Rules of life at the interface of calcium signaling and mechanobiology

Abstract

Living systems process a broad range of internal and external stimuli, respond to environmental constraints, and adapt to various conditions through tight coordination between signaling networks and cellular mechanics. Among these, calcium signaling and cytoskeletal regulation form an essential interplay that spans multiple scales of biological organization—from ion–protein interactions to intercellular communication and tissue-level behaviors. Calcium ions (Ca²⁺) act as universal messengers, integrating a wide range of cellular signaling inputs to modulate a broad range of cellular structures and functions through the spatiotemporal dynamics of their concentration changes. Ca²⁺ signals follow conserved principles, despite their diverse roles, that define regulatory “Rules of Life” (RoLs)—generalized mechanisms that operate across biological contexts. This review focuses on how Ca²⁺ regulates and is regulated by cytoskeletal dynamics, with a particular emphasis on computational modeling for predictive simulations. As key examples, we highlight three specific RoLs: (1) Ca²⁺ dynamics facilitate cytoskeletal reorganization following stress and damage, (2) Ca²⁺ regulates actin dynamics to control synapse processes supporting both synapse formation and exocytosis, and (3) reciprocal coupling of spatiotemporal Ca²⁺ signaling and cellular dynamics defines distinct cellular roles in emergent multicellular behavior. Finally, we outline future directions toward developing multimodal computational simulations for identifying new RoLs, integrating them into multi-scale computational frameworks, and applications in bioengineering, pharmacology, and regenerative medicine.

INTRODUCTION

Living systems are remarkably adaptive, capable of reorganizing after injury, communicating complex information, and self-organizing for robust performance. Underlying these emergent properties are the modular interactions between mechanical cues and chemical signals, which can be described as “Rules of Life” (RoLs). RoLs generalize mechanistic principles that explain how biological systems behave across multiple biological contexts or scales. Furthermore, RoLs enable predictive computational models that are generalizable and extensible for analyzing biological systems (Tables I and II, see Appendix).¹ Many RoLs that govern the interplay between biomechanical and biochemical pathways remain to be identified.^2–7 Through a systematic review of literature, we identified a set of candidate RoLs centered on calcium-mediated regulation of the cytoskeleton. As ubiquitous second messengers, calcium ions (Ca²⁺) link environmental inputs to biological processes and are central for coordinating cellular responses, tissue organization, and organism behavior.^8–10 This review provides an extensible starting point for generating a digital representation of Ca²⁺-mediated regulation of the cytoskeleton.

A systems-level understanding of cell and tissue mechanics depends upon deciphering the coupling between biochemical signaling and cytoskeletal dynamics. For instance, insights into Ca²⁺-cytoskeletal coupling reveal how cells process mechanical and chemical inputs and also further inform the development of computational models for accelerated progress in bioengineered tissues, self-organizing biomaterials, and predictive digital twins.^11–15 Such models range from mechanochemical reaction–diffusion systems for signal regulation,¹⁶ to mechanistic models simulating force generation and mechanical behavior.¹⁷ These frameworks are often built on ordinary and partial differential equations (ODEs/PDEs) and can be integrated within agent-based or finite-element simulations.^18,19 Through careful calibration and validation with experimental data, these simulations reveal how calcium signaling and cytoskeletal remodeling impact force generation and regulate cellular function across multiple biological systems and spatial scales.^6,20 A RoL framework explains organismal traits, such as development, function, and environmental response across biological contexts.¹ However, a major challenge lies in understanding how these RoLs operate across diverse spatial and temporal contexts. Meeting this challenge requires a collective effort of both biologists and engineers to distill them into transferable, computationally defined functions that map input–output relationships.^21,22 Predictive, quantitative RoL frameworks that span ionic to tissue scale interactions will allow researchers to simulate how biological systems integrate multiple cues. Such frameworks can support hypothesis testing, perturbation analysis, and iterative refinement through integration with experiments,²² with translational impact ranging from agriculture to medicine and tissue engineering.

Here, we highlight the essential roles of computational modeling as a toolkit for data compression and integration of generalizable biochemical and biophysical mechanisms and then examine how Ca²⁺-cytoskeleton coupling shapes biological functions across contexts. We propose three key Rules of Life involving the interplay between Ca²⁺ signaling and the cytoskeleton, distill them into a generalized framework, and explore their translational applications (Table I, see Appendix). As a starting point, we review multi-scalar principles governing the interplay between calcium signaling and cellular mechanics and organization:

• •RoL 1: Ca²⁺ dynamics facilitate cytoskeletal reorganization following stress and damage.
• •RoL 2: Ca²⁺ regulates actin dynamics to control synapse processes supporting both synapse formation and exocytosis.
• •RoL 3: Reciprocal coupling of spatiotemporal Ca²⁺ signaling and cellular dynamics defines distinct cellular roles in emergent multicellular behavior.

By defining these RoLs and illustrating their cross-context applications, this review describes a conceptual foundation for computational modeling, experimental hypothesis generation, and the engineering-based analysis of living systems that are robust, adaptive, and responsive to their environments.

