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Double exponential neuron evolution versus merely exponential Artificial Intelligence (AI): Reconsideration of Kurzweil's Singularity. 双指数神经元进化与单指数人工智能(AI):对库兹韦尔奇点的重新思考。
IF 1.9 4区 生物学 Q2 BIOLOGY Pub Date : 2026-01-20 DOI: 10.1016/j.biosystems.2026.105709
Varshith Madishetty, Lalith Bharadwaj Baru, S Hussain Ather, Richard Gordon

Reanalysis of recent data has led to two unexpected conclusions. 1) Animals with regulating embryos show exponential growth in the number of cell types (NCT) over geological time, while animals with mosaic embryos remain merely flat or linear on average, highlighting fundamentally different evolutionary strategies; 2) Recent evolution of the number of nerves in adult regulating animals has been doubly exponential. Mosaic animals tend to yield a pair of cells at each cell division that are differentiated from one another and their mother cell during embryogenesis, while regulating animals usually produce large numbers of presumably identical cell types at each step of embryogenesis, possibly via bioelectric fields. (The mother cell is usually different from both of its daughter cells in mosaic development, and is transient.) For some animals, these categories overlap. Nevertheless, plots of the number of cell types (NCT) versus estimates of when their first ancestors appeared show no increase on average for NCT versus geological time for animals whose embryos are generally categorized as mosaic, whereas animals with regulating embryos show an exponential increase in NCT versus geological time. An attempt to confine NCT to neurons failed due to sparse data, but did suggest that the total number of neurons in animals with regulating embryos increased as a double exponential over geological time (i.e., they have exponential behavior even on a logarithmic scale). AI has only been increasing exponentially with respect to the number of simulated neurons used in state-of-the-art algorithms. Thus, amalgamating human brains with AI, even if Ray Kurzweil's "Singularity is Nearer", may prove premature. Furthermore, amalgamation might lead to atrophy of portions of the human brain.

对近期数据的重新分析得出了两个意想不到的结论。1)具有调节胚胎的动物在细胞类型(NCT)数量上呈指数级增长,而具有镶嵌胚胎的动物在细胞类型(NCT)数量上平均保持扁平或线性增长,这突出了根本不同的进化策略;2)近年来,成年调节动物神经数量的进化呈双指数增长。嵌合动物在每次细胞分裂时往往产生一对细胞,这些细胞在胚胎发生过程中从另一个细胞和它们的母细胞中分化出来,而调节动物通常在胚胎发生的每一步都产生大量可能相同的细胞类型,可能是通过生物电场。(在马赛克发育过程中,母细胞通常与其子细胞不同,并且是短暂的。)对一些动物来说,这些分类是重叠的。然而,细胞类型(NCT)的数量与它们的第一个祖先出现的估计时间的图显示,胚胎通常被归类为镶嵌的动物的NCT与地质时间相比平均没有增加,而具有调节胚胎的动物的NCT与地质时间相比呈指数增长。由于数据稀疏,试图将NCT限制在神经元上的尝试失败了,但确实表明,具有调节胚胎的动物的神经元总数在地质时间内以双指数增长(即,它们即使在对数尺度上也具有指数行为)。相对于最先进的算法中使用的模拟神经元的数量,人工智能只会呈指数级增长。因此,即使雷·库兹韦尔(Ray Kurzweil)的“奇点更近了”(Singularity is closer),将人类大脑与人工智能结合起来可能还为时过早。此外,合并可能导致人类大脑的部分萎缩。
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引用次数: 0
Measures of gene indispensability reveal the parallelism between phylogeny and ontogeny 基因不可或缺性的测量揭示了系统发育和个体发育之间的相似性。
IF 1.9 4区 生物学 Q2 BIOLOGY Pub Date : 2026-01-19 DOI: 10.1016/j.biosystems.2026.105710
Juraj Bergman , Robert Bakarić , Krunoslav Brčić-Kostić
Haeckel's biogenetic law, or the recapitulation theory remains a controversial subject to this day since it is not based on quantitative regularities. Currently, the modern version of the biogenetic law is the hourglass model with its phylotypic period. Importantly, the hourglass model does not provide evidence that ontogeny recapitulates phylogeny, and it is often presented as the alternative model to recapitulation theory. However, the hourglass model and recapitulation are not mutually exclusive, and there are several examples of recapitulation-like processes observable after the phylotypic period of ontogeny. At the level of transcriptomics, all attempts to demonstrate recapitulation failed. Using a novel approach, combining transcriptomics with phylostratigraphy, we demonstrate that recapitulation exists as a quantitatively testable law. We show that the mean indispensability of genes decreases for phylogenetically younger genes, as well as genes expressed during later stages of ontogeny. We also define the ontotypic period of phylogeny, an analog to the phylotypic period of ontogeny. Since it starts from the beginning of phylogeny, it is reasonable to hypothesize that recapitulation starts from the phylotypic period. We conclude that parallelism, or recapitulation, is explainable by the fact that genes that emerged later in phylogeny have tendencies to be expressed during later stages of ontogeny. This is expected from the fundamental properties of Darwinian evolution which is based on conservation of existing gene functions by purifying selection and addition of new gene functions by positive selection. According to this, our result (the existence of parallelism or recapitulation) represents the empirical evidence for macroevolution.
