Effective Pairwise Potentials Research Articles

Effective mechanical potential of cell-Cell interaction explains three-dimensional morphologies during early embryogenesis.

Mechanical forces are critical for the emergence of diverse three-dimensional morphologies of multicellular systems. However, it remains unclear what kind of mechanical parameters at cellular level substantially contribute to tissue morphologies. This is largely due to technical limitations of live measurements of cellular forces. Here we developed a framework for inferring and modeling mechanical forces of cell-cell interactions. First, by analogy to coarse-grained models in molecular and colloidal sciences, we approximated cells as particles, where mean forces (i.e. effective forces) of pairwise cell-cell interactions are considered. Then, the forces were statistically inferred by fitting the mathematical model to cell tracking data. This method was validated by using synthetic cell tracking data resembling various in vivo situations. Application of our method to the cells in the early embryos of mice and the nematode Caenorhabditis elegans revealed that cell-cell interaction forces can be written as a pairwise potential energy in a manner dependent on cell-cell distances. Importantly, the profiles of the pairwise potentials were quantitatively different among species and embryonic stages, and the quantitative differences correctly described the differences of their morphological features such as spherical vs. distorted cell aggregates, and tightly vs. non-tightly assembled aggregates. We conclude that the effective pairwise potential of cell-cell interactions is a live measurable parameter whose quantitative differences can be a parameter describing three-dimensional tissue morphologies.

A multiscale approach to uncover the self-assembly of ligand-covered palladium nanocubes.

Ligand-mediated superlattice assemblies of metallic nanocrystals represent a new type of mesoscale materials whose structural ordering directly influence emergent collective properties. However, universal control over the spatial and orientational ordering of their constitutive components remains an open challenge. One major barrier contributing to the lack of programmability in these nanoscale building blocks revolves around a gap in fundamental understanding of how ligand-mediated interactions at the particle level propagate to macroscopic and mesoscale behaviors. Here, we employ a combination of scaling theory and coarse-grained simulations to develop a multiscale modeling framework capable of bridging across hierarchical assembly length scales for a model system of ligand-functionalized nanocubes (here, Pd). We first employ atomistic simulations to characterize how specific ligand-ligand interactions influence the local behaviors between neighboring Pd nanocubes. We then utilize a mean-field scaling theory to both rationalize the observed behaviors as well as compute a coarse-grained effective pairwise potential between nanocubes capable of reproducing atomistic behaviors at the mesoscale. Furthermore, our simulations reveal that a complex interplay between ligand-ligand interactions is directly responsible for a shift in macroscopic ordering between neighboring nanocubes. Our results, therefore, provides a critical step forward in establishing a multiscale understanding of ligand-functionalized nanocrystalline assemblies that can be subsequently leveraged to design targeted structures exhibiting novel, emergent collective properties.

Magic v.3: An integrated software package for systematic structure-based coarse-graining

Molecular simulations of many phenomena related to biomolecular systems, soft matter and nanomaterials require consideration of length scales above 10 nm and time scales longer than 1μs, which necessitates the use of coarse-grained (low resolution) models, where each site of the model represents a group of atoms, and where the solvent is often omitted. Our software package MagiC is designed to perform systematic structure-based coarse-graining of molecular models, in which the effective pairwise potentials between coarse-grained sites of low-resolution molecular models are constructed to reproduce structural distribution functions obtained from modeling of systems in a high resolution (atomistic) description. The software takes as input atomistic trajectories generated by an external molecular dynamics package, and produce as an output interaction potentials for coarse-grained models which can be directly used in a coarse-grained simulations package. Here we present a major update (v.3) of the software with substantially improved functionality, compatibility with several major atomistic and coarse-grained simulations packages (GROMACS, LAMMPS, GALAMOST), analysis suite with graphical possibilities, diagnostics, documentation. We describe briefly the coarse-graining methodology, the structure of the software, describe users actions, and illustrate the whole process with two complex examples: cholesterol containing lipid bilayers and condensation of DNA caused by multivalent ions. Program summaryProgram Title: MagiCProgram Files doi:http://dx.doi.org/10.17632/9gnfxyshj8.1Licensing provisions: GPLv3Programming language: Fortran, PythonNature of problem: Systematic bottom-up multiscale modeling is a complex multi-stage process, in which results of simulations of a high-resolution (atomistic) model are used to construct a low resolution (coarse-grained) model, providing the same structural properties for the coarse-grained system as for the high-resolution system. Within the approach, structural properties of the high-resolution model are computed in terms of radial distribution functions and distributions of intramolecular degrees of freedom. Then the inverse problem is solved, in which the interaction potentials for the low-resolution model are determined which provide distribution functions coinciding with those obtained in the high-resolution simulations. The low-resolution model can be then used for simulations of the same system on larger length and time-scale.Solution method: The presented software package implements all stages of the systematic structure-based coarse-graining. It works as an integrated pipeline, giving the user ability to easily derive a coarse-grained model for a multicomponent complex molecular system and then use it for large-scale simulations. MagiC implements two approaches to solve the inverse problem: (i) the Inverse Monte Carlo method in which the inverse problem is solved using the Newton–Raphson method, with inversion of the Jacobian for the discretized relationship between interaction potentials and structural distribution functions; and (ii) the Iterative Boltzmann approach in which the inverse problem is solved using approximative relationships neglecting correlations between different degrees of freedom. The inverse solver includes also variational Inverse Monte Carlo approach when some of the coarse-grained potentials are fixed while others vary in order to fit the whole set of reference distribution functions.Additional comments: The MagiC main module can be also used for conventional Monte Carlo simulations of molecular systems described by tabulated pairwise potentials in the canonical ensemble.

