🔬 mesoscale physics

Cotunneling-Assisted Redistribution of Nonpassivity in a Photosynthetic Junction

This study demonstrates that in a Photosystem II reaction center modeled as a nonequilibrium molecular junction, cotunneling redistributes extractable nonequilibrium energy among various electronic states and can induce microscopic passive-state rearrangements that are often concealed by the thermodynamic smoothness of ergotropy and energetic capacitance.

Original authors: Manjet Rajak, Trishna Kalita, Debasish Sharma, Himangshu Prabal Goswami

Published 2026-10-08

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CC BY 4.0

Original authors: Manjet Rajak, Trishna Kalita, Debasish Sharma, Himangshu Prabal Goswami

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the quiet, microscopic world inside a leaf, a single photon of sunlight strikes a molecule and sets off a chain reaction that powers nearly all life on Earth. This process begins in a tiny machine called Photosystem II, where light energy is captured and converted into a flow of electrons. Scientists have long understood that this machine works by moving these electrons from one place to another, but a deeper question has remained: how is the energy stored within this system, and what happens when the rules of simple, one-by-one electron movement are broken? To understand this, one must first grasp the idea of "passivity." In a passive system, energy naturally settles into a calm state where the lowest energy levels are the most crowded, much like water settling at the bottom of a cup. In such a state, no useful work can be extracted because the system is already as relaxed as it can be. However, living systems are not passive; they are constantly being pushed by the sun, creating a busy, non-equilibrium state where energy is trapped in higher levels, waiting to be used. The challenge for researchers is to figure out exactly how this trapped energy is arranged and what happens when complex interactions, where electrons move in pairs rather than singles, begin to influence the flow.

A team of researchers at Gauhati University and the Indian Institute of Science has taken a detailed look at this problem using a sophisticated computer model of the Photosystem II reaction center. They treated the reaction center not as a static structure, but as a dynamic junction where electrons are constantly being pumped in by light and drained out to a reservoir, creating a steady flow of energy. Their goal was to see how a specific, complex process called cotunneling affects the arrangement of these electrons. Cotunneling is a rare event where two electrons move together through the system in a correlated way, rather than hopping along one by one. The researchers built a model that included all the key players: the light-harvesting pigments, the intermediate charge carriers, and the final electron acceptors. They then simulated how the populations of these different states changed as they varied the strength of the electrical repulsion between electrons, a force known as Coulomb interaction. By tracking these changes, they could measure two specific quantities: the amount of work that could theoretically be extracted from the system, and the total range of energy the system could hold if its electron populations were rearranged in every possible way.

The study revealed a surprising truth about how energy is stored in this biological machine. When the electrical repulsion between electrons is weak, the system behaves in a way where the ability to extract work increases as the rate of electron flow increases. In this regime, the energy is shared between the primary electron path and a complex, correlated state involving the final electron acceptor. However, as the researchers increased the electrical repulsion to a higher level, the behavior flipped. The ability to extract work began to decrease, even as the electron flow continued. This shift happened because the high repulsion changed which parts of the system were most important for storing energy. The primary electron path, which usually carries the most traffic, became less significant for storing extractable energy, while a different set of pigments on the inactive side of the reaction center took on a larger role. This finding challenges the simple idea that the most populated or most active parts of the system are always the most thermodynamically important.

One of the most striking discoveries was that the system can undergo significant internal rearrangements without showing any obvious signs on the surface. The researchers found that as they changed the conditions, the order in which the different energy levels were populated shifted multiple times. These shifts, where one state suddenly becomes more populated than another, should theoretically cause sharp jumps in the amount of extractable energy. Yet, the measurements showed a smooth, continuous curve. The reason for this smoothness was that while the specific order of the states changed, the overall balance of energy remained dominated by the same few key players. The system was quietly reorganizing its internal structure, swapping which states were paired with which energy levels, but the total amount of work available did not spike or crash. This means that looking only at the total energy or the flow of current would miss these critical microscopic changes. The researchers had to look deeper, at the specific arrangement of the populations, to see that the system was constantly shifting its strategy for storing energy.