THE CALCIUM–CYTOSKELETON TOOLKIT

Calcium ions (Ca²⁺) function as critical intracellular messengers, enabling cells to respond to various stimuli.^10,23,24 For instance, ligands binding to plasma membrane receptors, such as G protein-coupled receptors (GPCRs), stimulate Ca²⁺ release from the endoplasmic reticulum (Table II, see Appendix). These extracellular signals regulate cytoplasmic Ca²⁺ levels, creating specific spatiotemporal dynamics, termed Ca²⁺ signatures.^24–26 Such increases in cytosolic Ca²⁺ concentration are essential for a wide range of cellular responses to stimuli, including dynamic actin reorganization, which in turn supports the formation and function of critical cellular and tissue structures.^6,26–29 Proteins that respond to Ca²⁺ activities, either by direct binding or via Ca²⁺-binding partners, undergo conformational changes that respond to Ca²⁺ signals to regulate processes, such as exocytosis, contraction, metabolism, egg activation during fertilization, and morphogenesis.^10,29–33 The interplay between calcium signaling and the cytoskeleton in these processes spans across species and kingdoms.^9,28,33–35 One core cytoskeletal component is actin. It exists in two primary forms: monomeric globular actin (G-actin) and polymeric filamentous actin (F-actin). F-actin undergoes continuous cycles of polymerization and depolymerization, enabling significant remodeling essential for cellular processes such as migration, division, and maintaining cell shape.^36,37 Calcium signaling regulates actin filament dynamics, both directly and indirectly, by interacting with actin-binding proteins (ABPs).^5,7,38–40 External stimuli create changes in intracellular Ca²⁺ levels and, through ABPs, are essential for maintaining cellular morphology and allow for structural reorganization by influencing the severing, capping, and cross-linking of actin.^7,41,42 Beyond direct regulation, Ca²⁺ indirectly controls actin architecture through signaling cascades involving Ca²⁺-binding proteins such as calmodulin (CaM), which activates downstream effectors such as calcium/calmodulin-dependent protein kinase II (CaMKII), protein kinase C (PKC), and phosphatases like calcineurin.^24,43 These enzymes regulate, in turn, the activity of small Rho GTPases (RhoA, Rac1, Cdc42) by modulating the phosphorylation of guanine nucleotide exchange factors and GTPase-activating proteins (GAPs), altering actin polymerization, branching, or cross-linking.^44–47 While actin filaments provide a structural framework for the cytoskeleton, myosin proteins bind to actin and convert chemical energy to generate force, enabling the reconfiguration of the cytoskeleton. Myosin proteins support diverse cellular functions, including apical constriction, cell mobility, cytokinesis, cargo and organelle transport, and muscle contraction. Myosin activity relies on actin binding and is regulated by chemical and mechanical cues, with calcium signaling playing a central role.^48–54 Myosin proteins contain IQ motifs (Table II, see Appendix), which bind essential and regulatory light chains (ELCs, RLCs) and Ca²⁺-dependent calmodulin (CaM).^48,55,56 Among the 30+ myosin families, myosin II is the most studied and relies on Ca²⁺-bound CaM to activate myosin light-chain kinase (MLCK) to phosphorylate its RLCs, enabling motor activation and filament assembly,^53,55 exemplifying how Ca²⁺-myosin regulation integrates with actin to coordinate force generation and cytoskeletal dynamics.

COMPUTATIONAL MODELS FOR DATA COMPRESSION AND INTEGRATION OF BIOLOGICAL MECHANISMS

Quantitative data-driven representations of hypothesized RoLs, expressed through calibrated computational models, provide powerful tools for investigating complex processes, such as wound healing or pathogenic infection. These models recapitulate system components as functional, interdependent elements, enabling simulation of dynamics and generation of predictive outcomes, often with greater specificity and capability than wet lab experimentation alone,⁵⁷ because of the identification of quantitative measurements for physical parameters.⁵⁸ Computational modeling thus serves as a rigorous test of biological hypotheses and whether a proposed mechanism can explain the input/outputs of a system. As the field of computational mechanobiology grows and matures, a central goal is to synthesize, through rational design, a solution to fundamental translational problems in the life sciences, including health and disease. Achieving this requires multi-scale frameworks that capture the functional interplay and spatiotemporal dynamics of calcium signaling, actin reorganization, and motor protein activity, spanning both localized Ca²⁺ spikes and global cytoskeletal reorganization.

Rules of Life (RoLs) describe the functional relationships between biological components and link systems across hierarchical levels to predict responses to perturbations. By unifying reductionistic mechanisms into computational modeling frameworks,^21,22 computational systems biology attempts to condense vast data sets through calibration of data-driven mechanistic models to validate a proposed mathematical description.⁵⁹ Computational modeling thus serves as a foundational effort for identifying more generalized heuristics and for facilitating knowledge transfer across scientific fields.

Figure 1 shows a representative pathway connecting experimental data with mathematical models. The dynamics of filamentous (F-actin) and globular (G-actin) actin are modeled as reversible reactions using rate constants representing polymerization ( $k_{+}$) and depolymerization ( $k_{-}$), respectively [Eq. (1)]

$$\frac{d\left[F.\mathit{\text{Actin}}\right]}{dt}=k_{+}\left[G.\mathit{\text{Actin}}\right]\left[Filament Ends\right]-k_{-}\left[Filament Ends\right].$$ (1)

FIG. 1.

Design–test–iterate, coupling computational and experimental workflows. Experimental Ca²⁺ and actin observations are shown with a simple model to predict actin response from input Ca²⁺ data. Comparison and interpretation of the experimental and computational results can be used for calibration, sensitivity analysis, and model comparison to test predictions across systems.

This ODE model of F-actin (F.Actin) concentration dynamics encodes the regulatory principle of dynamic balance.⁶⁰ To account for Ca²⁺ feedback, these rate constants can be further parameterized as functions of Ca²⁺ concentrations [Eqs. (2a) and (2b)]

$$k_{+}=f\left({\text{Ca}}^{2+}\right)=\alpha \frac{{\left[{\text{Ca}}^{2+}\right]}^n}{{\beta }^n+{\left[{\text{Ca}}^{2+}\right]}^n},$$ (2a)

$$k_{-}=g\left({\text{Ca}}^{2+}\right)=\gamma \frac{{\left[{\text{Ca}}^{2+}\right]}^m}{{\delta }^m+{\left[{\text{Ca}}^{2+}\right]}^m},$$ (2b)

where $\alpha$ and $\gamma$ are maximal rates or scaling factors; $\beta$ and $\delta$ are the [Ca²⁺] at which $k_{+}$ and $k_{-}$ are half maximal, respectively; and $n$ and $m$ are the cooperativity constants representing sensitivity to Ca²⁺. These coupling functions constitute biological relationships, and their parameterization requires data from biological systems. Analyzing these system-specific parameters reveals underlying rules directly associated with Ca²⁺ regulation of actin polymerization.

