Compositional Analysis of Mouse Sperm Subpopulations During Capacitation In Vitro

40 Mammalian sperm must undergo capacitation to become competent for fertilization, yet this process is marked 41 by substantial phenotypic heterogeneity among sperm cells. How such variability emerges and how it relates to 42 fertilizing potential remain unresolved, in part because sperm subpopulations are typically analyzed 43 independently despite being intrinsically interdependent. Here, we combine large-scale single-cell spectral flow 44 cytometry with compositional statistical modeling to quantify how sperm population structure responds to 45 controlled capacitation signals in vitro. Using cauda epididymal mouse sperm, we implemented a two -46 dimensional assay that systematically varies extracellular bicarbonate and free calcium —key regulators of 47 capacitation—and classified millions of individual cells into four irreversible physiological states defined by cell 48 viability and acrosome reaction status. We show that bicarbonate and calcium interact nonlinearly to 49 redistribute sperm across these subpopulations, revealing structured responses that would be otherwise 50 obscured in measurements lacking single-cell resolution. Elevated intracellular calcium was associated with 51 increased cell death, while the highest proportions of live, acrosome -reacted sperm occurred under relatively 52 low extracellular calcium conditions. To enable subpopulation-level analysis, we applied a hierarchical 53 Dirichlet–multinomial regression model that accounts for multinomial sampling noise and between -male 54 variability, yielding posterior probability surfaces that describe how sperm subpopulations reallocate across 55 functional states as microenvironmental signaling conditions change. Together, these results demonstrate that 56 capacitation is a stochastic, cell-population level process shaped by structured phenotypic heterogeneity. This 57 framework provides a quantitative foundation for linking sperm subpopulation composition to measures of 58 fertility competence and for improving existing interpretation of flow cytometry –based assessments of male 59 fertility. 60

61 Mammalian sperm must undergo a post -ejaculatory maturation process, known as capacitation, before they 62 can fertilize an egg. Within the female reproductive tract, sperm encounter biochemical effectors such as 63 bicarbonate or progesterone in the luminal fluid microenvironment, and exposure to these agents in vitro 64 reproducibly induce capacitation1,2. Capacitation is a multifaceted maturation process, and the complete 65 understanding of its mechanistic constituents remains a matter of ongoing investigation1. However, several 66 decades of empirical work implicate a subset of highly conserved biochemical processes including potassium-67 dependent plasma membrane hyper -polarization3, increased intracellular pH 4, 3’,5’-cyclic adenosine 68 monophosphate (cAMP)-dependent PKA activation 5, protein tyrosine phosphorylation 6,7, and a sustained rise 69 in intracellular calcium8. This conserved system of regulatory contingencies explains multiple aspects of sperm 70 behavior including motility pattern s such as the progressive to hyperactive transition 9, acrosomal exocytosis 71 (a.k.a. acrosome reaction) 10, and other putative sperm guidance mechanisms such as chemotaxis and 72 chemokinesis11. Other conserved sperm behaviors do not require direct biochemical control, but rather 73 manifest from intrinsic cellular mechanics under the constraint of microscale physical forces, such as collective 74 motion, rheotaxis, and thigmotaxis12–14. 75 76 Despite ongoing attempts to develop a deterministic molecular control model of sperm capacitation, these 77 changes are often not uniformly or universally achieved within an ejaculate. Significant heterogeneity has been 78 reported at nearly every level of the proposed cell signaling control pathway 15, including calcium 79 permeability16,17, plasma membrane hyperpolarization 18, kinetics of intracellular ion transients 19, protein 80 tyrosine phosphorylation20, extent and rate of the acrosome reaction 21, and metabolic state 2. This conserved 81 variation highlights that the ejaculate is not a homogenous population of identical cells, but rather a collection 82 of stochastically varying individuals with distinct phenotyp es that manifest uniquely depending on 83 microenvironmental conditions . Furthermore, repeated measures sampling of sperm functional parameters 84 from the same males over time also reveals substantial heterogeneity, indicating that sperm phenotypic 85 variation is an extremely complex, multiscale stochastic phenomenon, yet how this complexity relates to fertility 86 competence remains largely unknown22,23. 87 88 The persistence of sperm heterogeneity raises a central question: why should sperm, whose ultimate 89 physiological function is to fertilize an egg , display such variable responses to common signaling inputs that 90 should ostensibly improve the likelihood that they will be successful ? One possibility is that heterogeneity 91 reflects an unavoidable and potentially maladaptive “noise” as a simple consequence of deleterious mutations 92 during meiosis24,25 or incomplete maturation during residence in the epididymis26. In this scenario, fitness would 93 (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. The copyright holder for this preprintthis version posted December 25, 2025. ; https://doi.org/10.64898/2025.12.23.696226doi: bioRxiv preprint most likely decrease with increasing variation. However, heterospermic experiments (such as those performed 94 in birds) indicate that the opposite is true, heterogeneity generally increases fitness 27. In contrast to 95 maladaptive noise, phenotypic heterogeneity among sperm may confer enhanced fitness as an exploratory 96 mechanism. Under this model, e ach sperm may be similar to others, but unique in their exact combination of 97 phenotypic characteristics. Importantly, sperm are transcriptionally and translationally repressed, and as such, 98 may access only a limited repertoire of adaptive behaviors in response to environmental stressors as a 99 function of their genotype28. 100 101 When large numbers of sperm search for an egg , each with slight variation, the phenotype distribution may 102 enable the cell population as a whole to hedge against environmental uncertainty better than any individual 103 sperm can on its own . In other words, large sperm numbers may have evolved as a way for sperm to off load 104 adaptability under the constraints imposed by transcriptional/translational repression . In this view, 105 heterogeneity is not strictly maladaptive noise, but an essential physiological feature that shapes fertility 106 competence when the conditions of the fertilizing microenvironment are not known to the male a priori . 