海克尔的生物遗传定律,或重述理论至今仍是一个有争议的话题,因为它不是基于定量规律。目前,生物发生规律的现代版本是具有进化期的沙漏模型。重要的是,沙漏模型并没有提供个体发育重述系统发育的证据,它经常被提出作为重述理论的替代模型。然而,沙漏模型和重述并不是相互排斥的,在个体发育的种型期之后,可以观察到几个类似重述过程的例子。在转录组学的水平上,所有证明重述的尝试都失败了。使用一种新颖的方法,结合转录组学和系统地层学,我们证明了重述作为一种定量可测试的规律存在。我们表明,在系统发育上较年轻的基因以及在个体发育后期表达的基因的平均不可或缺性降低。我们还定义了系统发育的单型期,类似于个体发育的系统发育期。由于重述从系统发育的开始就开始了,因此有理由假设重述从系统发育时期开始。我们得出的结论是,平行性,或重述,是可以解释的事实,即基因出现在较晚的系统发育有倾向表达在个体发育的后期阶段。这是达尔文进化的基本特性所期望的,它基于通过净化选择来保存现有的基因功能和通过积极选择来添加新的基因功能。据此,我们的结果(平行或重述的存在)代表了宏观进化的经验证据。
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引用次数: 0
Information transmission and processing in G-protein-coupled-receptor complexes g蛋白偶联受体复合物中的信息传递和加工
IF 1.9 4区 生物学 Q2 BIOLOGY Pub Date : 2026-01-16 DOI: 10.1016/j.biosystems.2026.105706
Roger D. Jones , Achille Giacometti , Alan M. Jones
We present a general theoretical framework for molecular computation in biological systems and apply it to G-protein-coupled receptors (GPCRs), which serve as central regulators of cellular information processing. Despite their importance, the physical principles underlying GPCR switching remain incompletely understood. Using nonequilibrium thermodynamics, we construct a model that identifies the parameters governing receptor-state transitions. The framework shows that the configuration of the switch is governed by two factors: the ATP/GTP-driven chemical flux through the receptor complex and the free-energy difference between competing switch states. The model predicts that GPCRs can occupy three quasistable configurations, corresponding to “on”, “off”, and an intermediate state, each representing a local maximum in information transmission. Switch states can also be characterized by whether the switch supports a net chemical flux. Active states support sustained chemical flux, whereas inactive states do not. The model incorporates reciprocal conformation-fit changes between ligand and receptor. As such, the model predicts that phosphatase activity, represented as an effective energy barrier, primarily determines whether the switch occupies the “on” or “off” state, whereas kinase activity maintains flux without directly setting state occupancy. These predictions based on experimental evidence point to new targets for drug design. Comparison with label-free impedance measurements supports the existence of multiple quasistable states that depend on ligand conformation. Because the framework relies on general nonequilibrium principles rather than system-specific biochemistry, it extends naturally to other biological switching systems driven by chemical flux.