The team also explored how the system responds when the rate of this rare, two-electron cotunneling process is changed. They found that increasing the rate of cotunneling caused the population of a specific, highly charged state to drop steadily. Surprisingly, the amount of extractable energy did not simply drop along with it. Instead, the energy first decreased, reached a minimum, and then began to rise again, even though the population of that specific state continued to fall. This counterintuitive result happened because the role of that state changed. As it became less populated, its position in the energy hierarchy shifted relative to other states, which altered how much work could be extracted from the system as a whole. The study showed that a state does not need to be heavily populated to be thermodynamically significant; its importance depends on where it sits in the energy landscape relative to the other states. A state with a very small population can still hold a large amount of potential work if it is positioned in a way that creates a large imbalance with the rest of the system.

These findings suggest that the efficiency of photosynthesis is not just about how many electrons are moving or how fast they are moving, but about the subtle, hidden architecture of how those electrons are arranged. The researchers demonstrated that the system uses a complex network of interactions to distribute its energy resources across different parts of the molecule, including parts that are not directly involved in the main electron transfer path. By using a method that tracks the specific ordering of populations, they were able to see that the system is constantly reorganizing itself to maintain its ability to do work, even as the conditions change. The study concludes that to truly understand how biological machines harvest energy, one must look beyond simple measures of flow and population size. The real story lies in the intricate, often invisible, rearrangements of the system's internal state, where the most important players are not always the most crowded, and where the smoothest curves can hide the most dramatic shifts in strategy.

Technical Summary: Cotunneling-Assisted Redistribution of Nonpassivity in a Photosynthetic Junction

Problem Statement
The paper investigates the thermodynamic properties of the Photosystem II reaction center (PSIIRC), modeled as a nonequilibrium molecular junction. While the PSIIRC is known to function as a charge-transfer network, its behavior as a finite nonequilibrium system involves complex population redistributions across many-body energy levels. The central problem is understanding how correlated many-electron transport processes, specifically cotunneling, influence the passivity of the system's steady state. Passivity refers to the ordering of state populations relative to their energies; a nonpassive (active) state contains extractable work because its population distribution violates the condition where lower-energy states have higher or equal populations than higher-energy states. The authors aim to determine how Coulomb interactions and cotunneling pathways reorganize these population orderings and alter the system's energetic capacity to perform work, beyond what is revealed by conventional transport observables like current or mean energy.

Methodology
The study employs a microscopic source-system-drain description of the PSIIRC, treating the oxygen-evolving complex (OEC) as the source and the downstream plastoquinone (PQ) pool as the drain.

Model Construction: The system is modeled as a thirteen-state finite quantum system comprising the ground state, six delocalized excitonic states, three intermediate charge-transfer states, a radical-pair state ( $|\alpha_1\rangle$ ), a terminal cationic state ( $|\beta_1\rangle$ ), and a cotunneling-assisted doubly reduced acceptor state ( $|\alpha_2\rangle$ ). The $|\alpha_2\rangle$ state is microscopically constructed from a reduced electronic subspace of the acceptor side, specifically representing two-electron configurations involving the terminal quinone $Q_B$ ( $|Q_B^{2-}\rangle$ , $|Q_A^- Q_B^-\rangle$ , and $|Pheo_{D1}^- Q_B^-\rangle$ ).
Dynamics: The reduced dynamics are formulated using the Nakajima-Zwanzig projection-operator framework.
- Optical excitation and relaxation are treated with second-order kernels.
- Vibrational redistribution within the excitonic manifold uses a modified-Redfield treatment.
- Internal transfer between excitonic and charge-transfer manifolds is treated in the Förster regime.
- Sequential electron exchange with reservoirs is calculated to second order.
- Cotunneling processes (correlated two-electron transfers) are retained to fourth order in the molecule-reservoir coupling. These rates ( $\omega_{xy}$ ) are regularized effective rates that depend on the Coulomb interaction energy $U$ .
Thermodynamic Quantification: The steady-state populations are used to calculate:
- Ergotropy ( $\mathcal{E}$ ): The extractable work, defined as the energy difference between the actual nonequilibrium steady state and its passive counterpart (populations reordered to minimize energy).
- Energetic Capacitance ( $C$ ): The total energetic range between the passive state and the anti-passive state (populations reordered to maximize energy) for the same population spectrum.
- Mean Energy ( $\langle E \rangle$ ): The average energy of the steady state.