Furthermore, the demonstrated simple model can be extended to build a multi-level modular model by incorporating a cellular-level Ca²⁺ oscillation modular function together with a tissue-level binding protein regulatory module to capture the detailed regulation and dynamic feedback. Depending on the complexity of the modular models, the simulation frameworks can be implemented with agent-based methods, ODE/PDE solvers, or a combination of approaches.

Directly measuring the parameters involved in biological processes remains a key bottleneck for validating computational models of biological systems. Nonetheless, parameter values can be estimated with quantifiable levels of uncertainty through model calibration to experimentally obtained metrics. Recent advances in artificial intelligence (AI) and machine learning (ML), including artificial neural networks (ANNs), physics-informed neural networks (PINNs), and Bayesian integrative models, have improved the efficiency of parameter optimization in biological–computational modeling, particularly in their application of surrogate models and active parameter range searching.^61–64 Multisystem optimization techniques have also been used to improve our understanding of how shared biological molecules or mechanisms function across systems, offering insights into conserved processes and their variability across species.^65–68

RoL 1: Ca²⁺ DYNAMICS FACILITATE CYTOSKELETAL REORGANIZATION FOLLOWING STRESS AND DAMAGE

Ca²⁺ mediates cellular responses to various stressors (physical damage, toxins, environmental extremes, pathogens, and antigens) by triggering a rapid cytosolic influx of Ca²⁺ and restructuring of the actin–myosin cytoskeleton.^69–72 This mechanism is shared across numerous cell types and species,²² and termed calcium-mediated actin reset (CaAR)⁶ [Fig. 2(a)]. In mammalian endothelial cells, damage-associated molecular patterns (DAMPs), like ATP, released following damage, initiate Ca²⁺ signaling,^73–75 in fungi and yeast, osmotic or oxidative stress serve as triggers,^76,77 and in plants, Ca²⁺ fluxes occur during drought, pathogen invasion, or wounding.^78–81 CaAR enables processes such as cell membrane repair, cell spreading, healing, gene expression, and immune responses,^3,60 responding to both Ca²⁺ and other co-factors like reactive oxygen species (ROS).^82–88

FIG. 2.

Calcium signaling and actin dynamics during wound response. (a) Single-cell Ca²⁺-actin dynamics in wound response. Localized wounding induces a rapid increase in Ca²⁺ concentration, which triggers the formation of an actin ring around the nucleus, followed by an actin reset to restore normal cytoskeletal organization once healed. (b) Ca²⁺ and actin dynamics at the multi-cell level in response to wounding. Tissue wounding triggers a Ca²⁺ increase in surrounding cells, propagating a Ca²⁺ wave across the tissue. This leads to the coordinated formation of an actin ring at the wound site, promoting collective wound closure. (c) Generalized intracellular Ca²⁺ dynamics upon wounding across species. Intracellular Ca²⁺ levels rise through calcium channel influx across the plasma membrane or release from the endoplasmic reticulum (ER) through the IP₃ Ca²⁺ signaling pathway following recognition of a damage/microbe-associated molecular pattern (DAMP/MAMP), chemokines, or other stimulus, activating G protein pathways. Figure created in BioRender.

Following tissue damage, Ca²⁺ influx initiates wound repair and immune activation.^89–91 In Caenorhabditis elegans, epidermal Ca²⁺ elevation promotes wound closure and survival,⁹² while in mammals, similar dynamics facilitate immune activation, wound closure, and scar formation.^89,93,94 Together with DAMPs, Ca²⁺ activates key signaling pathways (e.g., NFAT, AP-1, and NF-κB) that coordinate single and multicellular responses, such as actin reorganization, for immune activation, regeneration, and repair.^95–107 Beyond initiation, Ca²⁺ and actin form a feedback regulation loop that enhances cellular responses to stress. In plants, actin remodeling modulates Ca²⁺ levels during salt stress, wounding, or mechanical stimulation,^69,108–113 while in mammalian cells, actin contributes to Ca²⁺ homeostasis by regulating ion transporters such as the plasma membrane calcium ATPase (PMCA),^114,115 a feedback interaction important for blood clotting during wounding.^114–117 Ultimately, Ca²⁺, actin, and actin-binding proteins, dynamically regulate one another, forming a tightly regulated calcium–cytoskeleton coupled module that enables rapid, precise, and context-specific responses to environmental stress.

Computational models have begun to capture the role of Ca²⁺ signals in wound healing.¹¹⁸ Multi-scale calcium models in Drosophila integrate Ca²⁺ signaling and cellular dynamics with tissue-level injury responses,¹¹⁹ while finite-element (FE) frameworks test how actin-driven mechanics contribute to wound closure efficiency.¹²⁰ However, most existing models do not fully integrate signaling networks with mechanical responses.¹²¹ An important next step is to directly link Ca²⁺ dynamics to actin polymerization rates in single-cell models (Fig. 2), enabling predictive simulations of cell shape change and migration, and eventually extending to multiple cell agent models that capture tissue-level wound repair. Additionally, subcellular element models can provide finer granularity and there is a need to develop computational approaches that incorporate both subcellular elements, including single actin fibers and actin–myosin bridges with spatiotemporal descriptions of actin-binding proteins, and Ca²⁺ ions.

