STRC Research

STRC Sonogenetics Bifurcation Analysis

9 min read

STRC Sonogenetics Bifurcation Analysis

TL;DR: The 5-variable ODE model for sonogenetic STRC therapy is stable and safe (no oscillations, no runaway), but the self-dosing window is too narrow. System saturates at ~20 dB, behaving like a constitutive promoter in practice. Root cause: NFAT threshold and CaN binding constants are too low.

Full stability and safety analysis of the 5-variable ODE model for mechanosensitive STRC gene therapy. Answers: is the system safe, stable, and does self-dosing actually work?

Code: ~/DeepResearch/strc/bifurcation_analysis.py

Key Finding: Self-Dosing Window is Too Narrow

The system saturates at ~20 dB. At any realistic sound level (quiet room, hearing aid, conversation), protein output is identical: ~29,750 molecules (198% of target). The 29x dynamic range exists only between 0 and 14 dB, a range humans rarely experience.

Sound LevelProtein% TargetReal-world equivalent
0 dB2,41216%Anechoic chamber
8 dB7,82452%Near-silent room
14 dB18,516123%Whisper at 5 meters
22 dB29,097194%Quiet bedroom
70 dB29,752198%Hearing aid

Self-dosing via hearing aid gain modulation doesn’t work as designed. The system behaves like a constitutive promoter in practice.

Root cause: NFAT_threshold (0.05) and Kd_CaN (500 nM) are both too low. Even minimal Ca2+ influx at ambient sound levels is enough to fully activate the NFAT cascade.

Stability: System is Safe

Eigenvalue analysis at 70 dB

All eigenvalues have negative real parts. System is asymptotically stable. Five timescales identified:

  • Fast (seconds): Ca2+ dynamics
  • Medium (minutes): NFAT cycling
  • Slow (hours): mRNA accumulation
  • Very slow (days): protein accumulation

No oscillations

CV < 1% for all variables under constant stimulation. No limit cycles, no chaos.

No bistability

Hysteresis check (ramp up 0→80 dB vs ramp down 80→0 dB) shows path-dependence due to slow protein degradation (t1/2 = 30 days), not true bistability. One steady state per parameter set.

Safety Analysis

Protein: hard-capped, always safe

Even at 200x fold induction: 199.5% of target. The saturation factor (1 - protein/max_protein) prevents runaway expression. Max is 30,000 molecules. This is a physical limit: finite binding sites on stereocilia.

Ca2+ toxicity: the real risk

Buffer ratioCa2+ at 70 dB
103,164 nM (TOXIC)
201,617 nM (TOXIC)
301,101 nM (TOXIC)
50 (baseline)689 nM (safe)
100379 nM (safe)

At sustained >100 dB: Ca2+ exceeds 1,000 nM. But this is a property of all hair cells, not the construct.

Promoter strength: not a concern

Even if fold induction is 3x higher than Wu et al. 2023 (200x instead of 62x), protein stays under 200% of target. The saturation cap dominates.

Two-Parameter Map (Kd_CaN x NFAT_threshold)

Swept Kd_CaN (100-2000 nM) against NFAT_threshold (0.01-0.30) at 70 dB. Key finding:

  • Most of parameter space lands at 150-300% (over-production, not dangerous)
  • Therapeutic sweet spot (50-150%): only 4% of tested combinations
  • No combinations produce dangerous (>300%) over-expression
  • Sub-therapeutic (<10%): only at high Kd + high threshold

What This Changes

  1. Self-dosing narrative needs revision. The system is safe and effective, but it’s not truly self-dosing. It’s an activity-dependent promoter that activates at very low thresholds. Honest framing: “activity-gated ON/OFF switch” rather than “continuous dose modulation.”

  2. Still better than constitutive. Even if self-dosing is binary (ON above ~10 dB, OFF in silence), it’s still superior to CMV/CBA constitutive promoters: no expression during sleep, no expression during illness (when hearing aid is off), and a theoretical OFF switch by keeping the patient in silence.

  3. Parameter optimization needed. To move the switching threshold into the 40-70 dB range (where hearing aids actually modulate), need either:

    • Higher Kd_CaN (>1500 nM) — would require engineering calcineurin or using a different Ca2+ sensor
    • Higher NFAT_threshold (>0.15) — would require fewer NFAT binding sites (4x instead of 6x?)
    • Lower Ca2+ permeability — not controllable
    • Higher buffer ratio — not controllable

Parameter Optimization Results (2026-04-15)

Swept 245 combinations: Kd_CaN (500-5000 nM) x NFAT_threshold (0.05-0.40) x Hill (2-8).

