Frequency-dependent Interactions Research Articles

Abstract A031: Investigating the mechanism and impact of frequency-dependent interactions in non-small cell lung cancer

Abstract Introduction: Pre-treatment tumor heterogeneity in cancer is a major driver of drug resistance. Given that resistance mechanisms often impose a fitness cost, the presence of drug-resistant clones prior to treatment poses a paradox—less fit drug-resistant clones should be selected out of a growing population. Recent work has identified frequency-dependent interactions (FDIs) in cancer cell lines, where different proportions of drug-sensitive and resistant cells modulate their respective fitness. FDIs may help explain pre-treatment drug resistance in cancer. Here, we sought to characterize FDIs in a drug-resistant model of non-small cell lung cancer (NSCLC). Methods: We developed a drug-resistant cell line in NSCLC by transducing PC9 cells with BRAF V600E. We then quantified the frequency-dependent interaction between sensitive and resistant cell lines across a range of gefitinib concentrations using the previously published evolutionary game assay. We also implemented an agent-based spatial model of evolution to investigate the different potential molecular mechanisms of frequency-dependent interactions. Results: We found that, despite growing slower in monoculture, low proportions of resistant cells in co-culture with sensitive cells rescued their growth rate in the absence of drug. This phenomenon may help explain pre-treatment drug-resistance and may present a future targetable pathway. Using a computational model parameterized with this data, we investigated the impact of different molecular mechanisms of FDIs on tumor evolution. We found that a mechanism driven by compound diffusion, in contrast to a cell-cell contact mechanism, facilitates drug resistance to greater extent. Through a conditioned media transfer experiment, we found that the FDI in our experimental system is most likely governed by a compound released in the cell culture media. Conclusions: Here we have identified FDIs in an engineered model of drug resistance in NSCLC. Using a computational model, we demonstrated how different mechanisms of FDIs impact tumor evolution. Our ongoing work seeks to identify the specific molecular mechanism responsible for the observed FDIs. In the future, we may leverage this approach to modulate frequency-dependent interactions, allowing us to mitigate pre-treatment drug resistance in vivo. Citation Format: Eshan S. King, Dagim S. Tadele, Maximillian A. R. Strobl, Jacob G. Scott. Investigating the mechanism and impact of frequency-dependent interactions in non-small cell lung cancer [abstract]. In: Proceedings of the AACR Special Conference in Cancer Research: Translating Cancer Evolution and Data Science: The Next Frontier; 2023 Dec 3-6; Boston, Massachusetts. Philadelphia (PA): AACR; Cancer Res 2024;84(3 Suppl_2):Abstract nr A031.

Pandemic's Ripple Effect: Exploring Dynamic Connectedness of Indian Equity and Commodity Markets

This research investigates volatility spillovers between the Indian equity markets and commodity futures markets. The Nifty 50 index is chosen as a representative of the equity market, based on market capitalization, while Crude Oil, Copper, Zinc, Gold, and Silver are selected to represent the commodity market in India. The selection of each commodity is grounded in considerations of liquidity and physical market size. This research investigates how the volatility in the Indian stock market interacted with the volatility of five major commodity markets throughout the COVID-19 pandemic. In order to ascertain the direction of information flow, the study employs the Granger causality approach. The research investigates how volatility transmits from the Indian equity market to various commodity markets. Employing methodologies inspired by Diebold and Yilmaz (2012) for Time Varying Parameter and Vector Autoregression (TVP VAR) analysis, the study explores these connections. To further delve into the dynamic relationship between these markets, wavelet coherence analysis is also utilized. This methodologically robust approach goes beyond traditional correlation analysis by deconstructing the co-movements across different time scales, offering a more nuanced understanding of the complex relationships and potential transmission mechanisms at play during the unprecedented period of the COVID-19 pandemic. By analyzing the frequency-dependent interactions between these markets, the study aims to shed light on how economic shocks and market fluctuations in one sector might propagate and impact the other, providing valuable insights for investors, policymakers, and researchers alike.

