**Agentic reinforcement learning controllers trained via Hamiltonian-based policies (risk-reward optimization) will modulate junctional tension fluctuations in confluent epithelial monolayers to induce persistent Brownian motion regimes that resist jamming transitions, measurable via single-cell tracking.**

An agentic reinforcement learning (RL) controller — trained with a Hamiltonian-based policy that jointly optimizes a "risk" term (variance/uncertainty of junctional tension) and a "reward" term (maintenance of target tension setpoints or motility metrics) — when coupled in closed loop to a vertex-model or cell-based simulation (and, in the extended version, to optogenetic actuation of junctional myosin in a real epithelial monolayer), will produce a statistically significant increase in the fraction of cells exhibiting mean-squared-displacement (MSD) exponents α > 1.4 (persistent/super-diffusive regime) over a 2-hour window, and will suppress the fraction of cells with caged/sub-diffusive trajectories (α < 0.3) relative to (a) an untrained/random-policy controller and (b) a standard scalar-reward RL controller (no Hamiltonian risk term), at fixed mean tension and fixed cell density (confluency ≥ 0.95). The effect must be reproducible across ≥3 independent simulation seeds / monolayer replicates with effect size Cohen's d ≥ 0.5.

Phase 1 (in silico, primary): Self-propelled Voronoi (SPV) or vertex-model confluent monolayer (N=400–1000 cells, periodic boundary), tension-fluctuation actuation exposed as an RL action space. Train 3 controller variants: (i) random policy, (ii) scalar-reward PPO baseline, (iii) Hamiltonian risk-reward policy (custom actor-critic with Pontryagin-inspired costate/risk regularization). Run closed-loop control for simulated 2-hour windows, track all cell centroids at 1-frame/30s. Repeat ×10 seeds per condition.

Phase 2 (in vitro, confirmatory, optional/staged): MDCK monolayer expressing optoGEF-RhoA at junctions + membrane/nuclear marker for tracking. Blue-light patterned stimulation driven by the same trained policy (ported via a real-time image-analysis-to-actuation loop). Track single-cell trajectories via Bayesian multi-object tracking for 2h, N≥3 biological replicates, ≥300 cells/replicate analyzed.

# Environment
class MonolayerEnv(gym.Env):
    def __init__(self, vertex_model, n_cells=600):
        self.sim = vertex_model
        self.action_space = Box(low=0.5, high=2.5, shape=(n_edges,))
        self.observation_space = Dict(tension=Box(...), shape_index=Box(...), topology=Graph(...))

    def step(self, action):
        self.sim.apply_tension_modulation(action)
        self.sim.advance(dt)
        obs = self.sim.get_state()
        reward, risk = compute_reward_risk(obs, self.history)
        return obs, reward, risk, done, info

# Hamiltonian actor-critic
H = R(s,a) - lambda_t * Risk(s,a)
policy_grad = grad(H, theta)
lambda_t += eta * (Risk(s,a) - risk_budget)  # dual ascent on costate

# Training loop
for episode in range(N_EPISODES):
    s = env.reset()
    for t in range(T):
        a = policy(s)
        s2, r, risk, done, _ = env.step(a)
        buffer.store(s,a,r,risk,s2)
        s = s2
    update_actor_critic(buffer, H)
    update_lambda(buffer, risk_budget)

# Analysis
msd = compute_msd(trajectories, tau_range)
alpha = fit_power_law(msd)
chi4 = dynamic_susceptibility(trajectories)
stats = mixed_effects_model(alpha ~ condition + (1|seed))