4DN FOF-CT: Chromatin Tracing Standard

• 4DN FISH Omics Format–Chromatin Tracing (FOF-CT) is a standardized community-developed format for exchanging processed chromatin tracing data from multiplexed DNA FISH experiments.
• It uses a modular schema of tabular files to encode 3D spot coordinates, genomic annotations, and quality metrics for ball-and-stick chromatin traces.
• The format enhances cross-study comparability and integration with raw imaging data, enabling advanced spatial genomics analyses and interoperability with 4DN/OME infrastructures.

The 4DN FISH Omics Format–Chromatin Tracing (FOF-CT) is a community-developed standard for exchanging processed chromatin tracing data from multiplexed DNA FISH and FISH-omics experiments. It is designed for ball-and-stick chromatin traces and is implemented as a modular specification for tabular files (TXT/CSV/TSV) that encode per-bright-spot 3D positions, genomic coordinates, trace and cell identifiers, optional RNA-FISH and demultiplexing information, and quality and biological annotations, while remaining directly linkable to raw image data, microscope metadata, and 4DN/OME data infrastructures (Navelkar et al., 18 Aug 2025).

1. Scope, motivation, and conceptual domain

FOF-CT arose from a practical gap in spatial genomics data exchange. Before its introduction, laboratories commonly used bespoke formats such as MATLAB structs, spreadsheets, custom HDF5 layouts, and ad hoc CSV files for storing spot coordinates and traces. This impeded cross-study comparison, meta-analysis, and reuse, and often left chromatin tracing datasets inaccessible beyond figure panels. The standard was developed by the 4D Nucleome Imaging Working Group to address these limitations through a minimal mandatory core table and a set of optional but recommended companion tables aligned with OME, 4DN metadata schemas, and 4DN-BINA-OME-QUAREP microscopy metadata standards (Navelkar et al., 18 Aug 2025).

The format operates at the level of processed imaging results rather than raw image acquisition. Existing standards capture microscope configuration, acquisition metadata, and image organization, but do not specify how to represent chromatin traces as ordered sets of loci, how to bind those loci to genomic coordinates, how to connect them to biological annotations such as cell type or nuclear compartments, or how to store FISH-specific demultiplexing and quality-control information. FOF-CT fills this gap for DNA FISH-omics experiments that reconstruct chromatin folding by imaging arrays of genomic segments in single cells across multiple hybridization rounds (Navelkar et al., 18 Aug 2025).

Within the experimental space covered by the specification, current studies generally use one of two representations. In ball-and-stick methods, each targeted segment is represented by a single centroided bright spot per cell per hybridization round; this is the principal focus of FOF-CT. In volumetric methods, loci are represented as clouds of single-molecule localizations. FOF-CT does not yet define a full volumetric representation, but it already includes a Spot Demultiplexing table that stores per-localization events and is described as easy-to-extend to volumetric methods in future revisions (Navelkar et al., 18 Aug 2025).

The methods explicitly named as falling within the intended application space include Wang et al. 2016 chromatin tracing, ORCA, Hi-M, MINA, DNA seqFISH/seqFISH+, OligoFISSEQ, DNA-MERFISH, In situ Genomic Sequencing, and multi-omic extensions combining chromatin with RNA or protein measurements (Navelkar et al., 18 Aug 2025).

2. Modular schema and identifier architecture

FOF-CT is modular and comprises up to 12 interlinked tables. Every dataset must contain the DNA-Spot/Trace Core table; the remaining tables are optional or conditionally required depending on assay content and analysis outputs. All tables are plain text files with a header section and a column section. Header lines use three conventions: #key: value for human-readable metadata, ##key=value for mandatory machine-readable metadata, and #^key: value for user-defined column descriptions. Relationships across tables are defined by unique identifiers, and the first column of each table is always a UID such as Spot_ID, Trace_ID, Cell_ID, RNA_Spot_ID, Extra_Cell_ROI_ID, or Sub_Cell_ROI_ID (Navelkar et al., 18 Aug 2025).