Accuracy, Transferability, and Efficiency of Coarse-Grained Models of Molecular Liquids.

Coarse-graining (CG) approaches are becoming essential tools in the study of complex systems because they can considerably speed up computer simulations, with the promise of determining properties in a range of length scales and time scales never before possible. While much progress in this field has been achieved in recent years, application of CG methods is still inhibited by the limited understanding of a number of conceptual points that need to be resolved to open up the field of CG to a wide range of applications in material science and biology. In this paper, we present some of the key findings that emerged from the development of the integral equation theory of coarse-graining (IECG), which addresses some of the fundamental questions in coarse-graining. Although the IECG method pertains to the CG of polymer liquids, and specifically homopolymer melts are illustrated here, many of the results that emerge from the study of the IECG approach are general and apply to the CG of any molecular liquid. Through this method, we developed a formal relation between the statistical mechanics of CG and a number of predicted physical properties. On the basis of the theory of liquids, the IECG affords the analytical solution of the intermolecular potential for macromolecules represented by a Markov chain of CG sites, thus providing a transparent tool for analysis of the properties in coarse-graining. We identify three key requirements that render a CG model useful: accuracy, transferability, and computational efficiency. When these three requirements are fulfilled, the CG model becomes widely applicable and useful for studying regions in the phase space that are not covered by atomistic simulations. In the process, the IECG answers formally a number of relevant questions on how structural, thermodynamic, and dynamical properties are modified during coarse-graining. It sheds light upon how the level of CG affects the shape of the CG potential and how, in turn, the shape of the potential affects the physical properties. It tests the validity of selecting the potential-of-mean force as the effective pairwise CG potential and the role of higher-order many-body corrections to the pairwise potential to recover structural and thermodynamic consistency of the CG model. Because the IECG theory can be analytically formalized, it does not suffer from the problem of transferability and, in the canonical ensemble, leads to consistent pair distribution functions, pressure, isothermal compressibility, and excess free energy at variable levels of CG from the atomistic to the ultra-CG model, where macromolecules are represented as interpenetrable soft spheres.

Ultra-Coarse-Grained Models Allow for an Accurate and Transferable Treatment of Interfacial Systems.

Interfacial systems are fundamentally important in many processes. However, constructing coarse-grained (CG) models for such systems is a significant challenge due to their inhomogeneous nature. This problem is made worse due to the generally nontransferable nature of the interactions in CG models across different phases. In this paper, we address these challenges by systematically constructing ultra-coarse-grained (UCG) models for interfaces, in which the CG sites are allowed to have internal states. We find that a multiscale coarse-grained (MS-CG) representation of a single CG site model fails to identify the directionality of a molecule and is unable to reproduce the correct phase coexistence for aspherical molecules. In contrast with conventional MS-CG models, the UCG methodology allows chemical and environmental changes to be captured by modulating the interactions between internal states. In this work, we design the internal states to depend on local particle density to distinguish different phases in liquid/vapor or liquid/liquid interfaces. These UCG models are able to capture phase coexistence and recapitulate structures, notably at state points in which the MS-CG method yields poor results. Interestingly, effective pairwise forces and potentials from the UCG models are almost identical to those of the bulk liquids that correspond to each phase, indicating that the UCG approach can provide transferable interactions. This approach is expected to be applicable to other systems that exhibit phase coexistence and also to complex macromolecular systems by modulating interactions based on local density or other order parameters to unravel the complex nature underlying heterogeneous system boundaries.