107 Through statistical variation, an ejaculate may explore a multiplicity of phenotypes in parallel, hedging on the 108 probability that at least some sperm will be competent to achieve fertilization under variable conditions or 109 unknown time to egg availability11,27. 110 111 Understanding this balance between sperm individuality and collective adaptability may reveal new methods 112 for predicting male fertility from semen parameters , thereby improving accuracy of fertility diagnostics or 113 enhancing IVF efficiency. Under these assumptions, fertility depends on the statistical dynamics of phenotype 114 distributions, necessitating analysis methods that treat sperm subpopulations as dependent wherein a change 115 in the proportion of one subpopulation must reflect a change in another. This approach may augment current 116 ensemble averaging methods29, conferring a significant advantage because it does not require any a priori 117 assumptions about what constitutes the ‘best’ sperm30—a common but logically dubious approach that ignores 118 the context dependence of fitness31. 119 120 Developing and testing a generalizable model of sperm exploratory dynamics will require new experimental 121

and statistical tools that correlate fertility with the dynamics of sperm subpopulation composition al 122 change. Flow cytometry has proven extremely useful for single-cell assessment of sperm phenotype 123 distributions and played a key role in the initial discovery of sperm subpopulations15,17,32–34. Here, we develop a 124 novel flow cytometry approach to measure and model sperm subpopulation compositional responses across 125 millions of individual sperm—isolated from the cauda epididymis of mice . We use intracellular calcium, 126 acrosome reaction status, and cell viability as surrogate measures of phenotypic changes related to in vitro 127 capacitation. We employ a novel method of systematic cell signaling control through 2D scaling of a capacitive 128 signaling input (bicarbonate) and an essential second messenger (extracellular calcium) , as well as their 129 interaction (bicarbonate x calcium) . We then apply phenotypic classification and a hierarchical regression 130 modeling methods originally developed for compositional analysis of taxonomic distributions in microbial 131 ecology to study how sperm subpopulation proportions respond to microenvironments with a range of signaling 132 impulses. 133 134

135 Chemicals and reagents were sourced from Sigma -Aldrich (St. Louis, MO). Specific culture media were 136 employed to facilitate various experimental conditions. Human tubal fluid minimal media (HTF -min) was used 137 as a base medium with (in mM) sodium chloride (91.2) , potassium phosphate monobasic (0.37), magnesium 138 sulfate heptahydrate (0.20), potassium chloride (4.69), sodium L-pyruvate (0.33), sodium L-lactate (21), and D-139 glucose (2.78), Bovine serum albumin (BSA) (4mg/mL), Sodium 4-(2-hydroxyethyl)-1-piperazineethanesulfonic 140 acid (10.4) (HEPES), and HEPES free acid (14.6). pH was maintained at 7.4 at 37°C and stability was verified 141 using a pH microelectrode . Additional supplements such as ethylene glycol bis(2-aminoethyl ether)-N,N,N',N'-142 tetra-acetic acid (EGTA) (1), sodium bicarbonate (0-10), and calcium chloride (0-1.8), were incorporated for 143 specific purposes. Media were vacuum filtered through a PTFE membrane with 0.22 um pore size and stored 144 under sterile conditions. 145 Animals 146 Adult male outbred CD-1 retired breeder mice were selected for th is study due to having known fertility status. 147 These mice were obtained from Charles River (Wilmington, MA, USA) and received care in accordance with 148 (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. The copyright holder for this preprintthis version posted December 25, 2025. ; https://doi.org/10.64898/2025.12.23.696226doi: bioRxiv preprint the guidelines set by the National Research Council Guide for the Care and Use of Laboratory Animals. The 149 Institutional Animal Care and Use Committee of East Carolina University approved all experimental 150 procedures. Mice were maintained on a 12-hour light/dark cycle and had access to water and food ad libitum. 151 Sperm Isolation 152 Testes with intact epididymides were dissected into pre -warmed phosphate -buffered saline (PBS, 37°C). 153 Cauda epididymides were transferred to non-capacitating HTF medium lacking bovine serum albumin, sodium 154 bicarbonate, and calcium chloride, and gently dissected to allow sperm to swim out (~15 minutes at 37°C in a 155 CO₂ incubator). Residual tissue was removed by centrifugation at 100 x g, and sperm were collected by 156 centrifugation at 800 x g and washed. Sperm counts were obtained using a hemocytometer. 157 Validation of Subcellular Dye Localization 158 Dye localization was confirmed by Laser confocal microscopy (LSM 800) with a 40x Plan -Apochromat 1.4 oil 159 DIC 1.4 NA objective. Images were captured in Zen Lite (Zeiss, Jena Germany ), background -corrected, 160 converted to 8-bit with an applied 16-color LUT for each composite channel in Fiji ImageJ35. 161 Validation of the EGTA-Calcium Clamp 162 Media were prepared with ultrapure water to minimize baseline free calcium. 1 mM EGTA (ethylene glycol -163 bis(β-aminoethyl ether)-N,N,N′,N′-tetraacetic acid) was used to clamp the ‘free’ Calcium ion concentration in 164 assay preparations. Titrations were measured using reference and calcium ion selective electrodes ( Kwik-Tip 165 series; World Precision Instrument s (WPI), Sarasota FL). To capture the dynamic range of the media, two 166 standard curves were generated using either 0.1 M CaCl 2 filling solution or 0.001 M. Once determined, the 167 calcium buffered conditions were included in assay incubations to ‘clamp’ the free calcium within a desired 168 range in conjunction with sodium bicarbonate pseudo -titrations. Linear equations obtained from the standard 169 curves were used to interpolate free calcium concentrations using various combinations of EGTA (1mM) and 170 CaCl2. Because free calcium concentration is pH dependent a mixture of HEPES free acid and base were 171 used to buffer pH, which was monitored using a pH microelectrode (WPI). 172 Microtiter Fluorometry 173 Fluorescence measurements were performed using an ID3 Max plate reader (Molecular Devices, San Jose, 174 CA) equipped with Spectramax acquisition software. A two -dimensional 96-well format was designed to 175 maximize the number of experimental conditions evaluated over time. Each condition was monitored at 5-176 minute intervals, striking a balance between sufficient temporal resolution and minimizing light exposure. Three 177 fluorescent dyes were employed to monitor key physiological parameters: SNARF -1 Acetoxy Methyl Ester 178 (AM; 10 µM) for intracellular pH, Fura -2 AM (10 µM) for intracellular calcium, and Ethidium Homodimer -1 for 179 nuclear membrane permeability as a measure of cell viability. This multiplexed approach enabled time -180 resolved tracking of sperm responses across a matrix of extracellular calcium and bicarbonate concentrations. 