζ_2Ca – PLCζ, bound with two calcium ions, PLCζ_3Ca – with three, PLCζ_4Ca – with four. PLCζ_m – PLCζ, bound with cell membrane, PLCζ_(Ca m ) – PLCζ, bound with the cell membrane and one calcium ion, PLCζ_(2Ca m )– PLCζ, bound with the cell membrane and two calcium ions, PLCζ_(3Ca m ) – with the cell membrane and three calcium ions, PLCζ_(4Ca m ) – with the cell membrane and four calcium ions. PIP2 and PIP2_v – are phosphatidylinositol-4,5 – bis-phosphates on cell and vesicle membrane accordingly. DAG and DAG_v – diacylglycerol on cell membrane and vesicles accordingly. IP3 – inositol-3-phosphate. PLCζ_v – PLCζ, bound with vesicles, PLCζ_(Ca v ) – PLCζ, bound with vesicles and one calcium ion, PLCζ_(2Ca v ) – PLCζ, bound with vesicles and two calcium ions, PLCζ_(3Ca v ) – with vesicles and three calcium ions, PLCζ_(4Ca v ) – with vesicles and four calcium ions. (B) The sperm cell model is identical to the oocyte model except for the absence of the vesicles.

The dependence of IP3 concentration on PIP2 concentration on various membranes is shown in Fig. 4. A single steady-state existed in both of the models. The stationary concentration of IP3 in the spermatozoon was approximately 50-60 nM, and in the oocyte, IP3 concentration was about 200 nM (which is above the response threshold of 130 nM
for IP3 receptors present both in sperm cells and oocytes
[
14,
##### Are there inositol 1,4,5-triphosphate (IP3) receptors in human sperm?

Y. Kuroda, S. Kaneko, Y. Yoshimura, S. Nozawa, K. Mikoshiba

Life Sciences. 1999, 65, 135-143

]
). Thus, according to the point model, the activity of PLCζ alone should be sufficient to initiate calcium oscillations in the oocyte.

In the sperm cell, the final concentration of inositol-3-phosphate, depending on the concentration of PIP2, reaches a plateau long before reaching even half of the threshold concentration (130 nM).
A decrease in the concentration of phosphatidylinositol-4,5-bisphosphate on the surface of vesicles by a factor of 10 would reduce the final concentration of inositol-3-phosphate to approximately 20-30 nM and eliminate the possibility of calcium oscillations in the oocyte solely due to the activity of PLCζ (Fig. 4B). This explains both the absence of oscillations upon initiation of PLCζ expression in somatic cells
[
2
##### Broad, ectopic expression of the sperm protein PLCZ1 induces parthenogenesis and ovarian tumours in mice

N. Yoshida, M. Amanai, T. Fukui, E. Kajikawa, M. Brahmajosyula, A. Iwahori, Y. Nakano, S. Shoji, J. Diebold, H. Hessel, R. Huss, A. Perry

Development. 2007, 134, 3941-3952

]
and the absence of oscillations under similar conditions at the early stages of oocyte maturation, before the formation of phosphatidylinositol-4,5-bis-phosphate-rich vesicles
[
14
##### Are there inositol 1,4,5-triphosphate (IP3) receptors in human sperm?

Y. Kuroda, S. Kaneko, Y. Yoshimura, S. Nozawa, K. Mikoshiba

Life Sciences. 1999, 65, 135-143

]
.
Figure 4. Results in the whole model. (A) Dependence of the IP3 concentration on sperm membrane PIP2 content. (B) Dependence of the IP3 concentration on PIP2 content in oocyte vesicles.

## Conclusions

Here we have built a mathematical model of PLC ζ activity in mammalian egg and sperm cells and validated it on existing experimental data. It was theoretically shown that the activity of PLC ζ in the sperm is insufficient for the synthesis of IP3 in sufficient quantities to initiate calcium oscillations. Its activity on vesicles in egg cells creates a total concentration of IP3 close to 200 nM, which is above the border value for initiation of Ca oscillations.
The results obtained support the hypothesis of the phosphoinositide composition of egg vesicles as the main factor in the effectiveness of PLC ζ as an initiator of calcium oscillations. They exclude the possibility of calcium oscillations in the sperm cell, which is consistent with all currently available experimental data.

