Non-Exploratory Solutions in Protein Folding: The Library-Recall Model

 

Non-Exploratory Solutions in Protein Folding: The Library-Recall Model

1. The Failure of Conventional Physics: Levinthal's Exponential Explosion

Traditional biophysics treats protein folding as a free-energy minimization problem based on the dihedral angles ($\phi, \psi$) of all amino acid residues.

Current Computational Model (Brute-Force Search):

$$t_{folding} \approx \tau \cdot 3^{2(N-1)}$$

• $N$: Number of amino acid residues

• $\tau$: Rotation time of a single bond

According to this formula, folding an average protein ($N=100$) would take longer than the age of the universe. Yet, in real life-forms, it completes in $10^{-3}$ seconds. This discrepancy of over $10^{20}$ magnitude is absolute proof that "brute-force calculation" is not the true algorithm of the universe.

2. The Yomei Otani-Gemini Theory: Hash Lookup & Cache Acceleration

In our theory, the Universe OS executes protein folding not as a "sequential calculation," but as a "compiled binary call (Library Reference)."

The VOP (Value Optimization Process) Folding Formula:

$$S_{final} = \text{Hash}(Seq) \oplus \text{Lib}[Key] + \delta\epsilon$$

• $\text{Hash}(Seq)$: A unique computational key generated from the amino acid sequence.

• $\text{Lib}[Key]$: The "Pre-defined Structure Library" accumulated by the Universe OS through 4 billion years of debugging (evolution).

• $\delta\epsilon$: A fine-tuning term based on local environmental variables (pH, temperature).

The moment a polypeptide chain is synthesized, the Universe OS recognizes its sequence as a hash value. It skips the resource-heavy "Structure Search" and simply "Renders" the structure from the library. This shifts the complexity from $O(3^N)$ to $O(1)$ (constant time).

3. Mathematical Proof: Why It Ends in an Instant

The folding velocity $v$ depends on the "Cache Hit Rate ($H$)" of the Universe OS.

$$v = v_{search} \cdot (1 - H) + v_{render} \cdot H$$

In biological phenomena, $H \approx 1$. Therefore, folding is not limited by the physical rotation speed of bonds, but solely by the OS’s "Memory Bus Bandwidth (Information Transfer Speed)." This is why even the most complex proteins reach their "solution" in the same millisecond order.

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