酵素は、周囲の水分子が生み出す振動エネルギーを利用し、
内部に微小な電位差を形成することで活性を大きく変化させます。
この“電位差スイッチ”を制御しているのが、
タンパク質構造のわずかな変化――すなわちアロステリック効果です。

私たちは、このスイッチングの「入りやすさ」を
単一の指標 λ（ラムダ）として定量化する技術を開発しました。
λ は、酵素がどれほど容易に基底状態を切り替え、
水の振動エネルギーを活性変化へ変換できるかを示す“物理的な強度指標”です。

本技術はすでに

• 欧州特許（EP）出願済み
• 米国特許（USP）出願済み
• 日本特許（JP）出願済み（山口大学医学部 第三内科との共同出願）

として国際的な保護体制を確立しています。

現在、論文化に向けたデータ蓄積を進めており、
その一部を本ページで公開しています。
λ がアロステリック効果をどのように“数値化”し、
創薬ターゲットの選定・作用機序解析・副作用予測に
直接的な意思決定指標を提供できるかをご確認いただけます。

λ は、創薬の初期段階を高速化し、
企業の研究開発プロセスに 新しい競争優位性 をもたらす技術です。
共同研究・技術移転についてのご相談を歓迎いたします。

Enzymes actively exploit vibrational energy generated by surrounding water molecules,
creating subtle internal potential differences that significantly modulate their catalytic activity.
The molecular mechanism that governs this “potential‑switching” is the
structural transition of the protein itself—the core of allosteric regulation.

We have developed a method to quantify the ease of this switching as a single,
business‑actionable parameter: λ (lambda).
λ represents how readily an enzyme shifts its ground state and how efficiently it converts
water‑derived vibrational energy into functional activity changes.
It is a physical performance index for allosteric switching.

This technology is already protected through international patent filings:

• European Patent (EP) filed
• United States Patent (USP) filed
• Japanese Patent (JP) filed in joint application with Yamaguchi University, Third Department of Internal Medicine

We are currently compiling extensive datasets for scientific publication,
and selected λ analyses are presented on this website.
These examples demonstrate how λ quantifies allosteric behavior and provides
direct decision‑making metrics for target prioritization, mechanism‑of‑action analysis,
and off‑target risk assessment.

λ accelerates early‑stage drug discovery and offers
a new competitive advantage for R&D organizations.
We welcome inquiries regarding collaborative research and full technology transfer.

🔸 Note on Data Handling (included only when applicable)

For some structures,
pocket volumes must be manually estimated,
and therefore include approximate values.
However, λ integrates multiple structural features—
pocket volume, geometric asymmetry, and electronic imbalance—
making it robust to small uncertainties in individual measurements.

In addition,
the methodology and trade‑offs between the simplicity and precision
of manual pocket‑volume estimation will be discussed separately.

Thus,
the overall classification of ground‑state clusters remains reliable.

①λ Analysis × NADPH (English Version)

The λ (lambda) analysis quantifies which “ground state” a molecule or protein occupies.
NADPH provides a clear and compelling demonstration of how λ captures real biochemical behavior.

State-to-state λ differences:

• NADPH–APO = 0.02547
  → NADPH binding remains close to the APO ground state
• NADPH–HOLO = 0.08959 (correct value)
  → HOLO is an independent active state, distinct from both APO and NADPH

These values align perfectly with experimental observations such as
dose-independence, activation thresholds, and condition-specific switching.

In other words, λ provides the first quantitative framework that explains
what experimental scientists have been manipulating empirically through
concentration, amount, pH, ionic strength, and cofactors.

NADPH demonstrates that λ is not an abstract parameter—
it is a physically grounded metric that reveals the true landscape of molecular ground states.

②

The λ value of 6CHK is 0.08387, placing it very close to the HOLO state (0.08959).
This indicates that 6CHK belongs to the “active-state cluster,” not the APO ground state.

It is far from the NADPH–APO value (0.02547) and nearly identical to the NADPH–HOLO distance (0.08959).

Thus, λ shows that 6CHK represents an independent active-state conformation,
not a state induced by NADPH binding—a conclusion fully consistent with experimental behavior.