Strong ethanol- and frequency-dependent ecological interactions in a community of wine-fermenting yeasts

Natural wine fermentation depends on a complex consortium of native microorganisms rather than inoculation of industrial yeast strains. While this diversity of yeasts can result in an increased repertoire of wine flavors and aromas, it can also result in the inhibition of Saccharomyces cerevisiae, which is uniquely able to complete fermentation. Understanding how yeast species interact with each other within the wine-fermenting community and disentangling ecological interactions from environmental impacts on growth rates, is key to developing synthetic communities that can provide the sensory benefits of natural fermentation while lowering the risk of stuck ferments. Here, we co-culture all pairwise combinations of five commonly isolated wine-fermenting yeasts and show that competitive outcomes are a strong function of ethanol concentration, with frequency-dependent bistable interactions common at low alcohol and an increasingly transitive competitive hierarchy developing as alcohol increases. We also show that pairwise outcomes are predictive of five-species community outcomes, and that frequency dependence in pairwise interactions propagates to alternative states in the full community, highlighting the importance of species abundance as well as composition. We also observe that monoculture growth rates are only weakly predictive of competitive success, highlighting the need to incorporate ecological interactions when designing synthetic fermenting communities.

Frequency spectra analysis of space- and time-averaged quantum stress tensor fluctuations

Observing physical effects of large quantum stress tensor fluctuations requires knowledge of the interactions between the probe and the particles of the underlying quantum fields. The quantum stress tensor operators must first be averaged in time alone or space and time to confer meaningful results, the details of which may correspond to the physical measurement process. We build on prior results to characterize the particle frequencies associated with quantum fluctuations of different magnitudes. For the square of time derivatives of the massless scalar field in a spherical cavity, we find that these frequencies are bounded above in a power law behavior. Our findings provide a way to identify the largest quantum fluctuation that may be probed in experiments relying on frequency-dependent interactions.

The Time- and Frequency-Dependent Interactions of GDP, Unemployment, and Inflation

The Time- and Frequency-Dependent Interactions of GDP, Unemployment, and Inflation

Measuring competitive exclusion in non-small cell lung cancer.

In this study, we experimentally measure the frequency-dependent interactions between a gefitinib-resistant non-small cell lung cancer population and its sensitive ancestor via the evolutionary game assay. We show that cost of resistance is insufficient to accurately predict competitive exclusion and that frequency-dependent growth rate measurements are required. Using frequency-dependent growth rate data, we then show that gefitinib treatment results in competitive exclusion of the ancestor, while the absence of treatment results in a likely, but not guaranteed, exclusion of the resistant strain. Then, using simulations, we demonstrate that incorporating ecological growth effects can influence the predicted extinction time. In addition, we show that higher drug concentrations may not lead to the optimal reduction in tumor burden. Together, these results highlight the potential importance of frequency-dependent growth rate data for understanding competing populations, both in the laboratory and as we translate adaptive therapy regimens to the clinic.

Abstract A027: Exploring the effect of hypoxia and spatial interactions on the dynamics between gefitinib resistant and naïve NSCLC cell lines

Abstract Hypoxia and the development of spatially heterogeneous hypoxic and/or necrotic regions in non-small cell lung cancer (NSCLC) and other solid tumors is associated with chemotherapy and radiation resistance. One mechanism by which this could occur is through modification of the cell-cell interactions (or games) between the resistant and naïve cells within the tumor. Cell-cell interactions can modify the fitness of cells and thereby change the evolutionary dynamics of a tumor. Hypoxia may, in this way, change the game dynamics between cells and directly support maintenance of a population of resistant cells. To understand the mechanism by which hypoxic heterogeneity modulates evolutionary dynamics and therapy response, we combine computational modeling and in vitro experiments under a spatial hypoxia gradient. We utilize in-house game assay protocols to probe the evolutionary games between cell types. The experimental system is adapted from Carmona-Fontaine's MEMIC plate. This system allows us to create stable oxygen and nutrient gradients for 12 evolutionary replicates of NSCLC PC-9 cells. Fluorescence labeled gefitinib-resistant PC-9 cells and naïve parental PC-9 cells are co-cultured in a closed chamber with limited availability to oxygen and nutrient supply at one end. A green hypoxia probe is used to verify the establishment of a hypoxia gradient and a red Annexin V probe monitors apoptosis. Once microenvironmental gradients are established due to cellular consumption of oxygen and nutrients, images of cells are taken every 1.5 hours for 5 days. We carry out multiple experiments in which we vary the initial proportions of parental and resistant cells. Computationally, green and red fluorescence from the images captured by the microscopy system is quantified by an in-house image processing pipeline. We apply a random forest machine learning classifier, illumination correction, and object identification to each image to gather fluorescence counts for each well. These counts are used to compute the background rate of cell death and absolute vs. relative oxygen levels. The subsequent cell counts over time were used to calculate the growth rate (fitness) of the cell types in different environments and therefore the strength of environmental and frequency dependent interactions between the cell types. This framework allows for tightly coupled computational and in vitro experiments aimed at understanding and predicting the clinical implications of hypoxia resistance across a range of tumor types and microenvironments. We have measured the effect of hypoxia upon game interactions between gefinib-resistant and susceptible NSCLC cells. The evolutionary game changes with changing levels of hypoxia–and for the first time we are able to write down a continuous equation representing the game as a function of oxygen. Citation Format: Mina Dinh, Bezhou Feng, Jeff Maltas, Emily Dolson, Masahiro Hitomi, Steph Owen, Jacob Scott. Exploring the effect of hypoxia and spatial interactions on the dynamics between gefitinib resistant and naïve NSCLC cell lines [abstract]. In: Proceedings of the AACR Special Conference on the Evolutionary Dynamics in Carcinogenesis and Response to Therapy; 2022 Mar 14-17. Philadelphia (PA): AACR; Cancer Res 2022;82(10 Suppl):Abstract nr A027.