Table	Status	Primary role
DNA-Spot/Trace Core	Mandatory	Per DNA bright spot
Spot Demultiplexing	Optional	Per localization event
Trace Data	Optional	Trace-level attributes
RNA Spot Data	Optional	RNA spot coordinates and IDs
Spot Quality	Optional	DNA spot QC
RNA_Spot Quality	Optional	RNA spot QC
Spot Biological Data	Optional	DNA spot biological annotations
RNA_Spot Biological Data	Optional	RNA spot biological annotations
Cell Data	Optional	Cell-level properties
Extra-Cell ROI Data	Optional	Tissue or organoid ROI context
Sub-Cell ROI Data	Optional	Subcellular structures
Cell/ROI Mapping	Optional	Explicit ROI boundaries

The DNA-Spot/Trace Core table is the heart of the format. Each row corresponds to a DNA bright spot in a given cell and typically includes Spot_ID, Trace_ID, X, Y, Z, Chrom, Chrom_Start, Chrom_End, and Cell_ID, with optional Sub_Cell_ROI_ID, Extra_Cell_ROI_ID, fluorescence-channel information, and additional biological annotations. The Spot Demultiplexing table stores localization-level records such as Loc_ID, Spot_ID, X, Y, Z, and Fluor, allowing reconstruction of per-spot localization clouds and advanced QC. Trace Data stores attributes of a whole chromatin trace, RNA tables mirror the DNA tables for multiplexed RNA FISH, and Cell/ROI tables place traces within cellular, subcellular, tissue, or organoid context (Navelkar et al., 18 Aug 2025).

This organization makes the schema simultaneously minimal and extensible. A dataset can remain compact when only spot-level positions are available, yet it can also capture trace-level state, RNA co-assays, nuclear landmarks, segmentation geometry, and per-localization provenance without breaking identifier consistency (Navelkar et al., 18 Aug 2025).

3. Representation of chromatin traces and derived geometric objects

In ball-and-stick chromatin tracing, a trace is the reconstructed 3D path of a specific contiguous genomic region in a single cell and often per allele. Formally, a trace $t$ is an ordered list

$$t = \left( (g_1, \mathbf{x}_1), (g_2, \mathbf{x}_2), \dots, (g_N, \mathbf{x}_N) \right),$$

where each genomic segment $$g_i = (\text{Chrom}_i, \text{Start}_i, \text{End}_i)$$ is paired with a spatial coordinate $\mathbf{x}_i = (x_i, y_i, z_i)$ (Navelkar et al., 18 Aug 2025).

FOF-CT encodes this representation implicitly through the core table. All rows sharing the same Trace_ID belong to one trace, and genomic ordering is obtained from Chrom_Start and Chrom_End or a locus index if present. Trace reconstruction therefore consists of selecting rows with a common Trace_ID, sorting them by genomic order, and extracting the $(X,Y,Z)$ coordinates. Coordinate units and frame are supplied in header metadata such as ##coordinate_unit=µm, and the coordinates are defined with respect to the microscopy detection system, typically after drift and chromatic correction (Navelkar et al., 18 Aug 2025).

The format adopts BED-like genomic coordinates through Chrom, Chrom_Start, and Chrom_End. For modified genomes, it requires a description of the genomic modification, a supplemental VCF file specifying variants, names of inserted or deleted fragments, and targeted-segment coordinates relative to those modifications. This establishes a direct bridge from traced loci to reference and variant genome annotations (Navelkar et al., 18 Aug 2025).

Once traces are reconstructed, standard geometric objects follow directly. For a trace with coordinates $\mathbf{x}_i$, the single-cell pairwise distance matrix is

$$d_{ij} = \| \mathbf{x}_i - \mathbf{x}_j \|_2 = \sqrt{ (x_i - x_j)^2 + (y_i - y_j)^2 + (z_i - z_j)^2 }.$$

A contact map can be defined by thresholding distances at $d_0$, for example $250\,\mathrm{nm}$,

$$C_{ij}^{(c,t)} = \begin{cases} 1 & \text{if } d_{ij} < d_0 \ 0 & \text{otherwise}. \end{cases}$$

Across cells, one obtains mean distance matrices $$t = \left( (g_1, \mathbf{x}_1), (g_2, \mathbf{x}_2), \dots, (g_N, \mathbf{x}_N) \right),$$0 and mean contact probabilities $$t = \left( (g_1, \mathbf{x}_1), (g_2, \mathbf{x}_2), \dots, (g_N, \mathbf{x}_N) \right),$$1. The radius of gyration is likewise computed from coordinates as

$$t = \left( (g_1, \mathbf{x}_1), (g_2, \mathbf{x}_2), \dots, (g_N, \mathbf{x}_N) \right),$$2

with $$t = \left( (g_1, \mathbf{x}_1), (g_2, \mathbf{x}_2), \dots, (g_N, \mathbf{x}_N) \right),$$3 the trace centroid (Navelkar et al., 18 Aug 2025).

