論文紹介：Temporal tissue dynamics from a spatial snapshot

Nature | Vol 650 | 21 January 2026 Temporal tissue dynamics from a spatial snapshot Jonathan Somer, Shie Mannor & Uri Alon Technion Israel Institute of Technology · Weizmann Institute of Science 2026.05.08 Full | Shunichi Ito Somer, Mannor & Alon, Nature 2026 | Full 2026-05-08 Shunichi Ito

OSDR inference ▼ Spatial Proteomics snapshot ▼ Tissue biopsy ▼ Overview: Dynamics from spatial snapshot Phase portrait + simulation Fig. 1a 1. In silico Recover known phase portraits from simulated data ▼ 2. Real biopsies — Danenberg cohort, n = 715 patients (IMC) Fibrosis Immune circuit Subtypes Full 6D model Fibroblast × Macrophage (2D) F × M × Cancer cell (3D) → Survival T cell × B cell (2D) CD4 (helper T) × CD8 (T) × B (3D) → Pulses ER⁺ / PR⁺ / HER2⁺ / TNBC fixed-point comparison All 6 cell types, joint dynamics ▼ 3. Treatment Predict immunotherapy response from week-3 biopsy - NeoTRIP, TNBC, n = 279 Somer, Mannor & Alon, Nature 2026 | Full 2026-05-08 Shunichi Ito 1

Cell dynamics drive disease — humans give only snapshots Significance The catch Cell–cell communication circuits → new therapies. Human native context is only available as biopsy snapshots ex.) tumor recruits stroma + immune What we want many time point: infeasible W hat we have Snapshot from biopsy de Visser and Joyce J, Cancer Cell, 2023 time → Somer, Mannor & Alon, Nature 2026 | Full 2026-05-08 Shunichi Ito 2

Prior approaches study replicas, not the human tissue itself Studied so far Cell lines THIS PAPER no tissue context OSDR One-Shot tissue Dynamics Reconstruction different species Organ-on-chip engineered Organoids ex vivo ▼ Mouse models Human biopsy snapshot Cell-population dynamics None capture native human dynamics in vivo. Somer, Mannor & Alon, Nature 2026 | Full 2026-05-08 Shunichi Ito 3

Input data: Imaging Mass Cytometry (IMC) What OSDR needs from each cell: identity, Ki67 status, (x, y) position Charlotte G, et al., Nat Methods 2014 Why OSDR needs each piece Cell identity (x, y) coordinate Ki67 status Cell-type — fibroblast, T cell, tumour, … Location of each cell Division marker Somer, Mannor & Alon, Nature 2026 | Full 2026-05-08 Shunichi Ito 4

Method: each cell's neighbourhood → division probability Fig. 1b–d 1 Neighbourhood Cell counts within 80 µm radius 2 Somer, Mannor & Alon, Nature 2026 | Full 2026-05-08 Shunichi Ito Ki67 threshold Division: Ki67 > threshold 3 Logistic model Division probability from Neighbourhood 5

Two outputs: simulations + phase portrait Stochastic simulation Phase portrait Propagate populations over time. Fixed points & direction of change. Fig. 1e,f Somer, Mannor & Alon, Nature 2026 | Full 2026-05-08 Shunichi Ito 6

Validation & Application 1 . I n s il i c o Recover known phase portraits from simulated data ▼ 2 . R ea l b io psi e s — Da ne nbe rg coh ort, n = 71 5 p ati e nts (I MC ) Fibrosis Immune circuit Subtypes Full 6D model F × M (2D) F × M × C (3D) → Survival T × B (2D) CD4 × CD8 × B (3D) → Pulses ER⁺ / PR⁺ / HER2⁺ / TNBC fixed-point comparison All 6 cell types, joint dynamics ▼ 3 . Tre a tmen t Predict therapy response from week-3 biopsy - NeoTRIP, TNBC, n = 279 Somer, Mannor & Alon, Nature 2026 | Full 2026-05-08 Shunichi Ito 7

OSDR recovers known phase portraits in silico 1. I n si li co A few thousand cells per type → phase-portrait Result Inferred phase portraits matched ground truth (1–4 stable points). ✓ fixed point ✓ basins of attraction (direction of change) stable semi-stable Somer, Mannor & Alon, Nature 2026 | Full 2026-05-08 Shunichi Ito unstable Fig. 2d 8

Division probability was predictable from neighbourhood 2. Bi ops ie s Danenberg IMC cohort — 715 breast-cancer biopsies, 859 k cells INPUT RESULT Neighbourhoods Log-likelihood ratio test • • • • • Fibroblast Macrophage endothelial cell adaptive immune cells epithelial cells Somer, Mannor & Alon, Nature 2026 | Full 2026-05-08 Shunichi Ito P < 10⁻¹³ ▼ Fig. 3a Cell divisions are explained by neighbourhoods. Neighbourhoods may have Nutrient / hypoxia / inflammation info. 9