RoL 2: Ca²⁺ REGULATES ACTIN DYNAMICS TO CONTROL SYNAPSE PROCESSES SUPPORTING BOTH SYNAPSE FORMATION AND EXOCYTOSIS

Synapses facilitate cell-to-cell communication,^122,123 not only in neurons,¹²⁴ but also in other cell types such as immune cells,¹²⁵ and during fertilization.^{122,123,125,126} Despite differences in structure and function, synapse-like structures share conserved features, including adhesion molecules, signaling cascades, secretion, and precise localization of molecular arrangements.^122,123 Across neuronal, immune, and fertilization synapses, Ca²⁺ oscillations regulate actin cytoskeleton reorganization, enabling adhesion, vesicle position, and exocytosis (Fig. 3). Although electrical synapses (formed by gap junctions^127,128) also mediate intercellular signaling in a broad range of cells through cytoneme,^129,130 our focus here is on the conserved actin–Ca²⁺ coupling at chemical synapses found in three exemplary contexts.

FIG. 3.

Ca²⁺-facilitated actin remodeling that leads to vesicle exocytosis at the fertilization, immune, and neuronal synapse. Upon synapse formation, a rise in intracellular Ca²⁺ activates calmodulin, CaMKII, and Rho GTPases, leading to reorganization of the actin cytoskeleton and exocytosis of specialized vesicles: synaptic vesicles (SVs) in neurons, lytic granules (LGs) in T cells, and cortical granules (CGs) in oocytes. This conserved pathway suggests a common Ca²⁺-dependent mechanistic rule of life for organizing synapses between cells. Figure created in BioRender.

In neurons, both presynaptic and postsynaptic terminals rely on actin reorganization for function.^131–140 At the presynaptic terminal, Ca²⁺-mediated actin dynamics influence synaptic vesicle (SV) exocytosis.^141–146 Actin depolymerization transiently (20–50 ms) increases SV release by reducing the active zone (AZ) barrier, while actin polymerization assists vesicle transport and replenishment of the readily releasable pool of synaptic vesicles.¹⁴⁶ During SV release, SNARE proteins [soluble N-ethyl-maleimide-sensitive fusion protein (NSF) attachment protein receptor] drive merging of vesicles with the plasma membrane and Ca²⁺-bound synaptotagmin triggers this fusion process to release neurotransmitters.^147–149 At the postsynaptic terminal, Ca²⁺ influx from the synapse through NMDA (N-methyl-D-aspartate) receptors (NMDARs) initiates actin remodeling through Ca²⁺/CaM, RhoGTPase proteins, and actin depolymerizing factors (ADFs),^150–153 which further recruit additional NMDARs and AMPA receptors (AMPARs), accelerating future dendritic spine depolarization.^154,155 The dynamics of scaffolding proteins, including PSD95,¹⁵⁶ GKAP,¹⁵⁷ Shank,^158,159 and Homer^160,161 at the postsynaptic terminal, are essential for actin cytoskeletal dynamics and cellular morphology, all of which are integral for synaptic plasticity.^162–164 In summary, precise regulation of Ca²⁺ signaling, together with cytoskeletal protein function, is essential for neuronal synapse formation.

Within the immune synapse, interfaces form between T cells and antigen-presenting (AP) or target cells.^165–167 When T-cell receptor (TCR) microclusters recognize peptides bound to major histocompatibility complex (MHC) molecules,^{165,168–172} a signaling cascade is initiated, which recruits phospholipase C gamma 1 (PLCγ1) and drives Ca²⁺ release from the ER via the IP₃ pathway.^{165,173–175} Between ER Ca²⁺ release and store-operated Ca²⁺ entry (STIM1–Orai1) following ER depletion,^176,177 activated calmodulin, CaMKII gamma (CaMKIIγ), calcineurin, and Rho-family GTPases, including Rac1 and Cdc42, facilitate actin remodeling through ABPs like Arp2/3 and formins.^{165,176,178–182} One of the major immune cell functions is the release of lytic granules (LGs) for targeted cell death.^183–186 As in neuronal synapses, LG exocytosis at the immune synapse involves conserved machinery, such as synaptotagmin, Rab proteins, and SNAREs, which respond to Ca²⁺ dynamics to trigger granule release.¹⁸⁷

The fertilization synapse, formed by sperm–egg interaction, also employs Ca²⁺-driven actin remodeling.¹²³ Species-specific Ca²⁺ patterns^33,188–190 triggered by sperm-delivered phospholipase C zeta (PLCζ) or voltage-gated channels^{123,188,191–195} regulate actin reorganization and cortical granule (CG) exocytosis.^196–199 In response to increased cytosolic Ca²⁺, CGs exocytose multiple molecules, including metalloendopeptidase ovastacin, which contributes to the modification of the egg coat.^200,201 As in neurons, exocytosis of CGs involves proteins such as synaptotagmin, synapsin I, Rab3, Rabphilin-3A, and SNAREs,¹⁹⁶ suggesting that they may be key conserved players in the Ca²⁺-dependent exocytotic process during fertilization. Other components of the egg-to-embryo transition appear to be dependent on events associated with sperm–egg interaction and sperm entry into the egg cytoplasm.²⁰²

Despite distinct roles, all three synapses rely on Ca²⁺ oscillations as a conserved signal to remodel actin and coordinate vesicle trafficking and exocytosis (Fig. 3). Understanding the signaling cascades governing Ca²⁺-driven cytoskeletal changes enables the development of generalized computational models based on the translation of RoL principles into data-driven coupling relations. Quantitative measurements from super-resolution techniques, such as single-particle tracking photoactivated localization microscopy (sptPALM), which tracks actin-binding protein diffusion within dendritic spines, now provide parameters for such models.¹⁵⁶ Approaches using agent-based simulations have simulated CaMKII phosphorylation dynamics in response to Ca²⁺ signals, while stochastic models have analyzed how spine geometry modulates Ca²⁺ influx and its effects on structural plasticity.^156,203,204 Additionally, molecular simulations combined with experimental data have reconstructed CaMKII/F-actin bundle architectures to explain Ca²⁺-triggered cytoskeletal changes.²⁰⁵ Further development and integration of modeled systems can provide deeper mechanistic insight into how these shared principles enable multicellular communication, plasticity, and adaptation across multiple biological systems.