Quality and uncertainty are handled by auxiliary tables rather than a single imposed uncertainty field. Spot Quality includes quantities such as Centroid_Intensity and X_Drift, Y_Drift, Z_Drift, and optional metrics such as fit residuals, PSF width, chromatic aberration corrections, and localization uncertainty. Spot Demultiplexing can support localization-cloud-derived uncertainty estimates through the distribution of per-spot localizations. This architecture preserves the processed coordinates needed for downstream modeling while keeping assay-specific QC explicit (Navelkar et al., 18 Aug 2025).

4. Population heterogeneity, FISH–Hi-C reconciliation, and model-aware annotation

A central issue for chromatin tracing is that population-average contact assays and imaging-derived distance measurements are not related by a simple monotonic rule once cell populations are heterogeneous. In the Generalized Rouse Model for Chromosomes (GRMC), a homogeneous population yields a one-to-one relation between mean distance $$t = \left( (g_1, \mathbf{x}_1), (g_2, \mathbf{x}_2), \dots, (g_N, \mathbf{x}_N) \right),$$4 and contact probability $$t = \left( (g_1, \mathbf{x}_1), (g_2, \mathbf{x}_2), \dots, (g_N, \mathbf{x}_N) \right),$$5, with the asymptotic scaling

$$t = \left( (g_1, \mathbf{x}_1), (g_2, \mathbf{x}_2), \dots, (g_N, \mathbf{x}_N) \right),$$6

for small $$t = \left( (g_1, \mathbf{x}_1), (g_2, \mathbf{x}_2), \dots, (g_N, \mathbf{x}_N) \right),$$7. Under that expectation, $$t = \left( (g_1, \mathbf{x}_1), (g_2, \mathbf{x}_2), \dots, (g_N, \mathbf{x}_N) \right),$$8 implies $$t = \left( (g_1, \mathbf{x}_1), (g_2, \mathbf{x}_2), \dots, (g_N, \mathbf{x}_N) \right),$$9. The FISH–Hi-C paradox is the empirical observation that some locus pairs violate this ordering: a pair can have higher Hi-C contact frequency but also a larger mean FISH distance (Shi et al., 2019).

The proposed resolution is conformational heterogeneity. In a two-subpopulation mixture with fractions $$g_i = (\text{Chrom}_i, \text{Start}_i, \text{End}_i)$$0 and $$g_i = (\text{Chrom}_i, \text{Start}_i, \text{End}_i)$$1,

$$g_i = (\text{Chrom}_i, \text{Start}_i, \text{End}_i)$$2

and

$$g_i = (\text{Chrom}_i, \text{Start}_i, \text{End}_i)$$3

A pair that is tightly looped in only a subset of cells can therefore have a larger overall contact probability and simultaneously a larger ensemble-average distance than a more uniformly folded comparison pair. Using high-resolution Hi-C on human chromosome 5 and FISH data for eight locus pairs, the authors fit experimental FISH CDFs, inferred $$g_i = (\text{Chrom}_i, \text{Start}_i, \text{End}_i)$$4, $$g_i = (\text{Chrom}_i, \text{Start}_i, \text{End}_i)$$5, and $$g_i = (\text{Chrom}_i, \text{Start}_i, \text{End}_i)$$6, and obtained a Pearson correlation of 0.87 between model-derived relative contact frequencies and Hi-C, with robustness for reasonable choices of $$g_i = (\text{Chrom}_i, \text{Start}_i, \text{End}_i)$$7 such as $$g_i = (\text{Chrom}_i, \text{Start}_i, \text{End}_i)$$8–$$g_i = (\text{Chrom}_i, \text{Start}_i, \text{End}_i)$$9 (Shi et al., 2019).