我们提出了生物系统中分子计算的一般理论框架,并将其应用于作为细胞信息处理中心调节器的g蛋白偶联受体(gpcr)。尽管它们很重要,但GPCR转换的物理原理仍然不完全清楚。利用非平衡热力学,我们构建了一个模型,该模型确定了控制受体状态转换的参数。该框架表明,开关的结构由两个因素决定:ATP/ gtp驱动的通过受体复合物的化学通量和竞争开关状态之间的自由能差。该模型预测gpcr可以占据三种准稳定的构型,分别对应于“开”、“关”和一个中间状态,每一种状态代表信息传输的局部最大值。开关状态也可以通过开关是否支持净化学通量来表征。活性状态支持持续的化学流动,而非活性状态则不支持。该模型包含了配体和受体之间的相互构象匹配变化。因此,该模型预测,作为有效能量屏障的磷酸酶活性主要决定开关是否占据“开”或“关”状态,而激酶活性维持通量而不直接设置状态占用。这些基于实验证据的预测为药物设计指明了新的目标。与无标记阻抗测量的比较支持依赖于配体构象的多个准稳态的存在。由于该框架依赖于一般的非平衡原理,而不是系统特定的生物化学,因此它自然地扩展到由化学通量驱动的其他生物开关系统。
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引用次数: 0
Internal quantum constraints of natural computation in autopoietic systems 自创生系统中自然计算的内部量子约束。
IF 1.9 4区 生物学 Q2 BIOLOGY Pub Date : 2026-01-16 DOI: 10.1016/j.biosystems.2026.105707
Abir U. Igamberdiev
Time relates to actualization, which is physically interpreted as a quantum measurement. The measurement has a dual structure consisting of the reality being measured (externality) and the reality by which the measurement takes place (an agent or ontolon). These two constituents refer to the two types of time: physical time measured by clocks, and internal time, defined by Bergson as la durée (duration). The latter holds the coherent internal quantum state of entangled potentialities, while the former represents the collapse of this state, thereby flowing through quantum transactions. This view unifies the Everett (Many-worlds) and the Copenhagen (Wave function collapse) interpretations of the quantum measurement. Time as a duration can be estimated via the energy-time uncertainty relation, which links the precision of the measurement result to the value of energy dissipation during it and to its span. The precision of the measurement result enables the process of quantum computation, which emerges in the systems characterized by internal closure, i.e., autopoietic (living) systems operating at the state of sustainable non-equilibrium. Energy dissipation in the process of measurement occurs as the emission of quanta that trigger the collapse of the coherent entangled state. These quanta are recognized in the system, enabling the performance of higher-level control over elementary computational actions through their integration within the complex system. It is concluded that the energy-time uncertainty relation represents the fundamental internal quantum constraint of natural computation, the process that spans from enzymatic catalysis to complex regulatory and adaptive activities, and finally to reflexive consciousness.
时间与实现有关,这在物理上被解释为量子测量。测量具有双重结构,包括被测量的现实(外部性)和测量发生的现实(代理人或控制者)。这两个组成部分指的是两种类型的时间:由时钟测量的物理时间,以及由柏格森定义为持续时间的内部时间。后者持有纠缠势的相干内部量子态,而前者代表该态的坍缩,从而通过量子交易流动。这种观点统一了埃弗雷特(多世界)和哥本哈根(波函数坍缩)对量子测量的解释。作为持续时间的时间可以通过能量-时间不确定关系来估计,该关系将测量结果的精度与测量期间的能量耗散值及其跨度联系起来。测量结果的精确性使量子计算过程得以实现,量子计算过程出现在以内部闭合为特征的系统中,即在可持续非平衡状态下运行的自创生(生命)系统。测量过程中的能量耗散是由于量子的发射引起相干纠缠态的坍缩。这些量子在系统中被识别,通过它们在复杂系统中的集成,实现对基本计算行为的更高级别控制。结果表明,能量-时间不确定性关系代表了自然计算的基本内部量子约束,即从酶催化到复杂的调节和适应活动,最后到反射意识的过程。
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引用次数: 0
Ohmic–Polarization transition in hydrated DNA 水合DNA中的欧姆极化跃迁
IF 1.9 4区 生物学 Q2 BIOLOGY Pub Date : 2026-01-16 DOI: 10.1016/j.biosystems.2026.105708
Mariusz Pietruszka
A quasi-two-dimensional DNA–water system was investigated under a perpendicular magnetic field of 0.5 T and a constant 0.1 V bias at near-room temperature. Upon cooling, the system undergoes a sharp crossover near 20 °C from a regime with finite longitudinal conduction to a regime in which the longitudinal current Ixx collapses, while the transverse voltage Vxy and a correlated photovoltage remain finite and develop slow, coherent modulations. This decoupling of longitudinal and transverse responses cannot be explained by conventional charge transport and instead indicates a transition from ohmic conduction to polarization-dominated dynamics governed by displacement currents. Complementary magnetic-field sweeps in higher-concentration samples reveal a reproducible polarization cycle, including a pronounced inversion between Vxy and Vphoto and a highly elongated Lissajous portrait, consistent with near anti-phase locking of electrical and optical degrees of freedom. These results identify a field-tunable, polarization-coherent regime in quasi-2D hydrated DNA under ambient/biological conditions, in which macroscopic voltages arise from collective polarization dynamics rather than net charge flow.