RoL 3: RECIPROCAL COUPLING OF SPATIOTEMPORAL Ca²⁺ SIGNALING AND CELLULAR DYNAMICS DEFINES DISTINCT CELLULAR ROLES IN EMERGENT MULTICELLULAR BEHAVIOR

Collective behavior emerges when populations subdivide into functionally distinct groups.^206,207 This principle spans bacterial biofilms, metazoan tissues, and social behavior.^206–208 Cells and tissues rely heavily on ion-based signaling,^26,209–212 including Ca²⁺, to organize the division of cellular roles within cell populations (Fig. 4).^26,209 Through the division of cell populations into specialized groups, such as firing/non-firing,^209,210 initiator/standby,²⁶ or leader/follower,^211,212 the collective multicellular system achieves efficiency, resilience, and adaptive advantages. Quantifying these divisions can be complex and context-dependent, but they have potential applications in tissue engineering and health-related fields.^213,214 In bacterial biofilms, plants, and animals, percolation, a propagated signal through heterogeneous mediums, arises from a separation of cellular roles between active (firing) and passive (non-firing) cells [Fig. 4(a)]. This can be modeled using stochastic two-cell and multi-cell scenarios, incorporating the origin of the signal and the number of initiating cells [Fig. 4(b)].^208,215,216 Another aspect of percolation, “sparse coding,” efficiently translates complex environmental stimuli, such as light and sound, by reducing the number of variables that represent an input (dimensionality reduction).²¹⁷ This is achieved by relying on a small subset of active cells within a population to represent information, with experimental and computational evidence indicating that organized spatiotemporal dynamics, particularly traveling waves, support this process [Fig. 4(c)].^218–221 Ultimately, a percolation and role segregation strategy that incorporates mutual benefits between cells with distinct functional roles improves energy efficiency, enhances storage capacity (reduced crosstalk enables greater memory), and increases the data processing capabilities of the whole collective.²²²

FIG. 4.

Subdivision of cell populations. (a) Firing and non-firing in bacterial organization. Bacteria demonstrate percolation with distinct active (firing—blue) and passive (non-firing—gray) cells. (b) Initiator and standby dynamics in plant percolation. Ca²⁺ ions are used to propagate signals across tissue layers, originating from the initiating cell (darker blue) and diffusing through the standby cells (fading blue). (c) Neuronal dimensional reduction. In neurons, complex information is dimensionally reduced through sparse coding, organizing neurons from a single (dense) group into (sparse) subpopulations and networks (denoted by color). (d) Leader and follower segregation in multicellular migration. Leading cells (blue) direct cell migration, forming a protrusive leading edge, while followers (tan) maintain more symmetric contact with surrounding cells. Figure created in BioRender.

Another example where multicellular systems exhibit a division of functional roles is seen in the dynamics of intercellular signaling with initiator and standby cells. These cells are defined by their specific roles in calcium patterning,^{9,11,26,31,223} which result in multiple different classes of calcium signaling activity [Fig. 4(b)].^26,111 A computational model of the Drosophila wing disk captures these dynamics, showing that a small fraction of initiator cells (defined by elevated phospholipase C activity) produce sufficient IP₃ to stimulate oscillatory Ca²⁺ signaling across a larger fraction of standby cells.²⁶ This division, in which cell populations are partitioned by their internal signaling state, is conserved across multiple species: mammals and insects use gap junctions, while plants rely on plasmodesmata.^224–233 Such phenomena exemplify the role of Ca²⁺ signaling in facilitating long-range communication and percolation across cellular networks.

As another illustration of RoL 3, cellular migration relies on calcium signaling, facilitating cellular organization in many critical areas like wound healing and immunity.⁹¹ Multicellular migration divides cells into distinct subpopulations as either leaders or followers [Fig. 4(d)].^{2,210,211,234} This type of cellular organization is observed in many different systems from insects, mammals, and zebrafish.^235–238 This separation is driven by polarized signaling and physical asymmetry.^210,211,234 Leaders exhibit asymmetric contact with their environment, forming a protrusive leading edge, while followers maintain more symmetric contact with surrounding cells.²¹¹ This polarization of signaling in leader–follower dynamics is mirrored in internal Ca²⁺ levels, where a gradient of Ca²⁺ across the cell drives persistent forward migration.^2,239 Similar to multicellular migration, single cells create local Ca²⁺ pulses near the leading edge and maintain a back-to-front Ca²⁺ gradient.²³⁹ These calcium signaling events drive the processes of polarization, protrusion, retraction, and adhesion.^240,241 Modeling these segregated collective behaviors offers insights into how Ca²⁺ signaling scales from internal cellular dynamics (RoL 1) to cell–cell interactions (RoL 2) and tissue-wide coordination (RoL 3).

Computational models of the Drosophila wing disk highlight how variability in PLC production and gap junction permeability regulates spatiotemporal patterns of calcium ions.²⁶ Similarly, multi-scale approaches in plant systems, combining agent-based methods with partial differential equation (PDE) models, demonstrate how localized Ca²⁺ release propagates through tissues via Ca²⁺-activated Ca²⁺ channels, generating emergent patterns.¹¹¹ These studies illustrate the critical roles that computational modeling plays in revealing the mechanisms underlying complex intercellular Ca²⁺ dynamics. Building on these insights, next steps include developing modular computational building blocks that incorporate the RoL framework, enabling the unification of experimental observations across biological contexts, accelerating mechanistic discovery, and therapeutic testing in model organisms.^242,243

TRANSLATING RoLsINTO BIOENGINEERING ADVANCES

Formulating and calibrating computational modules that encode RoLs are essential for building predictive simulations that can test the efficacy of interventions for overcoming many health challenges facing our society, including poor diet, chronic wound healing deficiencies, or cancer.^244–247 We propose that biological RoLs can be compactly represented as generalized lambda functions (Table I, see Appendix),²⁴⁸ providing a foundation for engineering modular computational frameworks that capture complex multi-scalar processes.²⁴⁹ Such frameworks not only deepen our understanding of signaling mechanisms, but also enhance the fidelity and predictive power for Regulatory Science Tools [Fig. 5(a)] (Table II, see Appendix).^250–252 An example application includes atomistic-scale models of drug-ion channel interactions that are incorporated into digital twins of induced pluripotent stem cell-derived cardiac myocytes to predict patient-specific drug responses.²⁵³ Additionally, multi-scale simulations of Ca²⁺-actin stress response enable in silico pharmacology testing of cardiotoxic compounds and their effects on cytoskeletal integrity and mechanical function.²⁵¹

FIG. 5.