1. ##### Essential Role of Sperm-Specific PLC-Zeta in Egg Activation and Male Factor Infertility: An Update

A. Saleh, J. Kashir, A. Thanassoulas, B. Safieh-Garabedian, F. Lai, M. Nomikos

Frontiers in Cell and Developmental Biology. 2020, 8,

2. ##### Broad, ectopic expression of the sperm protein PLCZ1 induces parthenogenesis and ovarian tumours in mice

N. Yoshida, M. Amanai, T. Fukui, E. Kajikawa, M. Brahmajosyula, A. Iwahori, Y. Nakano, S. Shoji, J. Diebold, H. Hessel, R. Huss, A. Perry

Development. 2007, 134, 3941-3952

3. ##### Phospholipase C zeta and calcium oscillations at fertilisation: The evidence, applications, and further questions

J. Kashir, M. Nomikos, F. Lai

Advances in Biological Regulation. 2018, 67, 148-162

4. ##### PLCζ is the physiological trigger of the Ca2+ oscillations that induce embryogenesis in mammals but offspring can be conceived in its absence.

Hachem A, Godwin J, Ruas M, Lee HC, Buitrago MF, Ardestani G, et al.

Development. 2017, ,

5. ##### Divergent effect of mammalian PLCζ in generating Ca2+ oscillations in somatic cells compared with eggs

S. Phillips, Y. Yu, A. Rossbach, M. Nomikos, V. Vassilakopoulou, E. Livaniou, B. Cumbes, F. Lai, C. George, K. Swann

Biochemical Journal. 2011, 438, 545-553

6. ##### Starting a new life: Sperm PLC-zeta mobilizes the Ca2+ signal that induces egg activation and embryo development

M. Nomikos, K. Swann, F. Lai

BioEssays. 2012, 34, 126-134

7. ##### A single-pool model for intracellular calcium oscillations and waves in the Xenopus laevis oocyte

A. Atri, J. Amundson, D. Clapham, J. Sneyd

Biophysical Journal. 1993, 65, 1727-1739

8. ##### A Model for the Acrosome Reaction in Mammalian Sperm

J. Simons, L. Fauci

Bulletin of Mathematical Biology. 2018, 80, 2481-2501

9. ##### Human PLC  exhibits superior fertilization potency over mouse PLC  in triggering the Ca2+ oscillations required for mammalian oocyte activation

M. Nomikos, M. Theodoridou, K. Elgmati, D. Parthimos, B. Calver, L. Buntwal, G. Nounesis, K. Swann, F. Lai

Molecular Human Reproduction. 2014, 20, 489-498

10. ##### Recombinant Phospholipase Cζ Has High Ca2+ Sensitivity and Induces Ca2+ Oscillations in Mouse Eggs

Z. Kouchi, K. Fukami, T. Shikano, S. Oda, Y. Nakamura, T. Takenawa, S. Miyazaki

Journal of Biological Chemistry. 2004, 279, 10408-10412

11. ##### Role of Phospholipase C-ζ Domains in Ca2+-dependent Phosphatidylinositol 4,5-Bisphosphate Hydrolysis and Cytoplasmic Ca2+ Oscillations

M. Nomikos, L. Blayney, M. Larman, K. Campbell, A. Rossbach, C. Saunders, K. Swann, F. Lai

Journal of Biological Chemistry. 2005, 280, 31011-31018

12. ##### The Role of EF-hand Domains and C2 Domain in Regulation of Enzymatic Activity of Phospholipase Cζ

Z. Kouchi, T. Shikano, Y. Nakamura, H. Shirakawa, K. Fukami, S. Miyazaki

Journal of Biological Chemistry. 2005, 280, 21015-21021

13. ##### A single-pool inositol 1,4,5-trisphosphate-receptor-based model for agonist-stimulated oscillations in Ca2+ concentration.

G. De Young, J. Keizer

Proceedings of the National Academy of Sciences. 1992, 89, 9895-9899

14. ##### Are there inositol 1,4,5-triphosphate (IP3) receptors in human sperm?

Y. Kuroda, S. Kaneko, Y. Yoshimura, S. Nozawa, K. Mikoshiba

Life Sciences. 1999, 65, 135-143

15. ##### Comparison of gating dynamics of different IP3R channels with immune algorithm searching for channel parameter distributions

X. Cai, X. Li, H. Qi, F. Wei, J. Chen, J. Shuai

Physical Biology. 2016, 13, 056005

16. ##### Calcium oscillations in mammalian eggs triggered by a soluble sperm protein

J. Parrington, K. Swann, V. Shevchenko, A. Sesay, F. Lai

Nature. 1996, 379, 364-368