在近室温条件下,在垂直0.5 T磁场和恒定0.1 V偏置下研究了准二维dna -水体系。冷却后,系统在20°C附近经历一个急剧的交叉,从有限纵向传导到纵向电流Ixx崩溃的状态,而横向电压Vxy和相关光电压保持有限并发展缓慢的相干调制。这种纵向和横向响应的解耦不能用传统的电荷输运来解释,而是表明了从欧姆传导到由位移电流控制的极化主导动力学的转变。在较高浓度的样品中,互补磁场扫描揭示了一个可重复的极化周期,包括Vxy和Vphoto之间的明显反转和高度延长的Lissajous肖像,与电气和光学自由度的近反锁相一致。这些结果确定了在环境/生物条件下准二维水合DNA中的场可调谐极化相干区,其中宏观电压来自集体极化动力学而不是净电荷流。
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引用次数: 0
Relaxation effects in cell microtubule under the influence of an external electric field: The mean field approximation 外电场作用下细胞微管的弛豫效应:平均场近似。
IF 1.9 4区 生物学 Q2 BIOLOGY Pub Date : 2026-01-13 DOI: 10.1016/j.biosystems.2026.105705
V.A. Saenko , S.Eh. Shirmovsky , D.V. Shulga
The quantum relaxation processes in the microtubule dipole system under the action of an external electric field have been studied. The study is based on the Born–Markov equation. Tubulins dipole–dipole interaction and the internal dynamics of the dipole system that is determined by the quantum tunneling effect in the double potential well is taken into account. A system of differential equations defining the relaxation processes in a microtubule consisting of 676 tubulins is obtained. It was shown that the relaxation nature strongly depends on the magnitude of the dipole–dipole interaction, the internal dynamics of the dipole system, and the influence of the dissipative process. The decoherence time equal to 10−14 s – 10−9 s depending on the features of the relaxation process was determined. It has been proved that, the relaxation can have a twofold character, defining mixed or pure states.
研究了外电场作用下微管偶极子系统的量子弛豫过程。该研究基于Born-Markov方程。考虑了微管偶极-偶极相互作用和由双势阱中的量子隧穿效应决定的偶极系统的内部动力学。得到了定义由676个微管组成的微管弛豫过程的微分方程组。结果表明,弛豫性质在很大程度上取决于偶极-偶极相互作用的大小、偶极系统的内部动力学以及耗散过程的影响。根据弛豫过程的特点,确定了退相干时间为10- 14s ~ 10- 9s。已经证明,弛豫可以具有双重性质,可以定义混合状态或纯状态。
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引用次数: 0
First evidence supporting the theory of the sensorimotor paradox on the origins of mind and language. 第一个支持关于思维和语言起源的感觉运动悖论理论的证据。
IF 1.9 4区 生物学 Q2 BIOLOGY Pub Date : 2026-01-12 DOI: 10.1016/j.biosystems.2026.105691
Clémence Ortega Douville

For now 15 years, I have been developing a hypothesis on the origins of mind and language during our evolution, called theory of the sensorimotor paradox. The core neuroimaging part of the hypothesis is that the switch in our relation to our hands, coming with bipedal stance, would have allowed us to disrupt the function of sensory prediction to resolve into motor action and sensory feedback: we can't take our hand as an object of interaction and have it grasp itself at the same time. This would later on be autonomised as mental representation. From there, non-resolution of prediction into motor action would prevent a system from liberating tension in order to be available again and collect feedback (meta-prediction). Using Schalk, G. et al.'s extensive dataset of EEG recordings on motor movement and imagery (2009), I am now able to support some of the theory's claims. Notably, meta-analysis of movement and imagery recordings tends to stress a higher variability of frequency activation amongst motor signals than imagery's. This would indicate a greater difficulty for a system to release tension in an effort to produce and maintain mental representation. Similar short oscillatory predictive change, but greater uncoupling of frontal and prefrontal regions suggests sensory suppression of efference-copy and greater instability toward the eventuality of collecting feedback when motor action is triggered, relying on somatosensory support. Event-related time-frequency analysis on proprioceptive areas shows delay of neural signal to mental representation compared to motor action, which could be a strong evidence of dissociation.