Advancing RoL-guided Bioengineering. (a) Translating rules of life into predictive models for personalized medicine. RoL-based modules support translational medicine through the fusion of iterative cycles of data generation (from diverse model systems, e.g., Drosophila, zebrafish, plants, and available human data) and model creation with comparison of cross-species simulations. This enables model optimization and hypothesis generation followed by experimental validation. These predictive frameworks bridge gaps in human data to accelerate the robust development of diagnostics, therapeutics, and personalized medicine. (b) Pareto and Utopian Fronts in multi-objective optimization problems. The Pareto front (solid line) marks the trade-off boundary between competing objectives, where improving one compromises the other. The utopian front (dashed line) represents relaxed optimal solutions when subsystems or parameters are varied. Clusters of solutions from System 1 (red) and System 2 (yellow) highlight system-specific parameterization, and the global utopian point (gray star) denotes the unattainable ideal of optimizing all objectives simultaneously. This illustrates how conserved vs system-specific features can be distinguished across biological systems, and how comparative optimization reveals both shared constraints and system-dependent adaptation. Figure created in BioRender.

In translational medicine, RoL-based modules will enable predictive systems modeling across species. For instance, leveraging wound responses in Drosophila and zebrafish informs predictions for human tissue repair,^{119,242,254–256} while “digital cousins” strategies have extended this by optimizing a single Bone Morphogenetic Protein (BMP) signaling model across multiple species, which revealed a conserved core of parameters that serve as a shared backbone, while species-specific parameters provided flexibility for tuning.⁶⁵ This cross-species modeling is particularly valuable for translational applications, as it bridges gaps created by the inaccessibility of detailed mechanistic data in higher-level organisms, including humans, where experimental datasets are often limited due to invasiveness or availability of subjects.²⁵⁷

Using RoL modules derived from model organisms can provide a way to create predictive, quantitative frameworks that address translational challenges and accelerate biological discovery. Beyond predicting therapeutic outcomes, RoL frameworks can help identify novel drug targets and guide pharmaceutical development.²⁵⁸ Synthetic biology provides an approach for designing drugs that target processes such as wound healing or stress response computationally defined by modular functional programming approaches (the lambda functions in Table I are provided as a starting point). Realizing this potential, however, will require close coordination between experimental and computational studies.

Toward this vision, cross-species and context-specific optimization can be guided by Pareto front and Utopian front analysis, which explicitly quantifies trade-offs among performance objectives and identify parameter or input regimes that balance these objectives across systems [Fig. 5(b)].²⁵⁹ Combining such multi-objective optimization methods within a RoL-based framework provides a way to design digital twins and digital cousins that are both predictive and generalizable. These approaches may accelerate the design of engineered tissues and biomaterials with context-aware signaling capabilities—that is, modules that respond to their local environmental conditions (e.g., ionic composition or mechanical stress) and adapt their signaling responses accordingly.^260–262 Such simulations could dynamically model cytoskeletal organization, repair, or material properties, helping to identify key parameters for biological engineering applications. By unifying experimental insight with modular computational models, this RoL-centered approach lays the groundwork for cross-scale, cross-species understanding of Ca²⁺-actin dynamics and advancing both fundamental biology and its engineering applications.^263–265

CONCLUSIONS

Viewing “Rules of Life” (RoLs) as mechanistic, data-driven relationships provides a foundation for understanding complex and interconnected biological processes. As an example of Rules of Life related to mechanobiology, we have identified RoLs defining how Ca²⁺ signaling and cytoskeletal dynamics coordinate biological responses with bidirectional regulation²⁶⁶ across systems and scales. This foundational “starting point” highlights the versatility of Ca²⁺ in regulating cytoskeletal remodeling in stress response, cellular communication, and tissue organization—demonstrating how RoLs unify predictive models while remaining adaptable to molecular and environmental contexts. Similar efforts are needed to extend this framework to other signaling modules and biological questions.

Computational models simulating Ca²⁺-actin regulation from subcellular dynamics (RoL #1) to cell–cell interactions (RoL #2) and tissue-wide coordination (RoL #3) highlight how conserved, yet flexible Ca²⁺-actin principles can be translated into modular computational functions. By integrating experimental data and modeling, researchers can construct adaptable models that capture system-specific behaviors, while remaining transferable across species—despite differences in channel kinetics, effector sensitivity, feedback regulation, and spatial organization.^267–271 Importantly, such models enable closed-loop discovery by guiding experimental planning through approaches like model-based design of experiments (MBDoE).^272,273

Despite extensive studies of calcium dynamics and cytoskeletal coupling, key questions remain regarding how RoLs governing the nexus of calcium signaling and cytoskeletal regulation operate consistently across spatial and temporal scales and how variable Ca²⁺ dynamics influence collective responses across species. The modular RoL framework embeds these open scientific questions into computational models, which are organized as a collection of separate parameterized modules. This computational structure serves as a rigorous tool to systematically generate and test new hypotheses and structure future experiments. RoLs not only deepen our mechanistic understanding but also provide a foundation for predictive, scalable frameworks that connect fundamental biology to translational applications in bioengineering. Future research should focus on refining RoL modules through the integration of quantitative experiments and predictive modeling, advancing cross-scale and cross-species analysis that support systematic hypothesis testing, and constructing translational digital twins as engineering design tools.

