*4.4. Apoptosis Analysis*

We followed the same protocol of seeding and treatments as described above for cell cycle analysis. LCLs and DLBCLs (5 × <sup>10</sup><sup>5</sup> cells/well) cells were collected and washed with DPBS containing Ca2+. Then, they were stained with Annexin V-FITC (Biolegend) and PI (5μg/mL) for 15 min, in the dark, at RT. Stained cells were analyzed using a BD FACSCalibur flow cytometer and Kaluza Analysis 2.1 Software.

#### *4.5. Isolation of Healthy PBMC and Cell Subtypes (B- and T-Cells) for Apoptosis Assay*

Isolated peripheral blood mononuclear cells (PBMCs) from all healthy donors were obtained after written consent and were issued from the cell biological collection of the Tissue and Cell Bank CRBioLim of the Limoges Hospital University Center, this cell collection being declared to and authorized by the French Health Ministry with session n◦ "AC-2021-4790" according to French law. PBMCs were isolated from leukocyte buffy coats by lymphocyte medium separation (MSL, Eurobio Scientific) density gradient centrifugation. T-cells were purified from PBMC by CD3/CD4 EasySepTM human T-cell isolation kit (STEMCELL Technologies) according to the manufacturer's instructions. Activated T lymphocytes were obtained using T-cell activation/expansion kit (Anti-Biotin MACSiBead Particles and biotinylated antibodies against human CD2, CD3 and CD28) according to the manufacturer's protocol (Miltenyi Biotec). All cell subtypes were seeded in plates (5 × <sup>10</sup><sup>5</sup> cells/well) and, after 24 h, were treated or not with 100μg/mL of native fucoidan or vLMW-F. After 48 h, Annexin V/PI staining was performed for cell apoptosis analysis as described above for all cells groups. For flow cytometry analysis, B-cells were identified from mononuclear cells by staining with anti-CD19 (APC) conjugated antibody (Biolegend). The different antibodies and conjugated fluorochromes, as well as final dilutions, are listed in Table S1.