Best candidate: Kd=500 nM, threshold=0.30, Hill=8

Same Kd as current. Only two changes: higher NFAT threshold + steeper cooperativity.

Sound LevelCurrent ModelOptimizedWhat changed
0 dB11.6%0.1%Leak eliminated
20 dB (quiet room)179.7%0.1%Was saturated, now OFF
40 dB (quiet speech)198.3%5.7%Was saturated, now sub-therapeutic
45 dB~198%51.2%THE SWITCH POINT
50 dB198.3%163.3%Rapidly approaching therapeutic
60 dB198.3%197.5%Fully therapeutic
70 dB (hearing aid)198.3%198.1%Same as before

The switch now happens at 40-50 dB. Dynamic range at the switch: 35x over 10 dB window.

Biological implementation

Two changes needed:

  1. NFAT_threshold 0.05 → 0.30: Require 30% nuclear NFAT instead of 5%. Achievable by modifying the promoter.
  2. Hill 4 → 8: Steeper cooperativity. Achievable with more binding sites in tighter spacing.

Paradox: you need MORE binding sites (8x) but with HIGHER individual affinity threshold. This means 8xNFAT with weaker individual binding sites, or 8xNFAT with a spacer architecture that requires higher occupancy for activation.

Alternative interpretation: keep 6xNFAT but add insulator/spacer sequences between sites. This could raise the effective threshold while maintaining cooperativity.

Kd_CaN stays at 500 nM. No need to engineer calcineurin. The fix is entirely in the promoter.

Construct size impact

No change. Promoter stays ~300 bp whether 6xNFAT or 8xNFAT (each NFAT site is ~30 bp). Going from 6x to 8x adds ~60 bp. New total: 4,461 bp. Still fits with 239 bp margin.

Literature: NFAT Site Number Comparisons (2026-04-15)

Yamamoto et al. 2018 (PMC5855827) — Direct 3x/6x/9x comparison

Only study that directly compared different NFAT-RE repeat numbers in one experiment:

  • 3xNFAT-RE: minimal response to ionomycin stimulation
  • 6xNFAT-RE: significant response
  • 9xNFAT-RE: best fold-change (stimulated/basal ratio), selected for further work

9x gave the sharpest ON/OFF despite slightly higher basal. This supports our Hill=8 prediction.

Wu et al. 2023 — used 6xNFAT only

62x fold induction, zero leakage 3 weeks. Did NOT test other site numbers.

Pan et al. 2018 (PNAS) — composite promoter

Used SRE + CRE + NFAT-RE combined. Not pure NFAT. Exact site count not specified.

Liu et al. 2025 (Cell, EchoBack-CAR) — library screening

Screened promoter library with NF-kB + NFAT + CRE + SRE + 7x HSE. Found optimal combo for CAR T cells. Specific NFAT site data behind paywall.

Natural promoters

NFAT-dependent promoters in nature have 3-5 sites (IL-2, GM-CSF, TNFa). Evolution optimized for T-cell activation thresholds, not cochlear thresholds.

Proposed Promoter Design: 9xNFAT-weak

Resolution of the Hill=8 + threshold=0.30 paradox:

Use 9 NFAT binding sites, each with REDUCED individual affinity (1-2 nt mutation from consensus GGAAA). This gives:

  • High cooperativity (9 sites = steep Hill)
  • High threshold (weak sites need lots of nuclear NFAT to fill)
  • Zero leakage (in silence, no site is occupied)

Construct: 9 x ~30 bp = ~270 bp promoter. Total AAV: ~4,370 bp. Margin: 330 bp.

Standard synthetic biology approach: weakened sites + high multivalency = sharp switch with high threshold.

9xNFAT-weak Promoter Design (2026-04-15)

The entire self-dosing fix is ONE nucleotide substitution repeated 9 times.

NFAT-RE affinity ladder (from literature)

SequenceAffinityEffect
AGGAAAATStrong (consensus)Full binding. Current 6x uses this.
AGGAGAATSuboptimal (A4→G)~3-5x reduced. Documented in Crabtree 2003.
AGGAAAGTWeak (A5→G)~2-3x reduced
AGGAGAGTVery weak (double)~10x reduced
ATCAAAATDead (GG→TC)No binding. Negative control.