Prior work: co-culture reveals hot vs cold fibrosis 2. Bi ops ie s Mayer et al. — fibroblast × macrophage in vitro Hot fibrosis Hot fibrosis Fibroblasts: High Macrophage: High Cold fibrosis Cold fibrosis Fibroblasts: High macrophages: Absent Measured directly over days — OSDR must recover this from a snapshot. Fig. 3c (Mayer et al.) Somer, Mannor & Alon, Nature 2026 | Full 2026-05-08 Shunichi Ito 10

Fibroblast–macrophage dynamics in human breast cancer 2. Bi ops ie s Danenberg snapshot — fibroblast + macrophage only 2D model: Fibroblast × Macrophage Two-cell slice — first sanity check. From a si ngl e snapshot Hot-fibrosis fixed point high fibroblast + high macrophage Cold-fibrosis fixed point fibroblasts only, no macrophages → matches in vitro (Mayer et al.) Fig. 3f Somer, Mannor & Alon, Nature 2026 | Full 2026-05-08 Shunichi Ito 11

Hot fibrosis predicts poor survival 2. Bi ops ie s Kaplan–Meier by fixed point Median survival 192 → 132 months cold → hot fibrosis Statistical test log-rank P = 0.0046 n = 607 patients Independent of tumour count by cox model (Wald P = 0.01). Fig. 3h Somer, Mannor & Alon, Nature 2026 | Full 2026-05-08 Shunichi Ito 12

Cancer cells push tissue → hot fibrosis 2. Bi ops ie s 3D OSDR (fibroblast + macrophage + tumour) Fig. 3g The higher cancer, the more macrophage. Somer, Mannor & Alon, Nature 2026 | Full 2026-05-08 Shunichi Ito 13

T and B cells form an excitable circuit 2. Bi ops ie s A pulse-generating system Both populations collapse Excitable dynamics Above a T-cell threshold: B cells rise • T cells rise • B cells rise (delayed) • Both populations collapse Single stable point at zero — large enough perturbation triggers a pulse. T cells rise Fig. 4c Somer, Mannor & Alon, Nature 2026 | Full 2026-05-08 Shunichi Ito 14

Each pulse is followed by a refractory period 2. Bi ops ie s CD4 T initiates; B provides negative feedback Pulse (T → B → collapse) Refractory window Fig. 4d,e Cancer immunity may be pulsatile, like autoimmune flares. Somer, Mannor & Alon, Nature 2026 | Full 2026-05-08 Shunichi Ito 15

The role of different T cell subsets 2. Bi ops ie s CD4, CD8, B — same OSDR, more dimensions CD4 CD8 High CD4, Low B cells ▼ Neighbourhoods B CD8 CD4 Object B-cells Most proliferative Fig. 4f,g CD4 T cell density crossing threshold seems to trigger immune flare. Somer, Mannor & Alon, Nature 2026 | Full 2026-05-08 Shunichi Ito 16

TNBC shows a different fixed point 2. Bi ops ie s Only TNBC sustains a non-zero B-cell population HER2⁺ ER⁺ PR⁺ TNBC ER⁺ / HER2⁺ / PR⁺ Fig. S4J.B Consistent with clinically high lymphocyte infiltration in TNBC. Somer, Mannor & Alon, Nature 2026 | Full 2026-05-08 Shunichi Ito 17

From 2-cell slices to the full 6-cell-type model 2. Bi ops ie s F, M, CD4, CD8, B, Tumour — same OSDR, more dimensions 2D/3D models so far F M Tu Fibroblast × Macrophage T cell × B cell Selected cell types Full 6D model (this paper) F Tu M B CD4 All 6 types as inputs, all pairwise interactions. 6D state space. CD8 Somer, Mannor & Alon, Nature 2026 | Full 2026-05-08 Shunichi Ito Fig. S4K.A,B 6D model reproduced 2D phase-portrait 18

Can OSDR predict treatment response? 3 . Tr e a t m e n t NeoTRIP trial — TNBC, n = 279 Fig. 5a Chemotherapy n = 141 Chemotherapy + immunotherapy n = 138 immunotherapy Apply OSDR to the week-3 biopsy → predict tumour trajectory. Somer, Mannor & Alon, Nature 2026 | Full 2026-05-08 Shunichi Ito 19

OSDR predicts tumour collapse — only in responders 3 . Tr e a t m e n t Week-3 biopsy → 24-week trajectories Tumour Fibroblast Macrophage e T cells B cells Endothelial Chemotherapy Chemotherapy + Immunotherapy Fig. 5b Responders: tumour collapses Non-responders: tumour stable / grows Somer, Mannor & Alon, Nature 2026 | Full 2026-05-08 Shunichi Ito Mann–Whitney U-test P < 10⁻⁵ 20

