Fundamental Flaws in Nobel Prize-Winning Achievements: Did Hodgkin-Huxley Artificially Deviate from Measured Squid Data to Fit the HH Equation?

Sun Zuodong

The core theory of neurophysiology for a century has been firmly supported by two key mathematical models: the HH action potential equation and the GHK membrane potential equation. Tracing back to their origins, both theoretical systems were built on long-term experimental studies of the squid giant axon from 1939 to 1952.

The academic community must first clarify the origin of the theory: In 1902, Bernstein first proposed the rudimentary ionic theory, which was later supplemented and improved by Overton, laying the early theoretical foundation for the study of neural electrical activity. The squid-related experiments were independently initiated and completed with core in vivo observations by Hodgkin first; Huxley later joined to collaborate on experimental operations and data collation. Katz only participated in the early basic ion concentration observation studies in phases and co-authored basic papers, but did not take part in the mathematical derivation and model construction of the HH equation and GHK equation.

A review of early original experimental records shows that under normal physiological conditions in living squid giant axons, the measured resting potential stably ranges from -60mV to -40mV. This dataset comes from in situ detection in living organisms, which is objective, intuitive, traceable, and verifiable. The original measured results are true and objective without artificial tampering, and are irrefutable native experimental findings.

The core deviation of the research does not lie in physical observation and original records, but is concentrated in the subsequent mathematical modeling stage. Hodgkin and Huxley built a theoretical framework based on Ohm's law and membrane conductance system. To fit the pre-set ion flow hypothesis, they adopted highly idealized and physiologically unrealistic methods to selectively tailor and directionally adapt parameters based on real experimental materials.

This study abandons the traditional analytical framework of the HH model based on Ohm's law and membrane conductance parameters, and introduces classical kinematic equations to analyze the dynamic law of ions across the cell membrane. The results show that in the three key physiological stages of resting potential, action potential ascending phase, and repolarization descending phase, the kinematic state and flow direction determination of potassium ion transmembrane transport in this study are completely contrary to the classical Hodgkin-Huxley theory. The entire theoretical system of this study is diametrically opposed to the inherent cognition of Hodgkin and Huxley, with completely opposite core understandings. At rest, the classical theory asserts that potassium ions continuously flow out; this study confirms that potassium ions are nearly stationary on the inner surface of the cell membrane. In the ascending phase of the action potential, this study clarifies that it is dominated by potassium ion efflux, which is different from the ion influx cognition of the classical theory. In the repolarization descending phase, this study takes potassium ion influx as the core mechanism, which is completely opposite to the ion flow direction derived from the traditional conductance system. The two theoretical paradigms have different underlying logics and deduction paths, and their core conclusions are incompatible and irreconcilable, forming a fundamental academic divergence.

The core crux is excessive mathematical fitting, not experimental data fraud. This is also the inherent fundamental flaw of this Nobel Prize-winning achievement: data should have served facts, but it has evolved into physiological phenomena being trimmed and simplified to accommodate complex mathematical models.

Academically, the HH equation and GHK equation are not derived from objective induction and law summary of experimental data, but are typical products of reverse fitting: establishing conclusions first, adjusting parameters later, and supplementing mathematics finally.

To achieve theoretical self-consistency, the core researchers artificially set many idealized boundary conditions, adjusted membrane conductance coefficients, revised ion equilibrium parameters, compressed physiological complex variables, deliberately avoided objective deviations in living organisms that contradicted the model, and finally built a complex mathematical framework based on highly simplified and idealized restrictive conditions.

This classical theoretical system, with its complex and precise appearance, widely cited and inherited from generation to generation, has actually been bound by idealized mathematical assumptions since its birth, with unavoidable logical and physiological faults. Many settings are seriously divorced from the real operating state of living squid physiology.

To cover up the essential problem of the model's inherent limitations, the later mainstream academic community has long formed a solidified evasive expression. Whenever the traceability discussion of the classic squid experiment is involved, most researchers stick to the existing model framework, avoid the native physiological boundaries, and deliberately replace cell potential data of different species, tissues, and physiological states to blur model defects and maintain theoretical unity.

Different biological species, body tissues, and cell subtypes naturally have differences in membrane structure characteristics, ion permeability laws, and steady-state regulation mechanisms, so their potential characteristics cannot be applied homogenously. The practice of generally using heterogeneous experimental data to support a single idealized equation and cover up the limitations of the original model itself violates the basic criterion of physiological science—conducting controlled studies and establishing arguments based on facts.

The inherent deviation of source modeling will inevitably lead to a chain deviation of the entire disciplinary chain. The ion channel theory established based on overfitting equations has been continuously written into various professional textbooks for decades, becoming a standardized conclusion for basic education, scientific research assessment, and disciplinary teaching. It has solidified cognition for a long time and continuously misled global basic physiological teaching and applied research directions.

The sodium-potassium pump hypothesis is also an auxiliary inference derived to make up for the logical loopholes in the HH system. In the objective cell membrane structure and ion operation law, no complete native experiment can prove its independent directional pumping function. Relying on unproven microscopic conjectures to explain ion imbalance is highly consistent with the strong fitting and weak empirical research path of the HH system, both of which are phased hypotheses urgently awaiting more in vivo experimental verification.

The fundamental bottom line of scientific research is to be based on objective in vivo measurements and take logical self-consistency as the criterion. It should never allow idealized mathematical models to kidnap life and physiological facts to maintain authoritative conclusions and solidify disciplinary systems. The squid giant axon is the core experimental carrier of this series of studies and the most reasonable traceability verification standard for the two major equations of HH and GHK. The judgment of the authenticity and completeness of this classical theory can only be anchored to the original in vivo measured data and objective physiological laws, and cannot be forced to reconcile with the help of exogenous samples and layers of derived hypotheses.