181 All raw fluorescence data were analyzed using GraphPad Prism version 10.4.1. 182 183 Flow Cytometry 184 For high-resolution single-cell fluorescence measurements, d ata were acquired on a Cytek Aurora equipped 185 with 405, 488, 561, and 637 nm lasers with SpectroFlo V2.2 acquisition software (Cytek, Fremont, CA, USA). 186 Side scatter (SSC), side scatter –blue (SSC-B), and forward scatter (FSC) gains were optimized to distinguish 187 sperm from debris. Singlet sperm were gated using: Forward scatter Area (FSC-A) vs. Forward scatter height 188 (FSC-H) and Side scatter from the near -UV laser (SSC-B) vs. forward scatter ( FSC) to exclude doublets, 189 fragments, and media particles ( Initial gating and data export was performed with FlowLogic V8.7). Positive 190 controls were treated for 15 min utes prior to acquisition. The detergent digitonin was used to induce plasma 191 membrane permeability (death) and the calcium ionophore A23187 (10 µM) to induce calcium permeability and 192 stimulate maximal acrosom al exocytosis. The multiplexed dye panel included Indo-1, conjugated peanut 193 agglutinin lectin (PNA)-FITC (1 µg/mL), and TO-PRO-3 (0.1 µM) for simultaneous Ca²⁺, acrosome, and viability 194 measurement respectively. Notably, PNA-FITC fluorescence will increase in live mouse sperm as the 195 acrosome reaction progresses due to the presence of externalized inner-leaflet glycoproteins to the outer 196 surface of the plasma membrane36. This is sometimes confused with the opposite interpretation due to FITC 197 signal being lost following the acrosome reaction in sperm extracted with polar organic solvent. For solvent 198 (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. The copyright holder for this preprintthis version posted December 25, 2025. ; https://doi.org/10.64898/2025.12.23.696226doi: bioRxiv preprint extracted sperm, the lectin protein binds to the outer leaflet glycoproteins of the acrosomal vesicle made 199 available by solvent permeation of the plasma membrane ; thus the signal decreases following acrosomal 200 exocytosis. Raw data exported from FlowLogic were analyzed using a bespoke program written in Python 201 (V3.11)37–39. Source code for the program is publicly available at ( https://github.com/CAS-202 ReproLab/P009_Flow-Cytometry-Tools). 203 204 Classification into Subpopulations 205 Positive and negative control conditions were included at time of data collection for every assay. For cell 206 viability measured via TO-PRO-3, the positive control condition used digitonin to permeabilize the sperm. For 207 acrosome reaction measured via FITC conjugated peanut agglutinin lectin, the calcium ionophore A23187 was 208 used as a positive control to stimulate the acrosome reaction . A kernel density estimation (KDE) - naive Bayes 209 classifier was used to classify the cells as live/dead or acrosome reacted/unreacted using e xperimental 210 fluorescence intensity values and control data. Briefly, KDE’s were fit to the fluorescence intensity distributions 211 using Gaussian KDE methods from the Python scikit-learn library38. The KDE’s estimate the class condition al 212 probability densities p(x | Ck), where x is the observed fluorescence intensity and Ck is the class. Scott’s rule 213 was used to calculate the bandwidth40. The posterior probability was then calculated for experimental data in 214 each filtered treatment condition as follows. 215 𝑃(𝑝𝑜𝑠|𝑥𝑖) = 𝑝(𝑥𝑖|𝑝𝑜𝑠)𝑃(𝑝𝑜𝑠) 𝑝(𝑥𝑖|𝑝𝑜𝑠)𝑃(𝑝𝑜𝑠) + 𝑝(𝑥𝑖|𝑛𝑒𝑔)𝑃(𝑛𝑒𝑔) 216 Where lowercase p denotes probability density ( fluorescence intensity) and uppercase P denotes the prior 217 probability for positive (pos) or negative (neg) classes respectively. Prior probabilities were chosen based on 218 review of previous literature and descriptive analysis of the data. The decision rule (τ) assigns positive if the 219 posterior probability > τ, otherwise assigns negative. The decision rule was chosen for each biological replicate 220 (mouse) by plotting the unfiltered posteriors and manually identify ing the mid-point trough in the distribution 221 which was bimodal in all cases. 222 Statistical Modeling and Analysis 223 Model summary and motivation: All analyses were performed in Python (v 3.11) using the PyMC probabilistic 224 programming framework (v4.0)41. Posterior inference diagnostics and visualization were performed using ArviZ 225 (v0.22.0)42. The f low cytometry experiments in this report generate cell cou nts for mutually exclusive 226 subpopulations of sperm. The data are compositional and inherently constrained , meaning that an increase in 227 one subpopulation’s share of the total population must be compensated by a decrease in another. Modeling 228 approaches commonly used in flow cytometr y studies treat cell subpopulations independently, violating th is 229 important constraint. To avoid this issue and take full advantage of the power of single-cell measurements, we 230 employed a Dirichlet-Multinomial hierarchical regression model adapted from recent advances in compositional 231 analysis of cell subpopulations in microbial ecology 43–45. This approach accounts for 1) multinomial sampling 232 noise, 2) biological heterogeneity among replicate animals (overdispersion), and 3) treatment dependent 233 effects on subpopulation composition. 234 Model Overview: Let 𝑦𝑖,𝑘 denote the number of cells assigned to subpopulation 𝑘 in 2D assay well 𝑖 (i.e., 235 treatment condition) , with total sampled count from the assay well 𝑁𝑖 = ∑ 𝑦𝑖,𝑘𝑘 . The underlying true 236 subpopulation proportions for that assay well are denoted by the vector 𝜋𝑖 = (𝜋𝑖,1, … , 𝜋𝑖,𝐾), where 𝐾 = 4 (Live 237 acrosome reacted - LR; Live acrosome unreacted - LUR; Dead acrosome reacted - Dr; and Dead acrosome 238 unreacted- DUR). We modeled the observed counts as 239 𝑦𝑖 | 𝜋𝑖 ~ 𝑀𝑢𝑙𝑡𝑖𝑛𝑜𝑚𝑖𝑎𝑙(𝑁𝑖, 𝜋𝑖) 240 With a Dirichlet prior on the composition: 241 𝜋𝑖 | 𝛼𝑖 ~ 𝐷𝑖𝑟𝑖𝑐ℎ𝑙𝑒𝑡(𝛼𝑖) 242 where 𝛼𝑖 = (𝛼𝑖 1, … , 𝛼𝑖,𝐾 ) is a vector of Dirichlet concentration parameters . Large values of 𝛼𝑖 ,𝐾 correspond to 243 more stable (less variable) subpopulation proportions, whereas small values correspond to greater well-to-well 244 variability around the expected proportion. 245 (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. The copyright holder for this preprintthis version posted December 25, 2025. ; https://doi.org/10.64898/2025.12.23.696226doi: bioRxiv preprint Bayesian regression on concentration parameters: To model the effects of bicarbonate and calcium on the 246 subpopulation composition, we expressed the linear predictor 𝜂𝑖,𝑘 for each well 𝑖 and subpopulation 𝑘 as: 247 𝜂𝑖,𝑘 = 𝑋𝑖𝛽𝑘 + 𝑢𝑧[𝑖],𝑘 248 Where 𝑋𝑖 denotes the row of the design matrix corresponding to assay well 𝑖 (a 1 × 4 vector of predictors in 249 this case), and 𝛽𝑘 is a 4 × 1 column vector of fixed effects describing how each predictor shifts proportions of 250 subpopulation (𝑘). 