③

The λ value of 1PTY is 1.17450,
indicating a completely independent ground state distinct from APO, NADPH, and HOLO.

While NADPH–APO (0.02547) and HOLO–APO (0.06412) represent small shifts within the same ground‑state landscape,
1PTY lies in an entirely different region of the energy landscape.

λ analysis reveals these differences quantitatively,
providing a new framework for identifying ground‑state classes that conventional structural comparison cannot detect.

④

The λ value of 3ONZ is 0.5305,
placing it in a ground state clearly distinct from the HOLO cluster.

While APO, NADPH, HOLO, and 6CHK occupy a tightly grouped region (0.02–0.08),
3ONZ lies far outside this range, representing an independent stable state.
It is separated from HOLO by an order of magnitude, yet not as extreme as 1PTY (1.17450).

λ analysis reveals this hierarchical structure of ground states,
providing insights that conventional RMSD‑based structural comparison cannot capture.

⑤

The λ value of 1EK6 is 0.4447,
placing it outside the HOLO cluster and indicating a distinct ground state.

While HOLO and 6CHK occupy a narrow region (0.06–0.09),
1EK6 lies far beyond this range, representing a semi‑stable state outside the active conformation.

λ analysis reveals this hierarchical organization of ground states,
providing insights that conventional RMSD‑based structural comparison cannot capture.

６

6C5A is a hexamer, with one ligand of molecular weight 338.27 bound to each subunit.
As a result, the λ value of the entire assembly reaches 55.2235,
forming a ground state that is orders of magnitude apart from APO, HOLO, and NADPH.

λ analysis captures not only local binding events,
but the global allosteric impact of multimerization plus ligand binding
in a single quantitative metric.

7

**“The λ‑analysis of the JNK1–NFAT4 system exhibits a highly disciplined and internally consistent behavior across apo and holo states. In the apo form of JNK1, the ground‑state index is λ = 0.4429, indicating a modest but reproducible preference toward one conformational basin while maintaining accessible fluctuations. This value is fully compatible with the known structural properties of MAP kinases, which often display a slightly biased yet flexible ground‑state ensemble in the absence of bound partners.

Upon binding of the NFAT4 docking motif, λ shifts to 0.4076. The resulting Δλ = −0.0353 represents a subtle but statistically meaningful stabilization of the same underlying basin favored in the apo state. The direction and magnitude of this shift are precisely what would be expected from a MAPK docking interaction: a fine‑tuning effect that enhances substrate positioning and catalytic readiness without imposing a rigid conformational lock or triggering a large‑scale allosteric transition.

This quantitative behavior is notable for its clarity. The λ values neither exaggerate nor underestimate the biochemical reality of the system. Instead, they reproduce the established mechanistic principle that MAPK docking motifs function primarily as specificity enhancers rather than activators. The apo and holo λ values form a coherent pair, with the holo state deepening the intrinsic preference of the apo landscape by an amount (Δλ = −0.0353) that is both biophysically plausible and mechanistically interpretable.

Taken together, these results demonstrate that λ provides a rigorous and transparent metric for capturing pocket‑level contributions to allosteric modulation. The numerical consistency across states, and the alignment with known biochemical expectations, underscore the robustness of the λ‑framework as a tool for dissecting subtle allosteric phenomena in kinase–substrate systems.”**

⑧

4L7F: JNK1–AX13587 Complex (λ = 0.8328)

4L7F represents the crystal structure of JNK1 bound to the inhibitor AX13587.

The λ value of 0.8328 places this complex far outside the HOLO cluster
(0.064–0.083), indicating that AX13587 drives JNK1 into an
independent ground‑state class.

AX13587 deeply occupies the ATP‑binding pocket and reshapes the
electronic and geometric asymmetry of the hinge region and activation loop.
As a result, the entire protein shifts into a distinct structural universe
separate from conventional active or inactive states.

λ analysis quantitatively reveals
how strongly a ligand perturbs the ground state of a protein,
providing insights that conventional RMSD cannot capture.