APPENDIX: Definitions

Glossary of representative proposed rules of life and conceptual functions for calcium signaling – cytoskeleton regulation coupling (Tables I and II). The lambda functions represent conceptual mapping relationships, and key inputs and outputs are indicated.

TABLE I.

Proposed rules of life and conceptual mapping functions for calcium–cytoskeleton coupling.

RoL 1	Core principle	Ca2+ influx acts as a universal stress signal that drives cytoskeletal reorganization to restore homeostasis at the cellular level and initiates wound healing and regeneration at the tissue level.
	Biological contexts	Mammals89,93–95,100–105,115–117 and plants,69,82–86,108–110 as well as fungi and Caenorhabditis elegans,76,77,92 show a stimulated Ca2+ response to injury and stress.
	Functional insights	Calcium-mediated actin reorganization (disassembly/reassembly around nucleus) drives actin reorganization for various processes, like cell extension, blood clotting, and scarring.86,89,93,94,116,118
	Computational approaches	Single-cell models linking [Ca2+] to [actin] have been created to simulate cytoskeletal dynamics,118 as well as multi-scale Ca2+ models for tissue-level wound healing.121 To model wound closure and epithelial sheet deformation, finite-element (FE) mechanical models have been developed.19
	Conceptual Lambda functions	λ (injury signals, coupling matrix, geometry, time) → Ca2+ dynamics (position, time)   λ [Ca2+ dynamics (position, time), regulatory networks] → Cytoskeletal response [actin_dynamics (position, time), force, tissue closure]
RoL 2	Core principle	Ca2+ dynamics reorganize the actin cytoskeleton, facilitating both the formation and function of synaptic structures, specifically exocytosis of key signaling molecules.
	Biological contexts	Synapse-like structures are formed not only by neurons,124 but also by immune cells (T cells and antigen-presenting cells)125 and by sperm and egg during fertilization,123 while gap junctions also can serve similar synapse-like functions for intercellular calcium signaling.224
	Functional insights	Ca2+ facilitates exocytosis across synapse-like contexts. In neuronal synapses, vesicle release relies on Ca2+-mediated actin depolymerization/polymerization to reduce barriers and transport cargo.141–146 In immune synapses, T cells and natural killer cells exocytose lytic granules in a Ca2+-actin-dependent manner.165,181,183–186 During fertilization, cortical granule exocytosis is triggered by synapse formation and Ca2+ release from within the egg.187,200,201,274
	Computational approaches	Computational approaches include agent-based models of CaMKII-driven actin remodeling in neuronal spines,203,204,275 stochastic models of Ca2+ oscillations in fertilization,196,276 and multi-scale agent-based/partial differential equation (PDE) models of immune responses.111
	Conceptual Lambda functions	λ [Ca2+ dynamics (pre- and postsynaptic) (position, time), regulatory networks, cell_contact, cell_type] → synapse_formation/growth/plasticity [actin_dynamics (position, time), information_exchange, mediator_type]
RoL 3	Core principle	Ca2+ signaling exhibits diverse patterns that shape and are shaped by cellular dynamics, creating functional separations that facilitate signaling within and between cells and between tissues and organs.
	Biological contexts	Cell populations subdivide into organized groups of firing/non-firing,208,209 initiator/standby,26 and leader/follower210,211 for optimized efficiency, resilience, and adaptive advantages.
	Functional insights	Subdivision in population achieves tissue-wide organization while decreasing individual cost,209 efficiently translates complex environmental stimuli by reducing dimensionality,217 organizes cell migration,2,210,211,239 and immune responses.91
	Computational approaches	To simulate tissue-wide Ca2+ propagation during an immune response, multi-scale agent-based/PDE models have been created,111 as well as stochastic models simulating initiator vs standby dynamics, highlighting the importance of Ca2+ signaling pathways and gap junctions connecting cells.26
	Conceptual Lambda functions	λ (position, signaling state, permeability, geometry) → cell_role (leader, follower, initiator, standby)

TABLE II.

Glossary.