𝑢𝑧[𝑖],𝑘 is a random intercept for mouse 𝑧 from which the [𝑖] sample was collected, 251 accounting for baseline differences among animals due to biological variation. The linear predictors for all 252 subpopulations in assay well 𝑖 were collected in the vector 𝜂𝑖 = (𝜂𝑖 1, … , 𝜂𝑖,𝐾 ) . These were mapped to 253 subpopulation probabilities 𝑝𝑖 using a softmax link function: 254 𝑝𝑖,𝑘 = 𝑒𝜂𝑖,𝑘 ∑ 𝑒𝜂𝑖,𝑘𝐾 𝑘=1 255 this ensures each 𝑝𝑖,𝑘 > 0 and ∑ 𝑝𝑖,𝑘 = 1𝑘 . 256 𝛼𝑖,𝑘 = 𝜙𝑝𝑖,𝑘 257 Where 𝜙 > 0 is a global concentration (intensity) parameter shared across assay wells and 𝑝𝑖 = (𝑝𝑖,1, … , 𝑝𝑖,𝐾) is 258 a probability vector on the K-simplex (i.e., a 𝐾 − 1 dimensional space that represents all possible combinations 259 of subpopulation proportions that sum to one ). Under this parameterization, 𝑝𝑖 represents the expected 260 subpopulation proportions for assay well 𝑖, and 𝜙 controls the level of well-to-well variation. 261 Priors, standardization, and interpretation: To stabilize estimation and conservatively reflect weak prior 262 information, we used the following prior distributions in the PyMC implementation: 263 Fixed effects—for each predictor 𝑗 = 1, … , 𝐽 and subpopulation 𝑘 = 1, … , 𝐾, the fixed -effect coefficients were 264 assigned independent priors: 265 𝛽𝑗,𝑘 ∼ 𝑁𝑜𝑟𝑚𝑎𝑙(0,1) 266 Random effects (mouse -level intercepts )—for each assay well 𝑖 and subpopulation 𝑘 = 1, … , 𝐾, a random 267 intercept 𝑢𝑧[𝑖],𝑘 was included to account for baseline differences among mic e where 𝑧[𝑖] indexes the mouse 268 from which well 𝑖 was obtained. The random effects were assumed to be independent across mice and 269 subpopulations and were modeled as: 270 𝑢𝑧[𝑖],𝑘 ∼ 𝑁𝑜𝑟𝑚𝑎𝑙(0, 𝜎𝑢) 271 The standard deviation 𝜎𝑢, was assigned a 𝐻𝑎𝑙𝑓𝑁𝑜𝑟𝑚𝑎𝑙(1) prior. 272 Global concentration (overdispersion) hyperparameter: 273 𝜙 ∼ 𝐻𝑎𝑙𝑓𝑁𝑜𝑟𝑚𝑎𝑙(5) 274 Which serves as a prior favoring moderate to large values while allowing the data to determine the extent of 275 overdispersion. Continuous predictors (i.e., media bicarbonate, free calcium, and their interaction) were 276 standardized to z-scores prior to fitting the model to place them on a comparable scale so that the priors on 𝛽𝑘 277 corresponded to similar prior beliefs about effect sizes across predictors. 278 Because the mapping from the linear predictors to subpopulation proportions was nonlinear and coupled 279 across subpopulations via the SoftMax link function, the coefficients 𝛽𝑗,𝑘 could not be interpreted directly as 280 fold-changes in observed proportions. Instead, treatment effects are expressed in terms of posterior predicted 281 proportions: 282 𝐸[𝜋𝑖,𝑘 | 𝑝𝑎𝑟𝑎𝑚𝑒𝑡𝑒𝑟𝑠] = 𝛼𝑖,𝑘 ∑ 𝛼𝑖,𝑘𝐾 𝑘=1 = 𝜙𝑝𝑖,𝑘 𝜙 ∑ 𝑝𝑖,𝑘𝑘 = 𝑝𝑖,𝑘 283 These expected values represent the model’s estimate of the ‘true’ underlying probability of each 284 subpopulation for each treatment condition, accounting for both sampling noise and between animal variation. 285 (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. The copyright holder for this preprintthis version posted December 25, 2025. ; https://doi.org/10.64898/2025.12.23.696226doi: bioRxiv preprint For model fitting , the No -U-Turn Sampler (NUTS) from PyMC was used for Markov Chain Monte Carlo 286 sampling41. Hamiltonian Monte Carlo sampling that NUTS employs was previously found to result in greater 287 accuracy in compositional analysis of simulated datasets compared to other sampling methods 45. Sampling 288 was conducted with 4 independent Markov chains, each drawing 1000 posterior samples after 1000 tuning 289 iterations. The target acceptance probability was 0.9. Convergence was assess ed using the Gelman -Rubin 290 statistic (𝑅 ̂ 400 per parameter. Divergent transitions were not observed 291 with these hyperparameter choices. Posterior summaries, raw proportion counts, medians, and 95% credible 292 intervals were computed for all fixed and random effects. 293

294 295 A 2D subculture assay for assessing signaling interaction effects during in vitro sperm capacitation 296 We first sought to develop a culture assay system to measure average cell physiological state changes in 297 response to controlled signaling inputs, we employed 2D microtiter fluorometric assays (Fig ure 1A). The 298 assays enabled assessment of changes in response (e.g., intracellular calcium, cell viability, etc) to 1) 299 Figure 1. A 2D subculture assay for assessing signaling interaction effects during in vitro sperm capacitation. A) Diagram of a 96-well plate design allowing combinations of chemically ‘clamped’ free calcium and bicarbonate concentrations, each representing distinct microenvironments that sperm might encounter during the search for an egg. B) Kinetic plots showing Indo -1 ratios over time for sperm exposed to 0 and 10 mM bicarbonate concentrations over a corresponding range of chemically ‘clamped’ extracellular calcium , demonstrating the interaction effects apparent in bicarbonate signaling control of intracellular calcium uptake. C) Viability measurements using ethidium homodimer-1, a live-cell impermeable dye, showing how external conditions affect sperm viability over time. D–F) Conceptual examples of possible sperm subpopulation heterogeneity in responses to external signals wherein the same total signal can be reflected in completely different underlying distributions : D) A symmetric (Gaussian -like) distribution. E) A uniform respons e. F) A power distribution wherein 80% of the signal is localized among only 20% of the cells. (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. The copyright holder for this preprintthis version posted December 25, 2025. ; https://doi.org/10.64898/2025.12.23.696226doi: bioRxiv preprint increasing concentrations of bicarbonate and calcium , 2) the change over time, and 3) the interaction effects 300 between these two predictors. These measurements revealed that bicarbonate stimulation pro motes calcium 301 uptake in a time dependent manner using radiometric Indo-1 AM (Kd ~230nM) (Fig1B). Increasing extracellular 302 free calcium concentration increased Indo-1 ratio (i.e., bound /unbound) but did not exhibit kinetic effects , 303 Figure 2: Gating strategy for live-intact cell identification. A) Representative forward and side scatter area contour plot show ing all detected particles, including media, debris, and cells. B) Forward and side scatter area contour plot showing increased detection of small particles and cell debris after digitonin permeabilization. The intact cell gate remains highlighted in red. (C) Doublet exclusion using forward scatter area (FSC -A) versus height (FSC - H), used to aggregates from the analysis for intact cells . (D) Doublet exclusion using forward scatter area (FSC -A) versus height (FSC -H) to remove aggregates from permeabilized cell samples. (E) TO-PRO-3 viability staining revealed live (membrane -intact) cells as TO -PRO-3–negative, confirming a high proportion of intact sperm in this gate. (F) TO-PRO-3 staining labeling permeabilized whole cells with high TO-PRO-3 fluorescence signal, confirming membrane disruption and allowing clear discrimination between live-intact cells and dead-permeabilized cells. (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. The copyright holder for this preprintthis version posted December 25, 2025. ; https://doi.org/10.64898/2025.12.23.696226doi: bioRxiv preprint indicating that a relatively greater average baseline intracellular calcium concentration can be forced by 304 increasing free calcium in the media , but that bicarbonate is still required to facilitate uptake. The kinetics and 305 endpoint Indo -1 ratio were approximately matched between positive control conditions (calcium ionophore 306 ionomycin) and a bicarbonate + calcium condition (10mM and 1.3 mM respectively) (Figure 1B). Cell viability 307 was simultaneously monitored using live -cell impermeable (cationic) ethidium homodimer-1, which transitions 308 from weakly fluorescent to strongly fluorescent when it binds DNA (Figure 1C) . Positive control included 309 detergent treated (permeabilized) cells. Interestingly, treatment groups that included bicarbonate stimulated the 310 greatest loss of cell viability over time . Together these results predict that calcium uptake is kinetically 311 dependent on bicarbonate, and that 312 bicarbonate is positively correlated with loss 313 of cell viability. 314 Notably, there is a critical limitation of 315 interpreting bulk cell-population 316 measurements common to this sort of 317 approach—i.e., the inability to resolve how 318 individual cells within a population respond 319 to changes in the predictor. The fluorescent 320 signal in both cases (Indo -1 AM and 321 Ethidium homodimer-1) is the sum signal of 322 the entire cell population. The shape of the 323 distribution that signal is drawn from cannot 324 be assumed because the fluorescence 325 intensity may be distributed among the cells 326 in a ny number of different ways while still 327 retaining the same mean fluorescence 328 intensity. As examples the distribution of 329 signal could follow: 1) an exponential with a 330 small number of sperm being very bright ly 331 fluorescent (Figure 1D), 2) a uniform 332 distribution in which all of the cells exhibit 333 similar intensities (Figure 1E), or 3) a power 334 law distribution with ~20% of the sperm 335 accounting for ~80% of the signal (Figure 336 1F). There are many other possible 337 distributions not discussed here, and 338 importantly, the shape of signal distribution 339 could be different for various experimental 340 treatment conditions. Thus, this type of ‘bulk’ 341 measurement assay simply cannot 342 distinguish between the se very different 343 scenarios and has a limited utility as a result 344 - a fact which is true for all similar assays 345 that do not make measurements with single-346 cell resolution such as western blotting, 347 mass spectrometry label-tracing analysis, 348 etc. 349 Gating strategy for live-intact cell identification 350 Flow cytometry measures particles at or above the size of the nano length scale, including media components, 351 cellular fragments, and intact cells —necessitating extensive controls for live -cell detection . To improve the 352 accuracy of cell identification, all replicates of spectral flow data included cell-free and single-stain controls. 353 When samples were treated with digitonin to permeabilize the cells resulting in loss of intracellular contents 354 and a shift in refractive index , the density of scanned events shifted notably (Fig. 2 A, B), consistent with 355 membrane permeabilization and increased detection of subcellular material. In untreated samples gated for 356 live cells, fewer total events were detected (Fig. 2C, D). After gating for single cells, all remaining events were 357 positively stained for TO-PRO-3, indicating loss of membrane integrity and widespread cell death (Fig. 2 E, F). 358 Figure 3: Validation of multiplex dye localization. Indo-1 localizes to the nucleus and midpiece, FITC conjugated peanut agglutinin (PNA) lectin labels whole cell with strong er relative signal at the acrosomal cap once exposed , and TO -PRO-3 fluorescence indicates nuclear DNA in non-viable (dye permeable) cells. Scale bar = 50 µm. Calibration bar = 16 -color for 8 -bit encoding. (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. The copyright holder for this preprintthis version posted December 25, 2025. ; https://doi.org/10.64898/2025.12.23.696226doi: bioRxiv preprint Mouse sperm are delicate cells and will ‘decapitate’ easily when the haploid nucleus separates from the 359 midpiece. To account for this common cell fragmentation pattern in the gating scheme , sperm were stained 360 with Hoechst 33342 and subjected to repeated shear stress (mechanical vortex) for 5 minutes to disrupt their 361 structure. Hoechst staining in combination with forward and side scatter measurements facilitated identification 362 of gating regions that contained decapitated cells (not shown). 363 Validation of multiplex dye localization 364 To examine capacitation responses under controlled conditions, the 2D fluorometric assay was modified to 365 include three bicarbonate concentrations (0, 5, and 10 mM) and four chemically ‘clamped’ extracellular free 366 calcium concentrations (0, 87.45, 660, and 1300 μM). To validate that the spectral flow cytometry 367 measurements accurately reflect biological interpretation, sperm were stained with the full dye multiplex group: 368 Indo-1 AM, PNA lectin –FITC, and TO -PRO-3 and imaged using laser scanning confocal microscopy . Indo-1 369 localizes to the head and midpiece, consistent with regions of high calcium signaling activity. PNA lectin -FITC 370 weakly labeled the entire sperm surface but intensely labeled the acrosomal region in reacted sperm 371 consistent with previous reports 36 (Figure 3). Live-cell impermeable TO-PRO-3 selectively stains nuclear DNA. 372 Together, the observed staining patterns confirm the expected spatial distribution of each dye and support their 373 use for downstream classification in our flow cytometry assays. 374 Classification of live sperm into subpopulations 375 Qualitative manual gating is common among flow cytometry studies. Here, we employed statistical 376 classification methods to reduce potential bias and automate the process of classifying sperm subpopulations. 