Multivalent Forces on Surfaces -- Theory

Theoretical framework for computing multivalent binding forces on surfaces, based on the model in Theory_v9_mp.py.

Directory structure

.
├── Theory_v9_mp.py          # Core theory module (force calculations)
├── Run_Fig2_all.py           # Consolidated script for Figure 2 variants
├── Run_Fig3_all.py           # Consolidated script for Figure 3 variants
├── Run_Fig4_all.py           # Consolidated script for Figure 4 variants
├── Run_Fig5_all.py           # Consolidated script for Figure 5 variants
├── Run_Fig5_2D_all.py        # Consolidated script for Figure 5 heatmaps
├── run_all_figures.sh        # Master bash script to regenerate all figures
├── final_plots/              # Output directory for generated figures
├── old_plots/                # Archive of previously generated plots
├── old_scripts/              # Archive of individual plotting scripts
├── *_cache.npz               # Cached computation results (auto-generated)
├── Manuscript/               # Paper source files
└── Final_Multivalent_.../    # Final submission bundle

Plotting scripts

All scripts output PDF and PNG files into final_plots/. Expensive computations are cached in .npz files at the project root; if a cache exists it is loaded automatically, otherwise the sweep is computed from scratch and cached for future runs.

Run_Fig2_all.py

Generates figures for the radial/vertical binding force vs binding strength.

Output file	Description
NEW_Fig2	|Fr*| vs DG0, 3 panels (sigma*_R = 0.06, 0.60, 6.00), NL = 2, 4, 6, 8. Secondary log K_D axis on top. Sigma labels bold inside panels.
NEW_Fig2_SI	Same as above but vertical force |Fz*|. Uses a denser 75-point DG0 grid.
Fig2_diff_rigidity	Same as Fig2 but with stiffer polymer (Nmono = 5 instead of 20). No K_D axis.

Caches: Fig2_cache.npz, Fig2_SI_cache.npz, Fig2_diff_rigidity_cache.npz

Run_Fig3_all.py

Generates figures for force scaling with number of ligands and receptor spacing.

Output file	Description
Fig3	|F*| vs N_L (log-log), 3 panels for DG0 = -10, -14, -18. Curves for different sigma* values. Includes N_L^2 reference line.
Fig3_SI	|Fz*| vs d_{R-R}* (receptor spacing), NL = 20, DG0 = -6, -10, -14, -18.

No cache (computes from scratch).

Run_Fig4_all.py

Generates figures for force vs receptor spacing.

Output file	Description
Fig4	|Fr*| vs d_{R-R}*, NL = 20, DG0 = -6, -10, -14.
Fig4_SI	|Fz*| vs d_{R-R}*, same parameters.

No cache (computes from scratch).

Run_Fig5_all.py

Generates figures for the effect of steric (inert) polymer chains on binding forces.

Output file	Description
NEW_Fig5	3 panels (|Fr*|, |Fz*|, |F*|) vs DG0, for N_steric/N_L = 0, 5, 10, 20. K_D axis on top.
NEW_Fig5_SI	Same layout but with custom 1/z^2 repulsive interaction for A_0* = 0, 5, 20, 50. K_D axis on top.
Fig5_B_2nd_version	4 panels (|Fr*|, |Fz*|, |F*|, theta) vs N_L at fixed DG0 = -14. Shows force direction angle.
NEW_Fig5_C_2nd_version	4 panels (|Fr*|, |Fz*|, |F*|, theta) vs DG0. K_D axis on top.

Caches: Fig5_cache.npz, Fig5_SI_cache.npz

Run_Fig5_2D_all.py

Generates 2D heatmap figures of force components.

Output file	Description
Fig5_2D	4x3 grid of heatmaps. Rows: N_steric/N_L = 0, 5, 10, 20. Columns: |Fr*|, |Fz*|, |F*|. Axes: DG0 vs N_L. Contour lines at integer force values.
NEW_Fig5_2D	Same as above with K_D secondary axis on the top row.

Cache: Fig5_2D_cache.npz

Physical parameters (shared across all figures)

• Nmono = 20, amono = 0.38 nm, akuhn = 0.76 nm
• Nkuhn = Nmono * amono / akuhn = 10
• R_ee = sqrt(Nkuhn) * akuhn ~ 2.40 nm
• k_ee = 3 kbT / R_ee^2
• Dimensionless force: F* = F * R_ee / kbT
• Dimensionless density: sigma* = sigma * R_ee^2
• K_D = exp(+DG0 / kbT) [M]

Running

# Generate all figures at once
bash run_all_figures.sh

# Or run individual scripts
python Run_Fig2_all.py
python Run_Fig3_all.py
# etc.

Figures 3 and 4 compute from scratch and may take significant time. Figures 2, 5, and 5_2D use cached results and are fast if caches exist.