Frequency-Dependent Hybridization Contributes to Habitat Segregation in Monkeyflowers.

AbstractSpatial segregation of closely related species is usually attributed to differences in stress tolerance and competitive ability. For both animals and plants, reproductive interactions between close relatives can impose a fitness cost that is more detrimental to the rarer species. Frequency-dependent mating interactions may thus prevent the establishment of immigrants within heterospecific populations, maintaining spatial segregation of species. Despite strong spatial segregation in natural populations, two sympatric California monkeyflowers (Mimulus nudatus and M. guttatus) survive and reproduce in the other's habitat when transplanted reciprocally. We hypothesized that a frequency-dependent mating disadvantage maintains spatial segregation of these monkeyflowers during natural immigration. To evaluate this hypothesis, we performed two field experiments. First, we experimentally added immigrants in varying numbers to sites dominated by heterospecifics. Second, we reciprocally transplanted arrays of varying resident and immigrant frequencies. Immigrant seed viability decreased with conspecific rarity for M. guttatus but not for M. nudatus. We observed immigrant minority disadvantage for both species, but it was driven by different factors-frequency-dependent hybridization for M. guttatus and competition for resources and/or pollinators for M. nudatus. Overall, our results suggest a major role for reproductive interference in spatial segregation that should be evaluated along with stress tolerance and competitive ability.

Coordination games in cancer.

We propose a model of cancer initiation and progression where tumor growth is modulated by an evolutionary coordination game. Evolutionary games of cancer are widely used to model frequency-dependent cell interactions with the most studied games being the Prisoner's Dilemma and public goods games. Coordination games, by their more obscure and less evocative nature, are left understudied, despite the fact that, as we argue, they offer great potential in understanding and treating cancer. In this paper we present the conditions under which coordination games between cancer cells evolve, we propose aspects of cancer that can be modeled as results of coordination games, and explore the ways through which coordination games of cancer can be exploited for therapy.

Cross-Frequency Coupling in Childhood Absence Epilepsy

Objective: Absence seizures are the prototypic primarily generalized seizures, but there is incomplete understanding regarding their generation and maintenance. A core network for absence seizures has been defined, including focal cortical and thalamic regions that have frequency-dependent interactions. The purpose of this study was to investigate within-frequency coupling and cross-frequency coupling (CFC) during human absence seizures, to identify key regions (hubs) within the absence network that contribute to propagation and maintenance. Methods: Thirteen children with new-onset and untreated childhood absence epilepsy had over 60 typical absence seizures during both electroencephalography-functional magnetic resonance imaging (fMRI) and magnetoencephalography (MEG) recordings. The spatial map of the ictal network was defined using fMRI and used as prior information for MEG connectivity. A multilayer network approach was used to investigate within-frequency coupling and CFC for canonical frequency bands. A rigorous null-modeling approach was used to determine connections outside the noise floor. Results: Strong coupling between beta and gamma frequencies, within the left frontal cortex, and between the left frontal and right parietal regions was observed. There was also strong connectivity between left frontal and right parietal nodes within the gamma band. Multilayer versatility analysis identified a cluster of network hubs in the left frontal region. Interpretation: Cortical regions commonly identified as being critical for absence seizure generation (frontal cortex, precuneus) have strong CFC and within-frequency coupling between beta and gamma bands. As nonpharmacologic treatments, such as neuromodulation, become available for generalized epilepsies, detailed mechanistic understanding of how "diffuse" seizures are generated and maintained will be necessary to provide optimal outcomes.