377 Figure 4: Effect of extracellular calcium and bicarbonate on cell viability and acrosome reaction . (A-C) Indo-1 ratio (intracellular calcium) as a function of chemically ‘clamped’ extracellular calcium (in µM) for classes grouped by live/dead status. Extracellular bicarbonate increasing from left to right (0-10 mM). Stacked Boxen plots show quantiles for visualization of underlying distribution shapes. Plots i nclude data pooled from N=6 mice , totaling approximately 4.62 million cells . (D-F) Indo-1 ratio (intracellular calcium) as a function of chemically ‘clamped’ extracellular calcium (in µM) for classes grouped by acrosome reacted status. Only live cells were included in plots. Extracellular bicarbonate increasing from left to right (0 -10 mM). Plots include live-cell data pooled from N=6 mice, totaling approximately 3.69 million cells. Outliers indicated by circles (1.5x interquartile range). (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. The copyright holder for this preprintthis version posted December 25, 2025. ; https://doi.org/10.64898/2025.12.23.696226doi: bioRxiv preprint Given the fluorescent dye compliment that we used, there were four possible subpopulation classes (Figure 378 4A): 1) Live/Acrosome Unreacted (L UR), 2) Live/Acrosome Reacted (L R), 3) Dead/Acrosome Unreacted (D UR), 379 and 4) Dead/Acrosome Reacted (D R). To scale the single cell responses to ground truth effects, positive and 380 negative control conditions were used in every biological replicate tested, with calcium ionophore (A23187) as 381 an acrosomal exocytosis positive control and permeabilizing detergent (digitonin) as a cell death positive 382 control. The positive controls contained exogenous clamped 1.3 mM CaCl 2 and 10 mM HCO 3. The negative 383 controls contained no exogenous CaCl2 or HCO3. The ToPro3 and PNA lectin-FITC responses were smoothed 384 using kernel density estimates to approximate a probability density function for each intensity (Figure 4B, C). 385 Representative probability density plots with KDE’s demonstrated distinct probability densities for positive 386 control condition. The probability density estimates were then used in conjunction with a naive Bayes classifier 387 Figure 5: Classification into subpopulations. (A) diagram demonstrating possible cell subpopulation classifications for the response variables measured in this study and corresponding fluroscent dye interpretations . L UR= Live/Unreacted, LR= Live/Reacted, DUR= Dead/Unreacted, and D R= Dead/Reacted. Notably, each class represents an irreversible physical process. (B,C) Representative probability density plots for positive and negative controls conditions demonstrating distinct probability distributions (fitted to kernel density estimates) for each condition class (i.e., live/dead, acrosome reacted/unreacted). (B) PNA-FITC fluorescence for positive control (10 µM A23187) and negative control (ionophore free, low calcium, low bicarbonate) conditions. (C) TO -PRO-3 fluorescence for positive control (1 06.6 µM digitonin) and negative control (detergent free, low calcium, low bicarbonate) conditions. (D) Representative kernel density estimate (KDE) plots for each classified subpopulation Vs. corresponding intracellular calcium (Indo-1 ratio). Plots organized by each pairwise combination of extracellular bicarbonate (mM) and calcium (µM). (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. The copyright holder for this preprintthis version posted December 25, 2025. ; https://doi.org/10.64898/2025.12.23.696226doi: bioRxiv preprint to assign every measured cell in the treatment groups to either positive or negative control classes. Joint class 388 distributions were assigned to one of each of the four subpopulations outlined above. 389 The observed off -target labeling of PNA lectin -FITC (described in the previous section) complicated the 390 spectral interpretation due to signal that increases within a relatively small dynamic range during acrosomal 391 exocytosis. However, the shift in probability density between positive and control conditions consistently 392 revealed a high signal intensity region with greater relative probability density (Figure 4B). Additionally, KDE’s 393 for ToPro3 gave very good separation between positive and negative control conditions, confirming 394 membrane-compromised (non-viable) cells with distinct nuclear fluorescence could be detected (Figure 4C). 395 The extent to which change in intracellular calcium controls acrosomal exocytosis during capacitation is an 396 ongoing topic of debate. We examined the distribution of Indo -1 ratio among in a representative population of 397 cells from a single mouse to qualitatively assess the effect of microenvironmental conditions on intracellular 398 calcium (Figure 4D). Indo-1 ratios of all subpopulations were relatively similar at low extracellular calcium 399 concentrations. High calcium x bicarbonate treatment shifted the distribution of subpopulations toward a low-400 density subpopulation of high intracellular calcium sperm dominated largely by dead cells. The live, acrosome 401 unreacted subpopulation remained the bulk of the total population under all treatment conditions. Together, 402 these data demonstrate that cauda epididymal sperm from the same animal can respond to a range of 403 Figure 6: Dirichlet-Multinomial hierarchical regression model of subpopulation composition as a n adaptive response to microenvironmental conditions. (A-C) Measured proportions of subpopulation classes across each of the treatment conditions (HCO3 x Calcium) for N=6 mice. Outliers indicated with filled diamonds (1.5x IQR). (D-F) Mean posterior probability estimates of the underlying multinomial sampling probabilities of subpopulation compositions for each treatment condition . Outliers indicated by circles (1.5x IQR). Bicarbonate concentrations for each treatment indicated at the top of the panel. Corresponding model credible intervals are provided in table 7. (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. The copyright holder for this preprintthis version posted December 25, 2025. ; https://doi.org/10.64898/2025.12.23.696226doi: bioRxiv preprint signaling impulse intensities by shifting the composition of cell subpopulations. Under each treatment 404 condition, the subpopulation distributions exhibited differing degrees of heterogeneity. 405 Effect of extracellular calcium and bicarbonate on cell viability and acrosome reaction 406 To extend our p revious qualitative analysis of within -mouse indo-1 ratio distributions for each subpopulation, 407 we examined the class distributions of sperm phenotypes using pooled data from N=6 mice (~4.6 2 million 408 sperm) and plotted each cell’s Indo -1 ratio against the experimental treatment conditions (bicarbonate x 409 calcium) for each mouse. Using a KDE-Bayes classifier, individual sperm were classified as either live or dead 410 based on TO-PRO-3 staining patterns compared with positive and negative controls. Data did not appear to be 411 symmetrically distributed, indicating that they would not fulfill assumption criteria for statistical designs that are 412 typically implemented in flow cytometry studies. At low calcium concentrations, median Indo -1 ratios were 413 greater in live cells than dead cells (Figure 5 A-C). Interestingly, this relationship flipped, and median Indo -1 414 ratios were greater in dead cells than live cells at high calcium concentrations (0.66 and 1.3 mM). For all 415 conditions, Indo-1 ratios were positively correlated with increasing extracellular calcium and bicarbonate, but 416 the effect was larger among dead cells likely because dead cells equilibrate calcium passively. Next, we 417 examined the distributions of cells classed as acrosome reacted or unreacted in live cells pooled from N=6 418 mice (~3.69 million live sperm). Surprisingly, no correlation was observed between Indo-1 ratio and acrosome 419 reacted status in any of the treatment conditions (Figure 5D-F). 