Hypernetted-chain-like closure of Ornstein-Zernike equation in multibody dissipative particle dynamics.

We have derived a hypernetted-chain-like (HNC-like) approximate closure of the Ornstein-Zernike equation for multibody dissipative particle dynamics (MDPD) system in which the classic closures are not directly practicable. We first point out that the Percus's method is applicable to MDPD system in which particles interact with a density-dependent potential. And then an HNC-like closure is derived using Percus's idea and the saddle-point approximation of particle free energy. This HNC-like closure is compared with results of previous researchers, and in many cases, it demonstrates better agreement with computer simulation results. The HNC-like closure is used to predict the cluster crystallization in MDPD. We determine whether the cluster crystallization will happen in a system utilizing the widely applicable Hansen-Verlet freezing criterion and by observing the radial distribution function. The conclusions drawn from the results of the HNC-like closure are in agreement with computer simulation results. We evaluate different weight functions to determine whether they are prone to cluster crystallization. A new effective density-dependent pairwise potential is also proposed to help to explain the tendency to cluster crystallization of MDPD systems.

Screened Effective Interaction Potential for Two‐Component Plasmas

AbstractThe linear density response formalism is used to analytically obtain an effective pairwise interaction potential of charged particles that simultaneously takes into account quantum mechanical and quantum statistical effects in weakly and moderately non‐ideal plasmas at thermal equilibrium. The static dielectric function is obtained by interpolating long ‐ and short wavelength asymptotic forms of the dielectric function in the random‐phase approximation. The exchange effects are neglected in the micropotential, while the quantum‐statistical effects are accounted for in the screening. The effective potential constructed in such a way takes a finite value at the origin and proves to be screened at large distances. The thermodynamic properties of two‐component plasmas are then calculated and comparison is made with some data available in the literature. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Systematic hierarchical coarse-graining with the inverse Monte Carlo method.

We outline our coarse-graining strategy for linking micro- and mesoscales of soft matter and biological systems. The method is based on effective pairwise interaction potentials obtained in detailed ab initio or classical atomistic Molecular Dynamics (MD) simulations, which can be used in simulations at less accurate level after scaling up the size. The effective potentials are obtained by applying the inverse Monte Carlo (IMC) method [A. P. Lyubartsev and A. Laaksonen, Phys. Rev. E 52(4), 3730-3737 (1995)] on a chosen subset of degrees of freedom described in terms of radial distribution functions. An in-house software package MagiC is developed to obtain the effective potentials for arbitrary molecular systems. In this work we compute effective potentials to model DNA-protein interactions (bacterial LiaR regulator bound to a 26 base pairs DNA fragment) at physiological salt concentration at a coarse-grained (CG) level. Normally the IMC CG pair-potentials are used directly as look-up tables but here we have fitted them to five Gaussians and a repulsive wall. Results show stable association between DNA and the model protein as well as similar position fluctuation profile.

Solvent-Free, Highly Coarse-Grained Models for Charged Lipid Systems.

We present a methodology to develop coarse-grained lipid models such that electrostatic interactions between the coarse-grained sites can be derived accurately from an all-atom molecular dynamics trajectory and expressed as an effective pairwise electrostatic potential with appropriate screening functions. The reference nonbonded forces from the all-atom trajectory are decomposed into separate electrostatic and van der Waals (vdW) forces, based on the multiscale coarse-graining method. The coarse-grained electrostatic potential is assumed to be a general function of unknown variables and the final site–site interactions are obtained variationally, where the residual of the electrostatic forces from the assumed field is minimized. The resulting electrostatic interactions are fitted to screened electrostatics functions, with a special treatment for distance-dependent dielectrics and screened dipole–dipole interactions. The vdW interactions are derived separately. The resulting charged hybrid coarse-graining method is applied to various solvent-free three-site models of anionic lipid systems.

Collecting high-order interactions in an effective pairwise intermolecular potential using the hydrated ion concept: the hydration of Cf³⁺.