Real-Frequency Response Functions at Finite Temperature.

Building on previous developments [A. Taheridehkordi, S. H. Curnoe, and J. P. F. LeBlanc, Phys. Rev. B 99, 035120 (2019); PRBMDO2469-995010.1103/PhysRevB.99.035120A. Taheridehkordi, S. H. Curnoe, and J. P. F. LeBlancPhys. Rev. B101, 125109 (2020); PRBMDO2469-995010.1103/PhysRevB.101.125109A. Taheridehkordi, S. H. Curnoe, and J. P. F. LeBlancPhys. Rev. B102, 045115 (2020)PRBMDO2469-995010.1103/PhysRevB.102.045115, B. Holm and U. von Barth, Phys. Rev. B 57, 2108 (1998)PRBMDO0163-182910.1103/PhysRevB.57.2108, J. Vičičević and M. Ferrero, Phys. Rev. B 101, 075113 (2020)PRBMDO2469-995010.1103/PhysRevB.101.075113], we show that the diagrammatic MonteCarlo technique allows us to compute finite-temperature response functions directly on the real-frequency axis within any field-theoretical formulation of the interacting fermion problem. There are no limitations on the type and nature of the system's action or whether partial summation and self-consistent treatment of certain diagram classes are used. In particular, by eliminating the need for numerical analytic continuation from a Matsubara representation, our scheme allows us to study spectral densities of arbitrary complexity with controlled accuracy in models with frequency-dependent effective interactions. For illustrative purposes we consider the problem of the plasmon linewidth in a homogeneous electron gas (jellium).

Frequency-Dependent Cortical Interactions during Semantic Processing: An Electrocorticogram Cross-spectrum Analysis Using a Semantic Space Model.

Convergent evidence has demonstrated that semantics are represented by the interaction between a multimodal semantic hub at the anterior temporal lobe (ATL) and other modality-specific association cortical areas. Electrocorticogram (ECoG) recording with high spatiotemporal resolutions is efficient in evaluating such cortical interactions; however, this has not been a focus of preceding studies. The present study evaluated cortical interactions during picture naming using a novel ECoG cross-spectrum analysis, which was formulated from a computational simulation of neuronal networks and combined with a vector space model of semantics. The results clarified three types of frequency-dependent cortical networks: 1) an earlier-period (0.2-0.8s from stimulus onset) high-gamma-band (90-150Hz) network with a hub at the posterior fusiform gyrus, 2) a later-period (0.4-1.0s) beta-band (15-40Hz) network with multiple hubs at the ventral ATL and posterior middle temporal gyrus, and 3) a pre-articulation theta-band (4-7 Hz) network distributed over widely located cortical regions. These results suggest that frequency-dependent cortical interactions can characterize the underlying processes of semantic cognition, and the beta-band network with a hub at the ventral ATL is especially associated with the formation of semantic representation.

Frequency-dependent interactions determine outcome of competition between two breast cancer cell lines

Tumors are highly dynamic ecosystems in which diverse cancer cell subpopulations compete for space and resources. These complex, often non-linear interactions govern continuous spatial and temporal changes in the size and phenotypic properties of these subpopulations. Because intra-tumoral blood flow is often chaotic, competition for resources may be a critical selection factor in progression and prognosis. Here, we quantify resource competition using 3D spheroid cultures with MDA-MB-231 and MCF-7 breast cancer cells. We hypothesized that MCF-7 cells, which primarily rely on efficient aerobic glucose metabolism, would dominate the population under normal pH and low glucose conditions; and MDA-MB-231 cells, which exhibit high levels of glycolytic metabolism, would dominate under low pH and high glucose conditions. In spheroids with single populations, MCF-7 cells exhibited equal or superior intrinsic growth rates (density-independent measure of success) and carrying capacities (density-dependent measure of success) when compared to MDA-MB-231 cells under all pH and nutrient conditions. Despite these advantages, when grown together, MCF-7 cells do not always outcompete MDA-MB-231 cells. MDA-MB-231 cells outcompete MCF-7 cells in low glucose conditions and coexistence is achieved in low pH conditions. Under all conditions, MDA-MB-231 has a stronger competitive effect (frequency-dependent interaction) on MCF-7 cells than vice-versa. This, and the inability of growth rate or carrying capacity when grown individually to predict the outcome of competition, suggests a reliance on frequency-dependent interactions and the need for competition assays. We frame these results in a game-theoretic (frequency-dependent) model of cancer cell interactions and conclude that competition assays can demonstrate critical density-independent, density-dependent and frequency-dependent interactions that likely contribute to in vivo outcomes.