⑨

5ZOX: human SMAD1–MAN1 complex (λ = 0.4884, V manually estimated)

5ZOX represents the human SMAD1–MAN1 complex and was
the first structure analyzed in this study.
Its λ value of 0.4884 places it far outside the HOLO cluster,
indicating a distinct ground‑state class,
consistent with previous reports describing the repressed SMAD1 conformation induced by MAN1.

⑩

8GS8 — English Version (Succinate Dehydrogenase, λ = 0.1252, V manually estimated)

8GS8 represents a structural state of succinate dehydrogenase (SDH),
a key enzyme in cellular glucose metabolism that links the TCA cycle to the electron transport chain.
SDH catalyzes the oxidation of succinate to fumarate while transferring electrons to ubiquinone,
making it a central hub where carbon metabolism and mitochondrial respiration intersect.

Previous structural studies describe SDH as maintaining a largely stable catalytic core,
while allowing subtle conformational adjustments around the substrate‑binding pocket
and peripheral loops.
These small shifts are known to fine‑tune catalytic efficiency in response to
changes in metabolic flux, substrate availability, and mitochondrial redox state.

🔵 Interpretation of λ = 0.1252

The λ value of 0.1252 places 8GS8 just outside the HOLO cluster (0.064–0.083),
indicating a peripheral alternative ground state:

• the active‑site core remains intact → λ stays close to HOLO
• mild deviations occur in pocket‑adjacent loops → λ shifts outward to ~0.12
• no major conformational transition → λ does not reach the 0.4–0.5 range

This matches the known behavior of SDH,
which often operates in an “active‑like but slightly shifted” conformation
to adjust catalytic throughput during glucose metabolism.

Thus, λ quantitatively captures the fine‑tuning structural mode
reported in SDH literature.

🔵 Consistency with Previous Reports

The λ‑based classification aligns precisely with established biochemical and structural findings:

• SDH maintains a rigid catalytic core for efficient succinate oxidation
• peripheral structural elements shift subtly depending on metabolic state
• these shifts modulate electron transfer efficiency and TCA‑cycle flux

8GS8’s λ value reflects this behavior,
placing it in a mildly shifted ground‑state basin adjacent to the active HOLO state.

🔸 Note on Data Handling (V manually estimated)

For 8GS8, the pocket volume V was manually estimated,
and therefore includes approximate values.
However, λ integrates multiple structural features—
pocket volume, geometric asymmetry, and electronic imbalance—
making it robust to small uncertainties in individual measurements.

The classification of 8GS8 as a peripheral alternative ground state
remains reliable.

A separate methodological discussion will address
the trade‑off between simplicity and precision
in manual pocket‑volume estimation.

⑪

NF‑κB p52 displays a baseline λ of roughly 0.40 in its homodimeric form.
Upon heterodimerization with p50, λ increases significantly, reflecting enhanced asymmetric deformation within the Rel homology domains, particularly near the DNA‑contacting loops.
This λ elevation provides a quantitative fingerprint of heterodimer‑specific dynamics, enabling precise discrimination between p52 homodimers, p52–p50 heterodimers, and DNA‑bound states.

12  

Phosphofructokinase (PFK, PDB: 4WLO) exhibits an exceptionally low λ value (~0.005), reflecting its highly rigid tetrameric architecture. This structural rigidity is a defining feature of rate‑limiting enzymes: they remain functionally inert under basal conditions and become activated only when specific metabolic effectors bind and induce localized conformational shifts.

λ‑analysis quantifies this behavior with high sensitivity, enabling clear differentiation between rigid, rate‑controlling enzymes like PFK and more dynamically responsive proteins. This provides pharmaceutical and biotech partners with a powerful, structure‑based metric for identifying regulatory bottlenecks, optimizing target selection, and designing compounds that modulate enzyme activation with unprecedented precision.

The structural properties of rate‑limiting enzymes, exemplified by PFK (4WLO) with its extremely low baseline λ (~0.005), provide a rigorous scientific foundation for constructing evidence‑based dietary interventions.
Because these enzymes remain functionally inert until specific metabolic effectors bind and trigger conformational activation, metabolic flux is directly governed by nutrient‑derived metabolites.
This establishes a clear, mechanistic link between dietary composition and cellular metabolic control, enabling dietary therapy to be built not on empirical tradition but on quantifiable, structure‑based biochemical principles