This work proposes a new methodology to build interaction potentials between a highly charged metal cation and water molecules. These potentials, which can be used in classical computer simulations, have been fitted to reproduce quantum mechanical interaction energies (MP2 and BP86) for a wide range of [M(H2O)n](m+)(H2O)ℓ clusters (n going from 6 to 10 and ℓ from 0 to 18). A flexible and polarizable water shell model (Mobile Charge Density of Harmonic Oscillator) has been coupled to the cation-water potential. The simultaneous consideration of poly-hydrated clusters and the polarizability of the interacting particles allows the inclusion of the most important many-body effects in the new polarizable potential. Applications have been centered on the californium, Cf(III) the heaviest actinoid experimentally studied in solution. Two different strategies to select a set of about 2000 structures which are used for the potential building were checked. Monte Carlo simulations of Cf(III)+500 H2O for three of the intermolecular potentials predict an aquaion structure with coordination number close to 8 and average R(Cf-O) in the range 2.43-2.48 Å, whereas the fourth one is closer to 9 with R(Cf-O) = 2.54 Å. Simulated EXAFS spectra derived from the structural Monte Carlo distribution compares fairly well with the available experimental spectrum for the simulations bearing 8 water molecules. An angular distribution similar to that of a square antiprism is found for the octa-coordination.

MagiC: Software Package for Multiscale Modeling.

We present software package MagiC, which is designed to perform systematic structure-based coarse graining of molecular models. The effective pairwise potentials between coarse-grained sites of low-resolution molecular models are constructed to reproduce structural distribution functions obtained from the modeling of the system in a high resolution (atomistic) description. The software supports coarse-grained tabulated intramolecular bond and angle interactions, as well as tabulated nonbonded interactions between different site types in the coarse-grained system, with the treatment of long-range electrostatic forces by the Ewald summation. Two methods of effective potential refinement are implemented: iterative Boltzmann inversion and inverse Monte Carlo, the latter accounting for cross-correlations between pair interactions. MagiC uses its own Metropolis Monte Carlo sampling engine, allowing parallel simulation of many copies of the system with subsequent averaging of the properties, which provides fast convergence of the method with nearly linear scaling at parallel execution.

Development and application of effective pairwise potentials for UO2n+, NpO2n+, PuO2n+, and AmO2n+ (n = 1, 2) ions with water

Intra- and intermolecular force field parameters for the interaction of actinyl ions (AnO2(n+), where, An = U, Np, Pu, Am and n = 1, 2) with water have been developed using quantum mechanical calculations. Water was modeled with the extended simple point charge potential (SPC/E). The resulting force field consists of a simple form in which intermolecular interactions are modeled with pairwise Lennard-Jones functions plus partial charge terms. Intramolecular bond stretching and angle bending are treated with harmonic functions. The new potentials were used to carry out extensive molecular dynamics simulations for each hydrated ion. Computed bond lengths, bond angles and coordination numbers agree well with known values and previous simulations. Hydration free energies, computed from molecular dynamics simulations as well as from quantum simulations with a solvation model, were in reasonable agreement with estimated experimental values.

A test of systematic coarse-graining of molecular dynamics simulations: Thermodynamic properties

Coarse-graining (CG) techniques have recently attracted great interest for providing descriptions at a mesoscopic level of resolution that preserve fluid thermodynamic and transport behaviors with a reduced number of degrees of freedom and hence less computational effort. One fundamental question arises: how well and to what extent can a "bottom-up" developed mesoscale model recover the physical properties of a molecular scale system? To answer this question, we explore systematically the properties of a CG model that is developed to represent an intermediate mesoscale model between the atomistic and continuum scales. This CG model aims to reduce the computational cost relative to a full atomistic simulation, and we assess to what extent it is possible to preserve both the thermodynamic and transport properties of an underlying reference all-atom Lennard-Jones (LJ) system. In this paper, only the thermodynamic properties are considered in detail. The transport properties will be examined in subsequent work. To coarse-grain, we first use the iterative Boltzmann inversion (IBI) to determine a CG potential for a (1-φ)N mesoscale particle system, where φ is the degree of coarse-graining, so as to reproduce the radial distribution function (RDF) of an N atomic particle system. Even though the uniqueness theorem guarantees a one to one relationship between the RDF and an effective pairwise potential, we find that RDFs are insensitive to the long-range part of the IBI-determined potentials, which provides some significant flexibility in further matching other properties. We then propose a reformulation of IBI as a robust minimization procedure that enables simultaneous matching of the RDF and the fluid pressure. We find that this new method mainly changes the attractive tail region of the CG potentials, and it improves the isothermal compressibility relative to pure IBI. We also find that there are optimal interaction cutoff lengths for the CG system, as a function of φ, that are required to attain an adequate potential while maintaining computational speedup. To demonstrate the universality of the method, we test a range of state points for the LJ liquid as well as several LJ chain fluids.