15年来,我一直在研究一个关于人类进化过程中思维和语言起源的假说,叫做感觉运动悖论理论。假设的核心神经成像部分是,我们与双手关系的转换,伴随着两足站立,将允许我们破坏感觉预测的功能,将其分解为运动动作和感觉反馈:我们不能把我们的手作为互动的对象,同时让它抓住自己。这后来被自主化为心理表征。在此基础上,预测无法转化为运动行动将阻碍系统释放紧张感,从而再次可用并收集反馈(元预测)。利用沙尔克等人关于运动和图像的大量脑电图记录数据集(2009年),我现在能够支持该理论的一些主张。值得注意的是,对运动和图像记录的荟萃分析倾向于强调运动信号之间频率激活的可变性高于图像信号。这将表明一个系统在努力产生和维持心理表征时释放紧张的难度更大。类似的短振荡预测变化,但额叶和前额叶区域更大程度的解耦表明,当运动动作被触发时,对收集反馈的可能性的不稳定性更大,依赖于体感支持。本体感觉区域的事件相关时频分析显示,与运动动作相比,神经信号向心理表征的延迟,这可能是分离的有力证据。
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引用次数: 0
Intelligence as high-dimensional coherence: The observable dimensionality bound and computational tractability 作为高维相干性的智能:可观察维度边界和计算可跟踪性
IF 1.9 4区 生物学 Q2 BIOLOGY Pub Date : 2026-01-08 DOI: 10.1016/j.biosystems.2026.105704
Ian Todd
Intelligence arises from the maintenance of high-dimensional coherent dynamics. High-dimensional systems are effectively nonergodic on relevant timescales—the curse of dimensionality confines trajectories to vanishingly small regions relative to the full space. This confinement is not a limitation but the foundation of biological computation: a system’s position in phase space functions as its memory, its constraints, its structured dynamics. Within these nonergodic regions, high entropy flow enables rich internal exploration; at the boundary, sparse outputs minimize free energy expenditure while defending the conditions for continued nonergodic existence. We formalize this through an Observable Dimensionality Bound: external observers cannot track systems whose effective dimensionality exceeds a critical threshold set by channel capacity and temporal resolution. This bound functions as protection—the opacity of high-dimensional dynamics shields internal structure from external disruption. Living systems exploit this by embodying the dynamics: the substrate is the high-dimensional field, information lives in geometric configuration, and irreversible commitments concentrate at sparse behavioral output events. The framework illuminates a thermodynamic pressure contributing to the efficiency gap between biological and artificial intelligence (brains concentrate irreversible commitments at behavioral boundaries rather than at every internal micro-update), provides a substrate-independent characterization of intelligence (capacity to maintain and defend coherent high-dimensional dynamics), and connects to the emergence of reusable codes through adaptive dynamics. Human cortex likely operates beyond this observable threshold, consistent with recent discussions of consciousness and dimensionality in the systems biology literature.