Exploring density- and frequency-dependent interactions experimentally: An r program for generating hexagonal fan designs.

Species interactions and diversity are strongly impacted by local processes, with both the density of a focal species and its frequency in the community having an impact on its growth, survival and fecundity. Yet, studies that attempt to control for variation in both frequency and density have traditionally required a large number of replicates.Hexagonal fan designs can include a range of both densities and frequencies in a single plot, providing large economies in space and material for studying local interactions such as competition and disease transmission. However, in practice such experiments can be difficult to plan and implement.This study presents an R program whereby the user can rapidly view a variety of designs and determine the configurations that work best with their space and material constraints. Simple instructions for implementing the fan in any design setting are also provided.We illustrate the implementation of a simple form of the hexagonal fan design in a field experiment to assess the impact of host density on pollinator movement and disease transmission.

Identifying the Frequency Dependent Interactions between Ocean Waves and the Continental Margin on Seismic Noise Recordings

This study presents an exploration into identifying the interactions between ocean waves and the continental margin in the origination of double-frequency (DF, 0.1–0.5 Hz) microseisms recorded at 33 stations across East Coast of USA (ECUSA) during a 10-day period of ordinary ocean wave climate. Daily primary vibration directions are calculated in three frequency bands and projected as great circles passing through each station. In each band, the great circles from all stations exhibit largest spatial density primarily near the continental slope in the western North Atlantic Ocean. Generation mechanisms of three DF microseism events are explored by comparing temporal and spatial variations of the DF microseisms with the migration patterns of ocean wave fronts in Wavewatch III hindcasts. Correlation analyses are conducted by comparing the frequency compositions of and calculating the Pearson correlation coefficients between the DF microseisms and the ocean waves recorded at selected buoys. The observations and analyses lead to a hypothesis that the continental slope causes wave reflection, generating low frequency DF energy and that the continental shelf is where high frequency DF energy is mainly generated in ECUSA. The hypothesis is supported by the primary vibration directions being mainly perpendicular to the strike of the continental slope.

Negative frequency-dependent selection maintains coexisting genotypes during fluctuating selection.

Natural environments are rarely static; rather selection can fluctuate on timescales ranging from hours to centuries. However, it is unclear how adaptation to fluctuating environments differs from adaptation to constant environments at the genetic level. For bacteria, one key axis of environmental variation is selection for planktonic or biofilm modes of growth. We conducted an evolution experiment with Burkholderia cenocepacia, comparing the evolutionary dynamics of populations evolving under constant selection for either biofilm formation or planktonic growth with populations in which selection fluctuated between the two environments on a weekly basis. Populations evolved in the fluctuating environment shared many of the same genetic targets of selection as those evolved in constant biofilm selection, but were genetically distinct from the constant planktonic populations. In the fluctuating environment, mutations in the biofilm-regulating genes wspA and rpfR rose to high frequency in all replicate populations. A mutation in wspA first rose rapidly and nearly fixed during the initial biofilm phase but was subsequently displaced by a collection of rpfR mutants upon the shift to the planktonic phase. The wspA and rpfR genotypes coexisted via negative frequency-dependent selection around an equilibrium frequency that shifted between the environments. The maintenance of coexisting genotypes in the fluctuating environment was unexpected. Under temporally fluctuating environments, coexistence of two genotypes is only predicted under a narrow range of conditions, but the frequency-dependent interactions we observed provide a mechanism that can increase the likelihood of coexistence in fluctuating environments.

The Immune Checkpoint Kick Start: Optimization of Neoadjuvant Combination Therapy Using Game Theory.