The same study reports that CTCF loops have $\mathbf{x}_i = (x_i, y_i, z_i)$0–$\mathbf{x}_i = (x_i, y_i, z_i)$1 almost independent of genomic separation, whereas peak-control pairs have larger distances of approximately $\mathbf{x}_i = (x_i, y_i, z_i)$2–$\mathbf{x}_i = (x_i, y_i, z_i)$3. For 212 locus pairs from optical imaging, reconstructed distributions $\mathbf{x}_i = (x_i, y_i, z_i)$4 were frequently broad and multi-modal, and the coefficient of variation $\mathbf{x}_i = (x_i, y_i, z_i)$5 was frequently $\mathbf{x}_i = (x_i, y_i, z_i)$6, indicating pervasive heterogeneity across scales from local loops to larger chromosome conformations (Shi et al., 2019).

Within a FOF-CT context, this suggests that per-cell coordinates alone are often insufficient when the objective is integration with Hi-C or polymer modeling. The full distribution of distances, empirical CDFs, contact thresholds $\mathbf{x}_i = (x_i, y_i, z_i)$7, sample sizes, and mixture-model quantities such as $\mathbf{x}_i = (x_i, y_i, z_i)$8, $\mathbf{x}_i = (x_i, y_i, z_i)$9, $(X,Y,Z)$0, or even continuous $(X,Y,Z)$1 reconstructions are analytically relevant metadata. A plausible implication is that FOF-CT-linked workflows are especially valuable when they preserve not only point estimates such as mean or median distances, but also the heterogeneity structure needed to interpret population-average contact maps (Shi et al., 2019).

5. Spectral loop detection and single-cell loop annotation

Multiplexed super-resolution FISH data support a second class of model-aware analysis in which loops are inferred from full 3D trajectories rather than from pairwise proximity alone. In the spectral framework applied to MERFISH data from Bintu et al. on chromosome 21 in HCT116 cells, each conformation is an ordered sequence of 83 3D points spanning $(X,Y,Z)$2 to $(X,Y,Z)$3 at approximately $(X,Y,Z)$4 resolution, with wild-type and auxin-treated conditions and roughly $(X,Y,Z)$5 configurations used to build $(X,Y,Z)$6-plots (Liefsoens et al., 2023).

The method treats the polymer as a discrete 3D signal indexed by locus number and applies a discrete cosine transform. Its core observable is the log-spectral ratio

$(X,Y,Z)$7

where $(X,Y,Z)$8 is the power spectral density at mode $(X,Y,Z)$9. Internal loops of unknown size and position are detected by scanning sub-chains defined by center $\mathbf{x}_i$0 and length $\mathbf{x}_i$1, producing a 2D $\mathbf{x}_i$2-plot over $\mathbf{x}_i$3. The theory gives a characteristic maximum at $\mathbf{x}_i$4 with $\mathbf{x}_i$5, so a detected maximum yields a loop midpoint $\mathbf{x}_i$6, an inferred loop size $\mathbf{x}_i$7, and corresponding anchor indices (Liefsoens et al., 2023).

The same framework derives loop frequency for mixed populations and complements the population-level spectral analysis with a neural-network classifier for single-cell loop presence. The network takes as input a normalized vector of symmetric distances around an inferred loop midpoint, uses a fully connected hidden layer with ReLU activation and a sigmoid output, and is trained on synthetic looped and non-looped random walks. The reported training sets comprise $\mathbf{x}_i$8 looped and $\mathbf{x}_i$9 non-looped samples, with $$d_{ij} = \| \mathbf{x}_i - \mathbf{x}_j \|_2 = \sqrt{ (x_i - x_j)^2 + (y_i - y_j)^2 + (z_i - z_j)^2 }.$$0 validation and $$d_{ij} = \| \mathbf{x}_i - \mathbf{x}_j \|_2 = \sqrt{ (x_i - x_j)^2 + (y_i - y_j)^2 + (z_i - z_j)^2 }.$$1 test samples per category, and the ideal synthetic test accuracy is approximately $$d_{ij} = \| \mathbf{x}_i - \mathbf{x}_j \|_2 = \sqrt{ (x_i - x_j)^2 + (y_i - y_j)^2 + (z_i - z_j)^2 }.$$2. Applied to MERFISH data, the method identified 14 loops in wild-type cells and 7 loops in auxin-treated cells, and yielded per-loop frequencies, per-cell loop probabilities, loop-positive and loop-negative subsets, average distance maps, subset-specific $$d_{ij} = \| \mathbf{x}_i - \mathbf{x}_j \|_2 = \sqrt{ (x_i - x_j)^2 + (y_i - y_j)^2 + (z_i - z_j)^2 }.$$3-plots, ShRec3D-like mean configurations, and loop-loop correlation matrices showing hierarchical, flower-like, and anti-correlated patterns (Liefsoens et al., 2023).