On-the-fly free energy parameterization via temperature accelerated molecular dynamics

We discuss a method for parametric calculation of free energy functions in arbitrary collective variables using molecular simulations. The method uses a variant of temperature accelerated molecular dynamics to evolve on-the-fly the parameters of the free energy function to their optimum values by minimization of a cumulative gradient error. We illustrate how the method performs using simple examples and discuss its application in the derivation of effective pairwise potentials for multiscale molecular simulations.

Thermodynamic properties of magnesium oxide: a comparison of ab initio and empirical models

The pressure–volume equation of state (P–V EOS) and isothermal bulk modulus, the volume–temperature (V–T) EOS and thermal expansivity are investigated for magnesium oxide (MgO) by using ab initio density functional theory (DFT) calculations combined with the quasi-harmonic Debye (QHD) model in which the phononic effects are considered and isothermal–isobaric ensemble molecular dynamics (MD) simulations with different effective pair-wise potentials that consist of the Coulomb, dispersion and repulsion interactions. Polarization and compression effects are considered in MD simulations through the shell model (SM) and breathing shell model (BSM), respectively. The P–V relationship and isothermal bulk modulus K of the MgO dependence of pressures up to 200 GPa at 300 K and the V–T relationship and volume thermal expansion coefficient α of the MgO dependence of temperatures up to 3000 K at 0.1 MPa have been obtained from MD and DFT calculations and compared with the available experimental data and other theoretical results. Particular attention is paid to the prediction of the first and second pressure derivatives K′ and K″ of the isothermal bulk modulus of MgO at a given temperature and pressure for the first time. Compared with the SM potential, MD simulations with the BSM and QHD models are highly successful in accurately reproducing the measured volumes of MgO. At extended pressure and temperature ranges, K, K′, K″, α and P–V–T EOS have also been predicted. Detailed knowledge of the thermodynamic behavior in extreme conditions is of fundamental importance for understanding the physical properties of MgO.

Coarse Grained Ion-Ion and Ion-Water Interactions

A detailed knowledge of ion transfer mechanisms between water and low-polarity media is crucial for many areas of chemistry and biochemistry such as phase transfer catalysis, separations, and biomembranes. [1,2] It has become clear from experiments [3] and simulations[4] that the transfer of small hydrophilic ions from water to an immiscible organic liquid is typically accompanied by the co-transfer of several water molecules. As a result, the ion exists in the organic phase as a hydrated cluster. To properly simulate biological phenomena at the coarse grained (CG) level, a proper treatment of the hydrated ions and solvent is crucial and is nontrivial. We have recently parameterized an uncharged and 4:1 mapped CG water with 3 interaction sites based on a generalized Morse -like potential which has greater flexibility in tuning the landscapes of CG effective pairwise potentials. [5] This new CG water becomes polarizable when it interacts with ions (Na+, Cl-) and or any other charged sites but not among its own species. The Morse interaction parameters for the CG ion-ion, ion-water, and ion-alkane are to be parameterized against the free energy of transfer of ions between water and liquid alkanes as well as radial distributions of ion-ion and ion-water. The target data are to be derived from atomic simulations.

Molecular dynamic study of the melting temperature in MgF 2 with the fluorite structure

The melting temperature of MgF 2 with cubic fluorite structure has been calculated by the constant temperature and pressure molecular dynamics (MD) simulation using the well-tested effective pair-wise potentials, which consist of the Coulomb, dispersion, and repulsion interaction by varying temperature from 300 to 2500 K. It is found that the potential parameters for MgF 2 derived from ab initio periodic Hartree-Fock calculations are very successful in reproducing accurately the DFT-GGA combined with quasi-harmonic Debye model calculated volumes of the cubic fluorite-type MgF 2 over a wide range of temperature at room pressure. Our simulated melting temperature of cubic fluorite-type MgF 2 is very close to the actual melting temperature 1539 K. Meanwhile, the radial distribution functions of Mg–Mg, F–F, and Mg–F ion pairs near the melting temperature are investigated from the isobaric and isothermal ensemble.