Key mutagenesis data from CD3gamma study (JBC 2002): changing 4th A in GGAAAA to G completely abrogated binding at individual sites. But our design uses 9 sites: each weak, but cooperative when NFAT is abundant.

Candidate construct: 9xNFAT-weak

9x [AGGAGAAT] + BglII spacers + TATA box = 161 bp
+ mini-STRC CDS (3,546 bp) + bGH polyA (250 bp) + ITRs (290 bp)
= 4,247 bp total (453 bp margin in AAV)

Full promoter sequence: see ~/DeepResearch/strc/promoter_design_9xNFAT.py

5 variants designed for comparative testing:

  1. 9xNFAT-strong (control, too sensitive)
  2. 9xNFAT-weak (CANDIDATE, switch at 40-50 dB)
  3. 9xNFAT-mixed (5 strong + 4 weak, fallback)
  4. 6xNFAT-weak (compact alternative)
  5. 6xNFAT-strong (Wu et al. reproduction, baseline)

All 5 fit in AAV with >400 bp margin.

Experimental validation

Phase 1 (50-80K, 3-6 months): AAV-mini-STRC with best promoter, cochlear explant Phase 3 ($150-300K, 12-18 months): In vivo Strc-/- mice, ABR/DPOAE

Code

  • Bifurcation analysis: ~/DeepResearch/strc/bifurcation_analysis.py
  • Parameter optimization: ~/DeepResearch/strc/parameter_optimization.py
  • Promoter design: ~/DeepResearch/strc/promoter_design_9xNFAT.py

Closed-Loop Model & Stress Tests (2026-04-15)

The missing piece: previous ODE used fixed sound profiles. Real self-dosing means the loop closes: protein → hearing improvement → HA gain reduction → less sound → less protein.

New model components

  1. Hearing function: protein → hearing loss (sigmoid, 45 dB at 0 protein → 0 dB at full)
  2. Hearing aid gain: loss × 0.46 (NAL-NL2 simplified fitting rule)
  3. Effective dB: ambient + HA gain (during waking hours)

Code: ~/DeepResearch/strc/closed_loop_model.py, ~/DeepResearch/strc/closed_loop_stress_test.py

Key result: 6x vs 9x difference appears under stress

Scenario6xNFAT-strong9xNFAT-weak
Normal operation (50 dB + HA)198% target184% target
HA lost 14 days-0.3% protein-26.8% protein
Hospital 30 days (25 dB, no HA)-1.0% protein-49.4% protein
Min ambient dB for therapy (no HA)0 dB45 dB
Recovery after HA restored100%98%

6xNFAT-strong is effectively constitutive. Works even in silence. No real self-dosing.

9xNFAT-weak is genuinely sound-dependent. TRUE self-dosing. But requires ~45 dB ambient for maintenance.

Clinical timeline (9xNFAT-weak, 50 dB ambient + HA)

TimeProtein% TargetHearing lossStatus
Day 0.53,08720.6%38.5 dBEarly improvement
Day 116,198108%7.9 dBFull therapeutic
Day 324,092161%4.0 dBHA gain → 0
Week 227,473183%3.1 dBEquilibrium

By day 3, hearing improves enough that HA adds zero gain. System self-regulates.

Equilibrium

At 90 days: 27,617 protein (184%), 3.1 dB residual loss, 0 dB HA gain. The system finds its own balance: enough protein for near-normal hearing, maintained by ambient sound alone.

Safety under loud exposure

EventPeak Ca²⁺Protein change
Concert (100 dB, 3h)1,038 nM (mild stress)+0.37%
Fire alarm (110 dB, 10min)1,108 nM+0.00%
Construction (90 dB, 8h)943 nM (safe)+1.92%

Protein barely changes from acute events. Accumulates over days, not hours. Ca²⁺ stress is the concern at >100 dB, but that affects all hair cells, not specific to construct.

Key insight

Self-dosing is a SLOW process (weeks/months), not fast (hours/days). The 30-day protein half-life acts as a buffer against daily sound fluctuations. This is a feature: therapy is robust to daily variation but responsive to sustained changes in sound environment.

Clinical implication for Misha

9xNFAT-weak is the right choice. Requires ~45 dB ambient during waking hours (normal home with speech). If sick at home 2 weeks without HA: -27% protein, hearing worsens from 3→5 dB loss. Recovers to 98% in 2 weeks after HA restored. Acceptable tradeoff for true activity-dependent gene therapy.

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