T-cell infiltration drives tumour collapse 3 . Tr e a t m e n t Fewer dividing tumour cells in T-cell-rich neighbourhoods Dividing tumour-cell fraction T-cell & tumour dynamics (immunotherapy) T cells Tumour Fig. 5c,d Cancer cells around T cell in responders is less likely to increase. Somer, Mannor & Alon, Nature 2026 | Full 2026-05-08 Shunichi Ito 21

Summary OSDR Dynamics from one snapshot (Ki67 + neighbourhood). Fibroblast– macrophage Hot & cold fibrosis recovered; hot → poor survival. T–B cells Excitable circuit → pulsatile cancer immunity. Treatment Week-3 biopsy predicts NeoTRIP response. Somer, Mannor & Alon, Nature 2026 | Full 2026-05-08 Shunichi Ito 22

Limitations & caveats 9 caveats from the paper, grouped into 3 categories A. MODELLING ASSUMPTIONS ? B. CONFOUNDERS & COVERAGE C. DATA & VALIDATION GAPS Dynamics doesn’t change Patient confounders Sample-size needs Drifts if dynamics shift over time. Stage / genotype / tumour size — check across subsets. Per-patient ≥ 0.2 cm². Cohort needs many patients. Constant death rate Spatial confounders State-space coverage Death rate ≈ mean division rate, not by neighbourhood. Hypoxia / inflammation gradients within tissue. Sparse regions in composition = less reliable. Migration not modelled Hidden subtypes No fine-timescale val. Subtypes outside the antibody panel = untestable. Only 24-week biopsies; need pulsechase / intravital. → External influx / fate change need explicit terms. Somer, Mannor & Alon, Nature 2026 | Full 2026-05-08 Shunichi Ito ? 23

Appendix A | Mathematical framework

Deterministic rate equation

𝑑𝑋
= Divisions − Deaths
Δ𝑡
X ∈ ℝⁿ : density of each cell type; functions learned from the snapshot.

Stochastic equation (OSDR core)

𝑑𝑋𝑖
= ෍ 𝑂𝑖,𝑡 𝑥
Δ𝑡

𝑤𝑖𝑡ℎ 𝑂(𝑖) ∈ { +1/Δ𝑡, −1/Δ𝑡, 0 }

𝑥∈𝑋𝑖

Division / death probabilities P⁺(N(x)) and P⁻(N(x)) depend on each cell's neighbourhood N(x).
Estimated with logistic regression — features = cell counts in 80 µm radius.

Somer, Mannor & Alon, Nature 2026 | Full 2026-05-08 Shunichi Ito

24

Appendix A | Mathematical framework Ordinary differential equations Somer, Mannor & Alon, Nature 2026 | Full 2026-05-08 Shunichi Ito 25

Appendix B | Datasets Cohort Size Used for Danenberg et al. (2022) 715 patients / 859 k cells Fibroblast–macrophage / T–B cells Wang et al. (2023) 279 patients (NeoTRIP) Treatment response prediction Fischer et al. (2023) + 1,012 patients / 2.1 M cells Additional validation Somer, Mannor & Alon, Nature 2026 | Full 2026-05-08 Shunichi Ito 26

Appendix B | Datasets: cell-type definition Cell-type definitions Fig. S2A Somer, Mannor & Alon, Nature 2026 | Full 2026-05-08 Shunichi Ito 27

Appendix C | Other dynamics-from-snapshot methods Single-cell RNA-seq RNA velocity Zman-seq Snapshot of expression Transcriptional dynamics Cell-fate in labelled animals mRNA expression per cell. Time not observed. Unspliced/spliced mRNA ratio → direction of change. Time-stamped labelling + scRNA-seq. W hat i t measures T ime-scale T ime-scale no time info minutes – hours hours – days OSDR: native human tissue · days–weeks · one IMC snapshot. Somer, Mannor & Alon, Nature 2026 | Full 2026-05-08 Shunichi Ito 28

Appendix D | Ki67 as a proliferation marker Cell-cycle expression Ki-67 Encoded by MKI67. Nuclear non-histone protein. G1 Expressed when in G2, or M phase M Cell cycle S Absent when quiescent (G0) / early G1 Function promotes proliferation; disperses mitotic chromosomes G2 Ki67-positive (S / G2 / M) Clinical use Ki-67⁺ fraction = proliferation index Ki67-negative (G0 / early G1) Somer, Mannor & Alon, Nature 2026 | Full 2026-05-08 Shunichi Ito 29