Self-consistent chemical model of partially ionized plasmas

A simple renormalization theory of plasma particle interactions is proposed. It primarily stems from generic properties of equilibrium distribution functions and allows one to obtain the so-called generalized Poisson-Boltzmann equation for an effective interaction potential of two chosen particles in the presence of a third one. The same equation is then strictly derived from the Bogolyubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy for equilibrium distribution functions in the pair correlation approximation. This enables one to construct a self-consistent chemical model of partially ionized plasmas, correctly accounting for the close interrelation of charged and neutral components thereof. Minimization of the system free energy provides ionization equilibrium and, thus, permits one to study the plasma composition in a wide range of its parameters. Unlike standard chemical models, the proposed one allows one to study the system correlation functions and thereby to obtain an equation of state which agrees well with exact results of quantum-mechanical activity expansions. It is shown that the plasma and neutral components are strongly interrelated, which results in the short-range order formation in the corresponding subsystem. The mathematical form of the results obtained enables one to both firmly establish this fact and to determine a characteristic length of the structure formation. Since the cornerstone of the proposed self-consistent chemical model of partially ionized plasmas is an effective pairwise interaction potential, it immediately provides quite an efficient calculation scheme not only for thermodynamical functions but for transport coefficients as well.

A minimal model of nanoparticle crystallization in polar solvents via steric effects

Motivated by recent experimental findings, we present here a minimal analytical model illustrating that the steric interactions among the ionic components can provide a simple, generic mechanism for like-charge crystallization in prototypical nanoparticle systems with counterions in polar solvents. In particular, the underlying steric interactions among these ionic components arise from the structural organization of the polar solvent molecules surrounding these ions as molecular dipole moments that may cooperatively enhance or counteract existing entropic depletion and electrostatic forces. Phenomenologically capturing these steric effects, we assume only the existence of a short-range pairwise Gaussian interaction, which has already been employed usefully for nanoparticles with hydrophillic surfaces or grafted-polymer coatings, among these ionic components (nanoparticles and counterions). The corresponding Gaussian interaction parameters characterize tunable interaction strengths. Making use of an analytically obtained effective pairwise potential between two nanoparticles, upon the contraction of counterions, we derive phase diagrams for nanoparticle systems of varying charge- and size-ratios as a function of particle densities, and observe crystallization for a range of parameters. We further demonstrate that our minimal model is compatible with the phenomenon of charge asymmetry.

Beyond co-localization: inferring spatial interactions between sub-cellular structures from microscopy images

BackgroundSub-cellular structures interact in numerous direct and indirect ways in order to fulfill cellular functions. While direct molecular interactions crucially depend on spatial proximity, other interactions typically result in spatial correlations between the interacting structures. Such correlations are the target of microscopy-based co-localization analysis, which can provide hints of potential interactions. Two complementary approaches to co-localization analysis can be distinguished: intensity correlation methods capitalize on pattern discovery, whereas object-based methods emphasize detection power.ResultsWe first reinvestigate the classical co-localization measure in the context of spatial point pattern analysis. This allows us to unravel the set of implicit assumptions inherent to this measure and to identify potential confounding factors commonly ignored. We generalize object-based co-localization analysis to a statistical framework involving spatial point processes. In this framework, interactions are understood as position co-dependencies in the observed localization patterns. The framework is based on a model of effective pairwise interaction potentials and the specification of a null hypothesis for the expected pattern in the absence of interaction. Inferred interaction potentials thus reflect all significant effects that are not explained by the null hypothesis. Our model enables the use of a wealth of well-known statistical methods for analyzing experimental data, as demonstrated on synthetic data and in a case study considering virus entry into live cells. We show that the classical co-localization measure typically under-exploits the information contained in our data.ConclusionsWe establish a connection between co-localization and spatial interaction of sub-cellular structures by formulating the object-based interaction analysis problem in a spatial statistics framework based on nearest-neighbor distance distributions. We provide generic procedures for inferring interaction strengths and quantifying their relative statistical significance from sets of discrete objects as provided by image analysis methods. Within our framework, an interaction potential can either refer to a phenomenological or a mechanistic model of a physico-chemical interaction process. This increased flexibility in designing and testing different hypothetical interaction models can be used to quantify the parameters of a specific interaction model or may catalyze the discovery of functional relations.