420 Dirichlet-Multinomial hierarchical regression model of subpopulation composition as a n adaptive 421 response to microenvironmental conditions. 422 Rather than treating subpopulations as statistically independent, we analyzed the conditional changes in 423 subpopulation distributions using a hierarchical Bayesian regression model . To examine the subpopulation 424 distributions among each treatment condition, we plotted the observed sampling proportions (Figure 6A-C). In 425 mouse sperm, bicarbonate activates soluble aden ylate cyclase, which increases calcium permeability through 426 cAMP dependent interactions with the sperm specific cation channel family (CatSper)8. Conditional effects on 427 the proportions of Live acrosome unreacted and all dead sperm were relatively stable across conditions. 428 Interestingly, the highest proportion of live acrosome reacted cells was observed at low extracellular calcium 429 concentrations independent of extracellular bicarbonate concentration (Figure 6A-C). 430 431 [HCO3] (mM) [Ca2+] (µM) Live Unreacted (LUR) Live Reacted (LR) Dead Unreacted (DUR) Dead Reacted (DR) 0 0 0.71 (0.58, 0.81) 0.14 (0.08, 0.24) 0.07 (0.04, 0.13) 0.05 (0.02, 0.08) 0 87.45 0.72 (0.59, 0.81) 0.14 (0.08, 0.24) 0.07 (0.04, 0.13) 0.05 (0.03, 0.10) 0 660 0.73 (0.61, 0.82) 0.12 (0.07, 0.20) 0.08 (0.05, 0.15) 0.05 (0.03, 0.09) 0 1300 0.74 (0.62, 0.84) 0.10 (0.05, 0.18) 0.09 (0.05, 0.17) 0.05 (0.02, 0.10) 5 0 0.68 (0.56, 0.78) 0.12 (0.07, 0.19) 0.12 (0.07, 0.19) 0.06 (0.04, 0.11) 5 87.45 0.69 (0.57, 0.79) 0.11 (0.06, 0.18) 0.12 (0.07, 0.20) 0.06 (0.04, 0.11) 5 660 0.75 (0.64, 0.83) 0.07 (0.04, 0.12) 0.10 (0.06, 0.18) 0.05 (0.03, 0.10) 5 1300 0.80 (0.70, 0.87) 0.05 (0.02, 0.08) 0.09 (0.05, 0.17) 0.04 (0.02, 0.08) 10 0 0.63 (0.49, 0.74) 0.10 (0.05, 0.16) 0.18 (0.10, 0.29) 0.07 (0.04, 0.14) 10 87.45 0.64 (0.51, 0.76) 0.09 (.04, 0.14) 0.17 (0.10, 0.28) 0.07 (0.04, 0.13) 10 660 0.75 (0.63, 0.84) 0.04 (0.02, 0.07) 0.13 (0.07, 0.23) 0.06 (0.03, 0.10) 10 1300 0.84 (0.73, 0.90) 0.02 (0.007, 0.04) 0.09 (0.05, 0.17) 0.04 (0.02, 0.09) 432 Table 1: Summary of median posterior probabilities 𝑬(𝝅𝒊,𝒌|𝒑𝒂𝒓𝒂𝒎𝒆𝒕𝒆𝒓𝒔). Expected multinomial sampling probabilities 433 for each subpopulation under each treatment condition. Accompanying 95% credible intervals (𝑞2.5%, 𝑞97.5%). N= 5 434 mice. 435 The posterior predictions from our hierarchical regression model indicate a few interesting patterns regarding 436 expected subpopulation probabilities under various microenvironmental signaling conditions (Table 1). First, 437 the expected proportion of live unreacted (LUR) sperm was inversely related to both bicarbonate and calcium 438 concentration reflected in an ~7-20% difference in LUR proportion between calcium/bicarbonate free conditions 439 (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. The copyright holder for this preprintthis version posted December 25, 2025. ; https://doi.org/10.64898/2025.12.23.696226doi: bioRxiv preprint and those of high concentrations. Second, the subpopulation of dead reacted ( DR) cells did not appreciably 440 change in a patterned way among any of the conditions , indicating that acrosomal exocytosis likely does not 441 predispose sperm to an increased probability of death. Finally, the predicted proportion of dead unreacted 442 (DUR) sperm indicated that the ratio of bicarbonate to free calcium may be important – with apparent toxicity 443 when bicarbonate was present at low relative calcium concentrations particularly at higher bicarbonate 444 concentration (i.e. 10mM). 445

446 This report reveals that mouse sperm capacitation is characterized by substantial and structured phenotypic 447 heterogeneity, even among cells originating from the same male and exposed to identical microenvironmental 448 conditions. Using spectral flow cytometry to assess sperm phenotype distributions with single-cell resolution, 449 combined with a controlled two -dimensional titration of bicarbonate and extracellular free calcium, we 450 demonstrate that sperm do not respond uniformly to capacitating signals. Instead, they redistribute across 451 distinct physiological subpopulations in a manner that depends nonlinearly on the impulse strengths of the 452 signaling inputs. 453 The findings are c onsistent with earlier work showing variability in calcium permeability 16,17, membrane 454 potential18,33, tyrosine phosphorylation 20, and acrosome reaction propensity 33,46–48. The diversity of responses 455 observed, and their sensitivity to microenvironmental conditions emphasizes that capacitation is not a simple 456 synchronized transition , but a population -level stochastic process shaped by complex biochemical 457 determinants that vary among large numbers of cells . For these reasons, ensemble averaging in sperm or 458 semen samples under the assumption that sperm vary independently is unlikely to carry strong predictive 459 value. This is important because the dynamic structure of sperm subpopulations is likely to be biologically 460 consequential for fertility and may provide useful information for the quantitative prediction of fertilizing 461 potential from semen analysis. 462 The interaction between bicarbonate and extracellular calcium revealed several unexpected and informative 463 patterns. Although both ions are required for canonical capacitation signaling 3–6,8, the highest proportions of 464 live, acrosome-reacted sperm were observed under relatively low extracellular calcium and low bicarbonate. 465 Though somewhat surprising, this finding is consistent with a previous report of biphasic effects on tyrosine 466 phosphorylation induced by controlled extracellular calcium in the presence of a chelating agent49. Increasing 467 either stimulus elevated intracellular calcium but simultaneously increased cell death, producing 468 subpopulations dominated by non -viable, calcium -loaded cells. These findings align with reports that 469 intracellular calcium elevation is necessary but not sufficient for spontaneous acrosomal exocytosis 5,8,9, and 470 that excessive calcium influx can compromise viability. Although notably, this effect may also result from non -471 viable cells inability to actively maintain a low intracellular calcium potential. The apparent associations 472 between bicarbonate, calcium load , and acrosom e reaction status in live cells suggests that capacitating 473 stimuli may push many sperm toward non -functional endpoints, reducing the fraction capable of fertilization. 