A State-Space and Trajectory-Evolution Formulation for Therapeutic Variability and Convergence in Cancer Therapy

Modern cancer therapy has achieved major advances through molecularly targeted therapies, immune checkpoint blockade, and antibody–drug conjugates, guided by the principles of precision oncology. Despite increasingly precise molecular interventions guided by actionable molecular targets and predictive biomarkers, therapeutic outcomes remain highly variable, making it a major bottleneck. Such variability suggests that therapeutic outcomes emerge not directly from molecular targeting, but through therapy-driven evolution of the tumor–host system. This intrinsically dynamical nature of cancer therapy motivates the introduction of concepts from dynamic systems theory.Here, a conceptual state-space formulation of therapeutic trajectory evolution, variability, and convergence is proposed. Within this framework, the tumor–host system is represented as an accessible state-space organization (θ) that constrains therapeutic trajectory evolution (T) and the attractor (A) from which therapeutic outcome (y) emerge. Therapeutic input (μ) drives system trajectory evolution, whereas state-space modulating operator (υ) modifies the accessible state-space organization θ, generating a modified accessible state-space organization θ_υ.The conceptual formulations y ~ A[T(θ, μ)] and y’ ~ A’[T’(θ_υ, μ)] represent therapeutic trajectory evolution within original and modified accessible state-space organization, respectively. Under modified accessible state-space organization, trajectory evolution may exhibit reduced diversity and increased convergence toward restricted attractors, thereby promoting therapeutic convergence.Bicarbonate-mediated tumor alkalization and intracellular lactic acidosis are discussed as representative examples of external and internal state-space modulating operators. In hepatocellular carcinoma, bicarbonate-enhanced transarterial chemoembolization and bicarbonate-augmented anti–PD-1 therapy demonstrated unusually high and convergent therapeutic responses, reflecting biased trajectory evolution within a modified accessible state-space organization. In contrast, intracellular lactic acidosis is represented as an endogenous state-space modulating operator arising from tumor metabolic adaptation.Taken together, the present framework provides a conceptual explanation for therapeutic variability as a major limitation of molecular-targeting-based cancer therapy and suggests that combining molecular targeting with state-space modulation may represent a promising direction for overcoming this limitation and improving therapeutic efficacy.