Appendix E | Breast cancer receptor subtypes ER⁺ PR⁺ HER2⁺ TNBC Oestrogen receptor Progesterone receptor ERBB2 overexpression Triple-negative ~70% of cases. Endocrine therapy (tamoxifen). Often with ER⁺. Better endocrine response. Aggressive. Targeted by trastuzumab. ER⁻/PR⁻/HER2⁻. Chemo ± immunotherapy. ∅ In this paper: TNBC = NeoTRIP cohort. All 4 subtypes compared in T–B analysis. Somer, Mannor & Alon, Nature 2026 | Full 2026-05-08 Shunichi Ito 30

Appendix F | Population-level dynamics Fig. S1H Sampling according to probability (Logistic Regressioin output.) This approach is dependent on initial density and stochastic. Somer, Mannor & Alon, Nature 2026 | Full 2026-05-08 Shunichi Ito 31

Appendix F | Population-level dynamics Fig. S1K.A,B,C Somer, Mannor & Alon, Nature 2026 | Full 2026-05-08 Shunichi Ito 32

Appendix F | The other approach: population-level dynamics Fig. S1M.A,B Somer, Mannor & Alon, Nature 2026 | Full 2026-05-08 Shunichi Ito 33

Appendix G | Simulations data generation 1. Sample a random initial number of cells for each cell type. 2. Sample a random spatial position in the tissue for each cell. 3. For 𝑛 steps: i. Compute the probability of division or death based on neighbourhood ii. Sample an event of division, death or none based on probability. iii. Take the action of the event. Somer, Mannor & Alon, Nature 2026 | Full 2026-05-08 Shunichi Ito 34

Appendix H.1 | Unmodeled terms effect (Fibroblast – Macrophage) Model hypothesis The change in cell counts = division – death + others. OSDR only models division and death Figure c.) shows the effect of unmodeled terms. Fig.S3M Somer, Mannor & Alon, Nature 2026 | Full 2026-05-08 Shunichi Ito The error field produces a net effect that disperses cells from the peak density. 35

Appendix H.2 | Unmodeled terms effect (T- and B-cells) Near-zero influx ▼ Migration of T- and B-cells into the tissue driving immune flare Fig.S4M Somer, Mannor & Alon, Nature 2026 | Full 2026-05-08 Shunichi Ito 36

Appendix I.1 | Neighbourhoods’ radius 𝒓 𝑟 = 80 µ𝑚 is based on in vivo cell-cell interaction ranges. However, prediction performance is robust to radius Fig.S4M Somer, Mannor & Alon, Nature 2026 | Full 2026-05-08 Shunichi Ito 37

Different Radius Appendix I.2 | Robustness to radius and Ki67 thresholds Using different radius and Ki67 thresholds, Model reproduced the same results. Different Ki67 Somer, Mannor & Alon, Nature 2026 | Full 2026-05-08 Shunichi Ito Fig.S3F 38

Appendix J | F-B model with different dataset Other IMC dataset also reproduced hot / cold fibrosis Fig.S3K Somer, Mannor & Alon, Nature 2026 | Full 2026-05-08 Shunichi Ito 39

Appendix K | Dynamics change with TNBC Fig.S5C Division rate decreases probably because of chemotherapy. Somer, Mannor & Alon, Nature 2026 | Full 2026-05-08 Shunichi Ito 40

Appendix L | Ki67 distribution and thresholds Ki67 of most cells are 0 (Note that this figs are semi-log plot) Fig.S1A Somer, Mannor & Alon, Nature 2026 | Full 2026-05-08 Shunichi Ito 41

Appendix L | Ki67 distribution and thresholds Fig.S1B Ki67 are detected with quite a few cells. Somer, Mannor & Alon, Nature 2026 | Full 2026-05-08 Shunichi Ito 42

Appendix L | Ki67 distribution and thresholds Adjusting Ki67 1. Select values where 𝑇𝑛 > Ki67. 2. Each Ki67 value, Ki67– 𝑇𝑛 Adjusted Ki67 = 𝜎 𝑇𝑛 is typical magnitude of experimental noise (Appendix M) Fig.S1D Somer, Mannor & Alon, Nature 2026 | Full 2026-05-08 Shunichi Ito 43

Appendix L | Ki67 distribution and thresholds Adjusting Ki67 1. Select values where 𝑇𝑛 > Ki67. 2. Each Ki67 value, Ki67– 𝑇𝑛 Adjusted Ki67 = 𝜎 Fig.S1E Somer, Mannor & Alon, Nature 2026 | Full 2026-05-08 Shunichi Ito 𝑇𝑛 is typical magnitude of experimental noise (Appendix M) 44

Appendix M | IMC marker detection is always with noise Even from nonCD8 cells, CD8 T-cell marker is detectable. ▼ Noise level was determined to be 0.5 from figs. Fig.S1C Somer, Mannor & Alon, Nature 2026 | Full 2026-05-08 Shunichi Ito 45