These analyses are not themselves part of the mandatory FOF-CT schema, but they map naturally onto FOF-CT-linked data products. The raw requirements of the spectral and neural-network workflow are ordered 3D coordinates, locus identity, genomic order, condition labels, and missing-data flags; all are native to the processed-data layer targeted by FOF-CT. A plausible extension is therefore to accompany core FOF-CT tables with derived spectral outputs such as $$d_{ij} = \| \mathbf{x}_i - \mathbf{x}_j \|_2 = \sqrt{ (x_i - x_j)^2 + (y_i - y_j)^2 + (z_i - z_j)^2 }.$$4-plots, loop annotation tables, per-cell loop probabilities, and subset-specific summaries, especially in studies centered on multiplexed super-resolution FISH data (Liefsoens et al., 2023).

6. Repositories, reuse, interoperability, and future directions

FOF-CT is designed for FAIR dissemination. Datasets are deposited in the 4D Nucleome Data Portal and the OME Image Data Resource (IDR), where they are linked to 4DN experiment and sample metadata, microscope hardware JSON files compliant with 4DN-BINA-OME-QUAREP standards, and raw images in OME-compatible formats. In IDR, FOF-CT-like analysis tables are queryable through a dedicated namespace, and Spot_ID can refer to an Image Shape identifier that is directly visualizable in the iViewer (Navelkar et al., 18 Aug 2025).

The scale of reuse is already substantial. Supplemental Table II in the FOF-CT report lists 212 public imaging datasets from 28 publications converted to the format. These include Wang et al. 2016, Bintu et al. 2018, Mateo et al. 2019, Su et al. 2020, Takei et al. 2021, ORCA-based datasets, Hi-M datasets, MINA datasets, and perturbative or disease-oriented studies. Reported use cases include cross-lab comparison of distance matrices, integration with Hi-C and other omics through genomic coordinates, multi-way contact analysis, polymer modeling, domain detection, loop detection, imputation, and reproducible exchange across tools such as pyHiM, traceratops, and CIMA (Navelkar et al., 18 Aug 2025).

Interoperability follows from several design choices. Genomic coordinates use BED conventions, variant handling uses VCF, microscopy metadata is aligned with OME and 4DN-BINA-OME-QUAREP standards, and standardized columns such as Chrom, Cell_ID, and Trace_ID allow search and indexing across repositories. Reusability is reinforced by rich header metadata describing lab, assay conditions, genome build, coordinate units, and analysis software versions, together with the explicit separation between raw imaging assets and processed FOF-CT tables (Navelkar et al., 18 Aug 2025).

Current limitations are also explicit. The present formulation focuses on ball-and-stick representations; volumetric data are only partially covered through Spot Demultiplexing. Metadata completeness can vary across legacy datasets, heterogeneity of imaging platforms complicates uniform representation of localization precision, and genome-scale datasets can make plain-text tables large even when compression and tooling remain practical. Future directions identified for the standard include full volumetric representations, integration of emerging methods such as LoopTrace, GOLD FISH, NOVA, Tn5-FISH, FRET-FISH, and perturb-tracing, stronger linkage to visualization platforms, and continued community extension of the specification and associated tooling (Navelkar et al., 18 Aug 2025).

In practice, FOF-CT functions as a processed-data exchange layer for single-cell chromatin trajectories. Its immediate strength is the standardized representation of spots, traces, RNA co-assays, QC, and spatial context. Its broader significance lies in enabling chromatin tracing datasets to be reused for heterogeneous-population modeling, cross-assay reconciliation, loop calling, imputation, and integrative 4D nucleome analysis without bespoke reverse engineering of every dataset (Navelkar et al., 18 Aug 2025).