474 Interestingly, bicarbonate appeared to be conditionally toxic to mouse sperm when extracellular calcium was 475 low. 476 The comparison between bulk cell spectrofluorometric measurements and single-cell flow cytometry further 477 highlights the importance of measuring sperm phenotype s with single -cell resolution . Population -averaged 478 fluorescence masked fundamentally different underlying distributions, underscoring longstanding concerns 479 about interpreting capacitation solely from ensemble measurements 1,15. Single-cell approaches are particularly 480 important because the fertilizing potential of an ejaculate is best understood as a statistical property of many 481 cells, not as the behavior of a hypothetical “best” sperm implied by ensemble averaging. 482 The Dirichlet–multinomial hierarchical regression model provide s a principled framework for quantifying how 483 treatments reshape the entire subpopulation composition while accounting for multinomial sampling noise and 484 biological variation among biological replicates. By modeling conditional changes in the expected proportions 485 of live unreacted, live reacted, dead unreacted, and dead reacted cells - this approach avoids the interpretive 486 pitfalls of treating subpopulations independently. The finding that between -male variation in baseline 487 subpopulation structure is substantial is also consistent with previous reports of high within - and between -488 individual variability in sperm functional phenotypes among human males 22,23. The resulting predictive 489 probability surfaces provide a quantitative representation of sperm subpopulation responses to extracellular 490 cues and complement mechanistic models that attribute capacitation heterogeneity to variable ion channel 491 expression or signaling kinetics17,19,21. 492 (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. The copyright holder for this preprintthis version posted December 25, 2025. ; https://doi.org/10.64898/2025.12.23.696226doi: bioRxiv preprint The results also relate to broader evolutionary questions about sperm number and diversity. Many species 493 produce sperm in numbers far exceeding those required for fertilization , but fertility also collapses at ‘low’ 494 sperm counts that may still consist of many thousands or even millions of cells24. Heterospermic insemination 495 experiments ha ve shown that phenotypic heterogeneity contributes to adaptive advantages in uncertain 496 reproductive environments such as female reproductive tracts of hybridizing species 27,50. Our findings support 497 the hypothesis that sperm populations hedge against uncertainty by distributing cells across multiple 498 physiological states that are sensitive to mechanistic signals through the statistical variability of sperm 499 subpopulations. In vivo, only a small minority of sperm that reach the oviduct display an intact acrosome 20,46, 500 and the timing of capacitation appears to align with anticipation of egg availability 11. A heterogeneous 501 distribution of phenotypes may therefore maximize the likelihood that some sperm encounter the egg in an 502 appropriately primed state. 503 Several limitations should be noted for this study. First, interpretation of acrosomal status is constrained by the 504 modest dynamic range of PNA -FITC in live cells and its susceptibility to off -target binding36. Though previous 505 reports have shown that live cell measurement of acrosome reaction using PNA -FITC correlates well with 506 measurements of acrosomal exocytosis in acrosin-GFP transgenic mice47,48, the proportion of AR positive cells 507 following calcium ionophore stimulation tends to be comparatively lower with use of PNA -FITC, indicating that 508 the AR subpopulation is not completely captured with this method. Despite that limitation, our results highlight 509 that distinguishing live from dead cells is essential, and that methods employing organic extraction with PNA-510 FITC significantly overestimate fertility competent cells because they cannot make the necessary distinction 511 between these subpopulations51. Second, although bicarbonate and calcium titrations capture key components 512 of capacitation signaling, in vitro conditions cannot fully reproduce the biochemical and physical complexity of 513 the oviductal environment, particularly fluid rheology, chemokinesis, and structural constraints 12–14. Third, the 514 design in this report is focused on a single timepoint rather than a full temporal trajectory; measuring time 515 dynamics of subpopulation transitions between capacitation states will require separate time-lapse flow 516 cytometry experiments. 517

518 In summary, this work demonstrates that sperm capacitation can be modeled as a stochastic, cell population-519 level adaptive process shaped by structured physiological heterogeneity. Importantly, the adaptability of the 520 whole cannot exceed the adaptability of the component subpopulations. Understanding how subpopulation 521 compositions vary under physiologically relevant microenvironmental signaling conditions will enable modeling 522 of fertilizing potential as a function of the whole ejaculate, rather than relying on assumptions about idealized 523 individual sperm phenotypes (i.e., the ‘best’ sperm). By integrating large-scale single-cell flow cytometry with a 524 hierarchical statistical framework for modeling sperm subpopulation compositions , we provide a quantitative 525 foundation for analyzing and predicting how changing microenvironmental conditions redistribute cells among 526 functional subpopulations. Future work should incorporate time -resolved measurements, physiologically 527 relevant media conditions, and functional assays linking subpopulation structure to measurable fertility 528 outcomes. 529 Author Contributions 530 BB, AH, AC, AW, MA, DH, DB, PV, and CAS designed experiments and collected data. BB and CAS authored 531 and edited the report. All co-authors reviewed and approved the work. 532 Funding 533 This work was supported by the Eunice Kennedy Shriver National Institute of Child Health and Human 534 Development (R01HD110170), as well as laboratory startup funding from the Thomas Harriot College of Arts 535 and Sciences at East Carolina University and the East Carolina University Research and Economic 536 Development Office. The funders had no role in study design, data collection and analysis, decision to publish, 537 or preparation of the manuscript. 538 Disclosures The authors declare no conflicts of interest. 539

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