Term/abbreviation	Definition/usage in manuscript
Actin regulatory proteins (ABP)	Actin-binding proteins (ABPs) directly bind to actin filaments, regulating their growth, severing, bundling, or depolymerization. Their activity is modulated by Ca2+ and small GTPases (e.g., RhoA, Rac1, Cdc42), which in turn are regulated by GTPase-activating proteins (GAPs). GAPs accelerate GTPase inactivation via the hydrolysis of bound GTP to GDP, further fine-tuning cytoskeletal dynamics.44
Agent-based/mechanistic models	Computational and mathematical frameworks that simulate system dynamics. Agent-based models (ABMs) simulate individual biological components (e.g., cells and proteins) following defined physical principles for behavior and interaction, while mechanistic models generate predictive outcomes providing insight into parameter values, such as rates or affinities. Combining ABMs and mechanistic models produces agent-based finite element simulations that model the larger environment of multiple agents to capture individual and group behavior.277
Artificial intelligence (AI)	Computational algorithms for problem-solving capable of performing human level tasks, such as reasoning, decision-making, and perception.278
Artificial neural networks (ANN)	General computational AI/ML models inspired by biological neurons; learns complex input–output relationships directly from data.62
Bayesian parameter estimation	Statistical parameter estimation that combines prior knowledge or assumptions with experimental data to update parameter values, yielding both estimates and their associated uncertainty.61
Ca2+	Calcium ion; a ubiquitous second messenger central to signal transduction, cells tightly regulate calcium homeostasis, keeping cytosolic concentrations low under resting conditions, with transient increases controlling processes such as cytoskeletal regulation and cellular communication.279
Ca2+-binding domains	Protein domains that bind Ca2+ and undergo conformational changes such as the EF-hand motif (a helix–loop–helix structure).280
Ca2+/CaM-dependent enzymes	Signaling proteins activated by Ca2+/CaM, which translate Ca2+ oscillations into downstream effects on cytoskeletal dynamics and gene regulation. Examples include calcineurin and CCaMKII (Ca2+/calmodulin-dependent protein kinase II).43
Calcium-mediated actin reset (CaAR)	Calcium-mediated actin remodeling involving disassembly/reassembly of cortical actin, often following stress or injury.6
Calmodulin (CaM)	Ca2+-binding protein that activates numerous downstream targets including kinases and phosphatases. Binds to IQ motifs [series of isoleucine (I) and glutamine (Q) residues].55
Cytoskeleton	Cellular structural network composed of actin filaments, microtubules, and intermediate filaments; regulated by Ca2+ in multiple contexts.2 Molecular motors, such as myosins, transport cargo along the cytoskeletal component actin and generate contractile forces in a Ca2+-dependent manner.48
Digital twins	Computational models that replicate biological systems to simulate, predict, and guide experiments or therapeutic strategies.12
Exocytosis	A Ca2+-regulated process in which intracellular vesicles fuse with the plasma membrane to release their contents (e.g., neurotransmitters, hormones). Depends on multiple components like the SNARE complex (syntaxin, SNAP-25, VAMP) and Ca2+ sensor synaptotagmin (Syt).148
Inositol triphosphate (IP3), Ca2+ signaling pathway	Ca2+ signaling cascaded initiated by G protein-coupled receptors (GPCRs) on the plasma membrane, which stimulate phospholipase C (PLC) that hydrolyzes membrane-bound phosphatidylinositol 4,5-bisphosphate (PIP2) into inositol 1,4,5-trisphosphate (IP3) and diacylglycerol (DAG). IP3 binds to its receptor (IP3R) on the endoplasmic reticulum (ER), triggering Ca2+ release, while DAG remains membrane-associated and activates protein kinase C (PKC) and other downstream effectors.24
Machine learning (ML)	A field of AI using statistical algorithms to make predictions from data sets without instruction.281
Model-based design of experiments (MBDoE)	A computational strategy that uses mechanistic or statistical models to optimize experimental design. MBDoE identifies the most informative experimental conditions.273
Ordinary/partial differential equations (ODE/PDE)	Ordinary/partial differential equations; mathematical frameworks used for modeling Ca2+ dynamics and cytoskeletal remodeling.61
Percolation	Signal propagation through heterogeneous mediums. In the context of calcium signaling, this involves signal cascades and information transfer across cells and tissues for coordinated and robust responses.208
Physics-informed neural network (PINN)	A type of neural network that integrates physical or mechanistic equations (e.g., PDEs/ODEs) into the training process, improving predictive power.282
Regulatory science tools	Technologies that support the development and evaluation of biomedical products, ensuring they meet safety, efficacy, and quality standards.245 In the context of calcium signaling and mechanobiology, such tools include computational models, biomarkers, or imaging platforms that inform regulatory decision-making.
Rules of life (RoLs)	Mechanistic, emergent properties of how biological systems behave across scales that can be used to predict phenotypes within an organism;1 in this manuscript, specifically applied to calcium–cytoskeleton interactions.
Store-operated calcium entry (SOCE)	Mechanism of Ca2+ influx activated by ER Ca2+ depletion. It is mediated by the ER Ca2+ sensor, STIM1 (stromal interaction molecule 1), which detects Ca2+ depletion and activates CRAC channels (Orai1) on the plasma membrane, allowing extracellular Ca2+ entry.177
Synapse	A specialized junction between two cells that enables directed communication through physical contact and/or localized signaling. Synapses can be electrical or chemical, while largely associated with neuronal communication, synapse-like structures are also found between immune cells and sperm–egg interactions.122–224

AUTHOR DECLARATIONS

Conflict of Interest

The authors have no conflicts to disclose.

Ethics Approval

Ethics approval was not required.

Author Contributions

Linlin Li and David Gazzo contributed equally to this work as co-first authors, while Shams Mowafak Saad, Nissa J. Larson, Eugene S. Kim, and Nilay Kumar contributed equally as co-second authors.

Linlin Li: Conceptualization (lead); Investigation (lead); Project administration (lead); Supervision (lead); Visualization (lead); Writing – original draft (lead); Writing – review & editing (lead). David Gazzo: Conceptualization (lead); Investigation (lead); Project administration (lead); Supervision (lead); Visualization (lead); Writing – original draft (lead); Writing – review & editing (lead). Shams Mowafak Saad: Conceptualization (equal); Investigation (equal); Visualization (lead); Writing – original draft (lead); Writing – review & editing (lead). Nissa J. Larson: Conceptualization (equal); Investigation (equal); Visualization (lead); Writing – original draft (lead); Writing – review & editing (lead). Eugene S. Kim: Investigation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Nilay Kumar: Investigation (equal); Writing – original draft (equal); Writing – review & editing (equal). Mayesha Sahir Mim: Conceptualization (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Mothishwar Jayaraman Krishnan: Writing – original draft (supporting); Writing – review & editing (supporting). Benjamin Speybroeck: Writing – original draft (supporting); Writing – review & editing (supporting). Chang Ding: Validation (supporting); Writing – review & editing (supporting). Shulan Xiao: Validation (supporting); Writing – review & editing (supporting). Mary C. Mullins: Validation (supporting); Writing – review & editing (supporting). Anjali S. Iyer-Pascuzzi: Validation (supporting); Writing – review & editing (supporting). Qing Deng: Validation (supporting); Writing – review & editing (supporting). Elsje Pienaar: Validation (supporting); Writing – review & editing (supporting). Janice P. Evans: Validation (supporting); Writing – review & editing (supporting). David M. Umulis: Validation (supporting); Writing – review & editing (supporting). Jeremiah J. Zartman: Conceptualization (equal); Funding acquisition (equal); Project administration (equal); Resources (equal); Supervision (equal); Writing – original draft (equal); Writing – review & editing (equal).

DATA AVAILABILITY

Data sharing is not applicable to this article as no new data were created or analyzed in this study.