---
title: 論文紹介：Temporal tissue dynamics from a spatial snapshot
tags: 
author: [Shunichi Ito](https://image.docswell.com/user/shunichi1100921)
site: [Docswell](https://www.docswell.com/)
thumbnail: https://bcdn.docswell.com/page/57GLL2DWEL.jpg?width=480
description: Temporal tissue dynamics from a spatial snapshot. Somer J, Mannor S, Alon U.  Nature. 2026;650(8101):490-499. doi:10.1038/s41586-025-09876-1 https://www.nature.com/articles/s41586-025-09876-1  Imaging mass spectrometryという空間プロテオミクスのsnapshotからdynamicsを推測した論文です。 1回のタイムポイントから得られるスナップショットから、癌免疫における興奮パルス回路、さらには治療効果の予測まで応用しています。
published: May 09, 26
canonical: https://image.docswell.com/s/shunichi1100921/53J3YY-paper_temporal_tissue_dynamics_from_spatial_snapshot
---
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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


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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
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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
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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
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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
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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


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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
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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
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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


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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.
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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
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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
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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
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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
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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
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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
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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
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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
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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


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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
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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


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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
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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
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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


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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
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Appendix A | Mathematical framework
Ordinary differential equations
Somer, Mannor & Alon, Nature 2026 | Full 2026-05-08 Shunichi Ito
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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
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Appendix B | Datasets: cell-type definition
Cell-type definitions
Fig. S2A
Somer, Mannor & Alon, Nature 2026 | Full 2026-05-08 Shunichi Ito
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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
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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
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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
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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
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Appendix F | Population-level dynamics
Fig. S1K.A,B,C
Somer, Mannor & Alon, Nature 2026 | Full 2026-05-08 Shunichi Ito
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Appendix F | The other approach: population-level dynamics
Fig. S1M.A,B
Somer, Mannor & Alon, Nature 2026 | Full 2026-05-08 Shunichi Ito
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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
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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


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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
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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
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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


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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
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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
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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
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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
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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
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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)
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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