Key Results

Redistribution of Nonpassivity: Cotunneling significantly redistributes the extractable nonequilibrium energy. At low Coulomb interaction ( $U$ ), the nonpassive energy is shared among the $D1$ radical pair ( $|\alpha_1\rangle$ ), the correlated acceptor state ( $|\alpha_2\rangle$ ), and excitonic states with strong $D2$ branch character ( $X_2, X_5$ ). At high $U$ , the contribution from the $D1$ radical pair becomes subdominant, while the $|\alpha_2\rangle$ state and $D2$ -weighted excitons remain dominant contributors to ergotropy.
Thermodynamic Smoothness vs. Microscopic Rearrangement: The study finds that thermodynamic observables (ergotropy and capacitance) can exhibit smooth, continuous behavior even when the underlying microscopic population ordering undergoes discrete changes. Specifically, "population crossings" (where the relative magnitude of populations of two states swaps) can alter the passive state permutation without causing abrupt changes in the total ergotropy, provided the dominant energy-weighted population differences remain structurally unchanged.
Distinct Roles of Molecular Sectors: The analysis reveals that kinetic participation, steady-state population magnitude, and thermodynamic importance are distinct properties. For instance, the $|\alpha_2\rangle$ state may have a small population that decreases further with increasing cotunneling rates, yet its energy-weighted deviation from the passive assignment remains a dominant term in the ergotropy. Conversely, highly populated states may contribute little to extractable work if their occupation is already close to the passive ordering.
Piecewise-Linear Relations: The paper identifies piecewise-linear relationships among ergotropy, energetic capacitance, and mean energy. These linear segments correspond to regions of fixed population ordering. Kinks or breaks in these linear relations occur precisely at population crossings, serving as a thermodynamic signature of microscopic reorganizations.
Interaction-Dependent Response:
- Low $U$ : Increasing the electron-ejection rate increases ergotropy while decreasing the work associated with the terminal transition. This suggests a network response where population redistribution enhances global nonpassivity to compensate for terminal work loss.
- High $U$ : Both ergotropy and the terminal work decrease with increasing ejection rates. However, energetic capacitance continues to increase, indicating that while the realized steady state becomes more passive, the underlying population spectrum retains (or increases) its potential energetic range.

Significance and Claims
The paper claims that a complete thermodynamic description of the PSIIRC must account for population ordering generated by the full kinetic network, rather than relying solely on conventional transport observables.

Passivity as a Diagnostic: Passivity analysis exposes reorganizations of the steady state that remain hidden in current, mean energy, or individual population curves. It provides a molecular criterion for identifying where thermodynamic importance resides, which cannot be inferred from population magnitude alone.
Role of Cotunneling: Cotunneling is shown to reorganize the thermodynamic importance of molecular populations distributed across the $D1$ charge-separated and $D2$ excitonic parts of the PSIIRC. It shifts the balance of extractable energy away from the productive $D1$ radical pair toward the terminal acceptor and $D2$ excitonic manifolds under strong Coulomb interaction.
Methodological Contribution: The work demonstrates that the combination of ergotropy and energetic capacitance can distinguish between a reduction in realized nonpassivity and a reduction in the available energetic range of the population spectrum. The piecewise-linear relations among energetic observables serve as a direct thermodynamic signature of successive microscopic population reorganizations driven by cotunneling.

The authors conclude that their findings are robust against reasonable variations in pigment-site parametrization and that the observed phenomena are intrinsic to the interplay between Coulomb interactions, many-body transport, and the nonequilibrium driving of the photosynthetic junction.

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