智力源于维持高维的连贯动态。高维系统在相关的时间尺度上是有效的非遍历的——维度的诅咒将轨迹限制在相对于整个空间逐渐消失的小区域。这种限制不是一种限制,而是生物计算的基础:系统在相空间中的位置就像它的记忆,它的约束,它的结构动力学。在这些非遍历区域内,高熵流使丰富的内部探索成为可能;在边界处,稀疏输出使自由能量消耗最小化,同时捍卫了持续非遍历存在的条件。我们通过可观察维度界限将其形式化:外部观察者无法跟踪有效维度超过由信道容量和时间分辨率设定的临界阈值的系统。这个边界起着保护的作用——高维动态的不透明性保护内部结构免受外部破坏。生命系统通过体现动力学来利用这一点:基底是高维场,信息以几何构型存在,不可逆转的承诺集中在稀疏的行为输出事件中。该框架阐明了导致生物智能和人工智能之间效率差距的热力学压力(大脑将不可逆的承诺集中在行为边界上,而不是在每个内部微更新上),提供了一种与底物无关的智能特征(维持和防御连贯高维动态的能力),并通过自适应动态与可重用代码的出现联系起来。人类皮层的运作可能超出了这个可观察的阈值,这与最近系统生物学文献中关于意识和维度的讨论一致。
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引用次数: 0
Nirmala indices bridge molecular connectivity and genetic stability: A graph-theoretic lens on purines and pyrimidines Nirmala指数桥接分子连通性和遗传稳定性:嘌呤和嘧啶的图论透镜
IF 1.9 4区 生物学 Q2 BIOLOGY Pub Date : 2026-01-08 DOI: 10.1016/j.biosystems.2026.105692
Nalini Devi K. , Srinivasa G.
<div><div>Molecular topology lies at the heart of biological complexity and degree-based topological indices serve as fundamental invariants for quantifying the structural and functional organization of biomolecular systems. In this work we present a unified graph-theoretic framework for analyzing the molecular graphs of purines and pyrimidines using the Nirmala index <span><math><mrow><mi>N</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> and its two inverse variants <span><math><mrow><mi>I</mi><msub><mrow><mi>N</mi></mrow><mrow><mn>1</mn></mrow></msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><mi>I</mi><msub><mrow><mi>N</mi></mrow><mrow><mn>2</mn></mrow></msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span>. Here <span><math><mrow><mi>G</mi><mo>=</mo><mrow><mo>(</mo><mi>V</mi><mo>,</mo><mi>E</mi><mo>)</mo></mrow></mrow></math></span> denotes the molecular graph of a purine or pyrimidine molecule, where vertices <span><math><mi>V</mi></math></span> represent heavy atoms (C, N, O) and edges <span><math><mi>E</mi></math></span> correspond to covalent bonds with hydrogens omitted in accordance with standard chemical graph theory conventions. The five canonical nucleobases-Adenine and Guanine (purines) and Cytosine, Thymine and Uracil (pyrimidines)-are modeled to enable systematic comparison between these two molecular classes. Rigorous degree-based theorems are established to derive extremal bounds for the indices in terms of the minimum and maximum vertex degrees, <span><math><mrow><mi>δ</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><mi>Δ</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> and to demonstrate analytical duality between <span><math><mrow><mi>I</mi><msub><mrow><mi>N</mi></mrow><mrow><mn>1</mn></mrow></msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><mi>I</mi><msub><mrow><mi>N</mi></mrow><mrow><mn>2</mn></mrow></msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span>. Explicit computations reveal that purines exhibit greater degree heterogeneity and larger <span><math><mrow><mi>N</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> values whereas pyrimidines display higher regularity with <span><math><mrow><mi>I</mi><msub><mrow><mi>N</mi></mrow><mrow><mn>1</mn></mrow></msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><mi>I</mi><msub><mrow><mi>N</mi></mrow><mrow><mn>2</mn></mrow></msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> approaching their theoretical upper bounds. Biologically this degree-sensitive quantification captures structural asymmetry, bonding regularity and intrinsic stability across purine and pyrimidine frameworks. The proposed Nirmala-type indices thus establish a concise mathematical-biological bridge linking molecular topology to functio
分子拓扑结构是生物复杂性的核心,基于度的拓扑指数是量化生物分子系统结构和功能组织的基本不变量。在这项工作中,我们提出了一个统一的图论框架,用于使用Nirmala指数N(G)及其两个逆变体IN1(G)和IN2(G)来分析嘌呤和嘧啶的分子图。这里G=(V,E)表示嘌呤或嘧啶分子的分子图,其中顶点V表示重原子(C, N, O),边E对应共价键,根据标准化学图论惯例省略氢。五种典型的核碱基——腺嘌呤和鸟嘌呤(嘌呤)以及胞嘧啶、胸腺嘧啶和尿嘧啶(嘧啶)——被建模,以便在这两类分子之间进行系统的比较。建立了严格的基于度的定理,以最小和最大顶点度δ(G)和Δ(G)来推导指标的极界,并证明IN1(G)和IN2(G)之间的解析对偶性。显式计算表明,嘌呤表现出更大程度的异质性和更大的N(G)值,而嘧啶表现出更高的规律性,IN1(G)和IN2(G)接近其理论上界。生物学上,这种程度敏感的定量捕获结构不对称性,键的规律性和嘌呤和嘧啶框架的内在稳定性。因此,提出的nirmala型指数建立了一个简明的数学-生物学桥梁,将分子拓扑结构与遗传结构的功能稳定性联系起来,在化学信息学、QSAR/QSPR建模和核酸系统级分析中提供了有前途的应用。