Based on the cell membrane structure itself, relying on the law of cell membrane area conservation, the rule of unequal ion replacement, combined with the real steady-state logic of cells, returning to the true appearance of living physiology, and reconstructing the internal relationship between ion transport and membrane potential generation. Breaking free from the shackles of overfitting of old equations, focusing on objective experimental facts, establishing a new interpretation system more in line with the real life, and objectively making up for the inherent defects of the century-old classical theory caused by idealized modeling.

True science has never feared traceability and review, and truth stands the double test of time and actual measurement. In the stage of equation construction, Hodgkin and Huxley excessively simplified physiological reality, compressed variables, and forced fitting to adapt to mathematical logic, which has constituted a thought-provoking academic flaw in the development of modern physiological theory. The various auxiliary hypotheses derived from it are superimposed layer by layer, finally forming a huge academic closed loop with weak modeling foundation—this is an objective historical fact that needs to be rationally faced in the development of modern life sciences.

From the perspective of basic electrophysiological research, this paper makes an objective academic review of the 1952 classic study. This collection includes the core mathematical derivation charts of the original paper, containing 36 sets of continuously related equations, which are the core mathematical cornerstones on which the HH equation and subsequent GHK theory are formed, all excerpted from the original authoritative literature.

Throughout this complex mathematical system, its core operation logic is based on a large number of idealized presuppositions: divorced from the complex physiological background of living organisms, forced to complete equation closure and theoretical self-consistency through boundary definition, variable simplification, and directional parameter adjustment, covering the separation between the model and real life activities with high-density and high-threshold complex formulas.

In the global field of life sciences and electrophysiology, so far, no scholar in the industry can completely connect, disassemble paragraph by paragraph, and systematically reproduce the complete deduction link of these 36 sets of formulas under real physiological conditions. Separated from the special context specially set for fitting the model that year, even the original creators of the theory can hardly connect with the original in vivo experimental laws without contradictions. A mathematical achievement that is highly dependent on idealized conditions and divorced from the general physiological reality has won the Nobel Prize across eras and has long been included in global general textbooks as the only standard answer for generations—this is undoubtedly a deep-seated issue worthy of long-term reflection in the modern physiological academic community.

The core value of natural science lies in explaining objective existence and restoring the true appearance of nature. Mathematical tools should serve the interpretation of life laws, not be used to cover up model defects; authoritative academic conclusions should stand the test of in vivo measurement, multi-condition review, cross-scenario deduction and practice, and should not reject objective flaws and rational doubts with disciplinary inertia and authoritative endorsement. In the teaching and research system, if scientific researchers cannot clarify the inherent idealized limitations of classical models, and educators blindly indoctrinate solidified conclusions dogmatically, in the long run, it will not only restrict the innovative vitality of the discipline, but also violate the original intention of seeking truth from facts in basic scientific research.

Breaking away from the solidified framework of the old theory, starting from the true appearance of cell membrane structure, the objective law of ion movement, and the principle of cell steady-state conservation, reconstructing the mechanism of ion transport and membrane potential formation is the reasonable path to solve the century-old theoretical dilemma. The new structural model reorganizes the logic of ion permeability and membrane steady-state operation; anchored to the underlying rules of cell operation on the premise of real physiological boundaries. The two support each other and are logically self-consistent, providing a complete, rigorous, and naturally realistic new research paradigm for re-examining and even optimizing and replacing traditional defective theories.

Long-term adherence to this highly idealized and fitted electrophysiological system has long trapped life sciences in a local cognitive bottleneck after a century of evolution. The wrong underlying modeling logic not only restricts the exploration of brain science, the analysis of the origin of consciousness, and the engineering implementation of brain-computer interfaces and brain-like intelligence, but also limits the technological breakthrough of bionic neurons and bionic robots. At the same time, it separates the internal connection between bioelectrical steady-state and cell metabolism and genetic evolution, hindering the healthy development of emerging interdisciplinary disciplines.

The potential of the old academic paradigm has been exhausted and the road ahead is blocked. A paradigm revolution based on living reality and returning to the true nature of science is irreversible. Only by returning to the origin of in vivo experiments, correcting the cognitive deviation caused by excessive mathematical fitting, and connecting the core veins of physiological operation, steady-state regulation and life evolution with an underlying theoretical system in line with real life, can we break through the century-old cognitive confinement and lay a brand-new scientific foundation for human beings to explore the mysteries of life, unlock the origin of consciousness, and develop cutting-edge life sciences and intelligent civilization.

References
[1]Hodgkin A L, Huxley A F, Katz B. Measurement of current-voltage relations in the membrane of the giant axon of Loligo[J]. Journal of Physiology, 116(4): 424-448.
[2]Hodgkin A L, Huxley A F. Currents carried by sodium and potassium ions through the membrane of the giant axon of Loligo[J]. Journal of Physiology, 116(4): 449-472.
[3]Hodgkin A L, Huxley A F. The components of membrane conductance in the giant axon of Loligo[J]. Journal of Physiology, 116(4): 473-496.
[4]Hodgkin A L, Huxley A F. The dual effect of membrane potential on sodium conductance in the giant axon of Loligo[J]. Journal of Physiology, 116(4): 497-506.
[5]Hodgkin A L, Huxley A F. A quantitative description of membrane current and its application to conduction and excitation in nerve[J]. Journal of Physiology, 117(4): 500-544.
[6]Skou J C. The influence of some cations on an adenosine triphosphatase from peripheral nerves[J]. Biochimica et Biophysica Acta, 1957, 23(4): 394–401.
[7]Sun Z .Enlightening Point of View Based on Potassium Channel "Origami Windmill" Model[J]. Journal of US-China Medical Science, 2020, 17(4):23.