In an upcoming clinical trial at the Moffitt Cancer Center for women with stage 2/3 estrogen receptor-positive breast cancer, treatment with an aromatase inhibitor and a PD-L1 checkpoint inhibitor combination will be investigated to lower a preoperative endocrine prognostic index (PEPI) that correlates with relapse-free survival. PEPI is fundamentally a static index, measured at the end of neoadjuvant therapy before surgery. We have developed a mathematical model of the essential components of the PEPI score to identify successful combination therapy regimens that minimize tumor burden and metastatic potential, on the basis of time-dependent trade-offs in the system. We considered two molecular traits, CCR7 and PD-L1, which correlate with treatment response and increased metastatic risk. We used a matrix game model with the four phenotypic strategies to examine the frequency-dependent interactions of cancer cells. This game was embedded in an ecological model of tumor population-growth dynamics. The resulting model predicts evolutionary and ecological dynamics that track with changes in the PEPI score. We considered various treatment regimens on the basis of combinations of the two therapies with drug holidays. By considering the trade off between tumor burden and metastatic potential, the optimal therapy plan was a 1-month kick start of the immune checkpoint inhibitor followed by 5 months of continuous combination therapy. Relative to a protocol giving both therapeutics together from the start, this delayed regimen resulted in transient suboptimal tumor regression while maintaining a phenotypic constitution that is more amenable to fast tumor regression for the final 5 months of therapy. The mathematical model provides a useful abstraction of clinical intuition, enabling hypothesis generation and testing of clinical assumptions.

Odd-frequency Berezinskii superconductivity in Dirac semimetals

We formulate a general framework for addressing both odd- and even-frequency superconductivity in Dirac semimetals and demonstrate that the odd-frequency or the Berezinskii pairing can naturally appear in these materials because of the chirality degree of freedom. We show that repulsive frequency-dependent interactions favor the Berezinskii pairing while an attractive electron-electron interaction allows for the BCS pairing. In the case of compensated Dirac and Weyl semimetals, both the conventional BCS and odd-frequency Berezinskii pairings require critical coupling. Since these pairings could originate from physically different mechanisms, our findings pave the way for controlling the realization of the Berezinskii superconductivity in topological semimetals. We also present the density of states with several cusp-like features that can serve as an experimentally verifiable signature of the odd-frequency gap.

Shared and connection-specific intrinsic interactions in the default mode network

Electrophysiological studies revealed that different neuronal oscillations, among which the alpha (8-13 Hz) rhythm in particular, but also the beta (13-30 Hz) and gamma (30-80 Hz) rhythms, are modulated during rest in the default mode network (DMN). Little is known, however, about the role of these rhythms in supporting DMN connectivity. Biophysical studies suggest that lower and higher frequencies mediate long- and short-range connectivity, respectively. Accordingly, we hypothesized that interactions between all DMN areas are supported by the alpha rhythm, and that the connectivity between specific DMN areas is established through other frequencies, mainly in the beta and/or gamma bands. To test this hypothesis, we used high-density electroencefalographic data collected in 19 healthy volunteers at rest. We analyzed frequency-dependent functional interactions between four main DMN nodes in a broad (1-80 Hz) frequency range. In line with our hypothesis, we found that the frequency-dependent connectivity profile between pairs of DMN nodes had a peak at 9-11 Hz. Also, the connectivity profile showed other peaks at higher frequencies, which depended on the specific connection. Overall, our findings suggest that frequency-dependent connectivity analysis may be a powerful tool to better understand how different neuronal oscillations support connectivity within and between brain networks.

Retarded hydrodynamic interaction between two spheres immersed in a viscous incompressible fluid

Retarded or frequency-dependent hydrodynamic interactions are relevant for velocity relaxation of colloidal particles immersed in a fluid, sufficiently close that their flow patterns interfere. The interactions are also important for periodic motions, such as occur in swimming. Analytic expressions are derived for the set of scalar mobility functions of a pair of spheres. Mutual hydrodynamic interactions are evaluated in one-propagator approximation, characterized by a single Green function acting between the two spheres. Self-mobility functions are evaluated in a two-propagator approximation, characterized by a single reflection between the two spheres. The approximations should yield accurate results for intermediate and long distances between the spheres. Both translations and rotations are considered. For motions perpendicular to the line of centers, there is a translation-rotation coupling. Extensive use is made of Faxén theorems, which yield the hydrodynamic force and torque acting on a sphere in an incident oscillating flow. The derived results are important for the study of velocity relaxation of two interacting spheres immersed in a fluid and for the study of swimming of assemblies of spheres.