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In this work we present a unified graph-theoretic framework for analyzing the molecular graphs of purines and pyrimidines using the Nirmala index &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; and its two inverse variants &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;I&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;I&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;. Here &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; denotes the molecular graph of a purine or pyrimidine molecule, where vertices &lt;span&gt;&lt;math&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; represent heavy atoms (C, N, O) and edges &lt;span&gt;&lt;math&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; correspond to covalent bonds with hydrogens omitted in accordance with standard chemical graph theory conventions. The five canonical nucleobases-Adenine and Guanine (purines) and Cytosine, Thymine and Uracil (pyrimidines)-are modeled to enable systematic comparison between these two molecular classes. Rigorous degree-based theorems are established to derive extremal bounds for the indices in terms of the minimum and maximum vertex degrees, &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;δ&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; and to demonstrate analytical duality between &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;I&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;I&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;. Explicit computations reveal that purines exhibit greater degree heterogeneity and larger &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; values whereas pyrimidines display higher regularity with &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;I&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;I&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; approaching their theoretical upper bounds. Biologically this degree-sensitive quantification captures structural asymmetry, bonding regularity and intrinsic stability across purine and pyrimidine frameworks. The proposed Nirmala-type indices thus establish a concise mathematical-biological bridge linking molecular topology to functio","PeriodicalId":50730,"journal":{"name":"Biosystems","volume":"260 ","pages":"Article 105692"},"PeriodicalIF":1.9,"publicationDate":"2026-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145928618","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Deciphering the dynamic binding of spicy odorants to human olfactory receptors 解读辛辣气味与人类嗅觉受体的动态结合。
IF 1.9 4区 生物学 Q2 BIOLOGY Pub Date : 2026-01-07 DOI: 10.1016/j.biosystems.2026.105703
Jingtao Wang , Chenglei Zhang , Juncang Peng , Jian Wu , Shan Wang , Wu Fan , Qingzhao Shi , Qidong Zhang , Guobi Chai
In this study, we compiled three categories of odorants with spicy aromas: anise class, clove class, and cinnamon class. We aimed to use molecular dynamics simulation techniques to uncover potential regularities in the activation mechanisms of the same odorant across different olfactory receptors, or vice versa, the activation mechanisms of different odorants on the same olfactory receptor. Here, molecular dynamics simulation results reveal that anisaldehyde and estragole preferentially bind to TYR residues, thereby activating the corresponding olfactory receptors. Both eugenol and isoeugenol activate OR5D18 at similar binding sites, but ultimately lead to differential conformational changes in the olfactory receptor. Additionally, the binding conformations of eugenol and methyl eugenol are nearly identical, whereas cinnamaldehyde and cinnamyl alcohol, methyl cinnamaldehyde, exhibit distinct binding conformations with the olfactory receptor. These results underscore how subtle structural changes can impact the binding mechanism of odorants.
在这项研究中,我们整理了三种具有辛辣香味的气味剂:八角类、丁香类和肉桂类。我们旨在利用分子动力学模拟技术揭示同一气味在不同嗅觉受体上的激活机制的潜在规律,反之亦然,揭示不同气味在同一嗅觉受体上的激活机制。分子动力学模拟结果表明,茴香醛和雌二醇优先结合TYR残基,从而激活相应的嗅觉受体。丁香酚和异丁香酚在相似的结合位点激活OR5D18,但最终导致嗅觉受体的不同构象变化。此外,丁香酚和甲基丁香酚的结合构象几乎相同,而肉桂醛和肉桂醇、甲基肉桂醛与嗅觉受体的结合构象不同。这些结果强调了细微的结构变化如何影响气味剂的结合机制。
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引用次数: 0
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Biosystems
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