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The physics of the urge to have freedom 渴望自由的物理学。
IF 2 4区 生物学 Q2 BIOLOGY Pub Date : 2024-07-18 DOI: 10.1016/j.biosystems.2024.105277
Adrian Bejan

Freedom, safety, and ease of movement are innate human urges attributed to conscience along with many other preferences such as attractiveness (beauty), economy, and life. This article addresses the physics basis of the innate urge to have freedom. It unveils the connection between animal freedom and the universal (constructal) tendency toward easier movement and greater access in all evolutionary systems throughout nature (animate & inanimate). The demonstration is made with a model of lack of freedom in animal movement: a man who walks his dog on a leash. When two animals are coerced to move at the same speed, their combined effort (the spent power) is greater than when they move freely, and independently. When the speed of the couple is dictated by the big body (man), the big one walks freely, and the small one must run. Participants in organized movement (life, society) are not equal. All participants move with less effort when they are not coerced to move the same way. The implications of this part of physics (nature) are numerous and help unify the animal realm with the design and evolution of human society. If you want diversity, give the population freedom, not prescriptions.

自由、安全和行动自如是人类与生俱来的冲动,它与许多其他偏好(如吸引力(美)、经济和生命)一样,都归因于良知。本文探讨了与生俱来的自由冲动的物理学基础。它揭示了动物自由与整个自然界(有生命和无生命)所有进化系统中更容易移动和更容易获得的普遍(构造)趋势之间的联系。我们用一个动物运动缺乏自由的模型来进行演示:一个用绳子牵着狗散步的人。当两只动物被迫以相同的速度运动时,它们的合力(消耗的力量)要大于它们自由和独立运动时的合力。当这对动物的速度由大块头(人)决定时,大块头自由行走,小块头必须奔跑。有组织运动(生活、社会)的参与者是不平等的。当所有参与者不被强迫以同样的方式运动时,他们的运动会更省力。这部分物理学(自然)的影响是多方面的,有助于将动物领域与人类社会的设计和进化统一起来。
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引用次数: 0
Circular cut codes in genetic information 遗传信息中的循环切割代码
IF 2 4区 生物学 Q2 BIOLOGY Pub Date : 2024-07-04 DOI: 10.1016/j.biosystems.2024.105263

In this work we present an analysis of the dinucleotide occurrences in the three codon sites 1–2, 2–3 and 1–3, based on a computation of the codon usage of three large sets of bacterial, archaeal and eukaryotic genes using the same method that identified a maximal C3 self-complementary trinucleotide circular code X in genes of bacteria and eukaryotes in 1996 (Arquès and Michel, 1996). Surprisingly, two dinucleotide circular codes are identified in the codon sites 1–2 and 2–3. Furthermore, these two codes are shifted versions of each other. Moreover, the dinucleotide code in the codon site 1–3 is circular, self-complementary and contained in the projection of X onto the 1st and 3rd bases, i.e. by cutting the middle base in each codon of X. We prove several results showing that the circularity and the self-complementarity of trinucleotide codes is induced by the circularity and the self-complementarity of its dinucleotide cut codes. Finally, we present several evolutionary approaches for an emergence of trinucleotide codes from dinucleotide codes.

在这项工作中,我们使用 1996 年 Arquès 和 Michel(1996 年)在细菌和真核生物基因中发现最大 C3 自互补三核苷酸循环码 X 的相同方法,计算了三组大型细菌、古生物和真核生物基因的密码子使用情况,并在此基础上对 1-2、2-3 和 1-3 三个密码子位点中出现的二核苷酸进行了分析。令人惊讶的是,在密码子位点 1-2 和 2-3 中发现了两个二核苷酸循环密码。而且,这两个代码是彼此移动的版本。此外,密码子位点 1-3 中的二核苷酸编码是环形的、自互补的,包含在 X 在第 1 和第 3 个碱基上的投影中,即通过切割 X 每个密码子中的中间碱基。我们证明了几个结果,表明三核苷酸编码的环形性和自互补性是由其二核苷酸切割编码的环形性和自互补性引起的。最后,我们提出了从二核苷酸编码演化出三核苷酸编码的几种方法。
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引用次数: 0
Cosmos MIND and matter: Is mind in spacetime? COSMOS 心灵与物质:时空中有心灵吗?
IF 2 4区 生物学 Q2 BIOLOGY Pub Date : 2024-07-03 DOI: 10.1016/j.biosystems.2024.105262

We attempt in this article to formulate a conceptual and testable framework weaving Cosmos, Mind and Matter into a whole. We build on three recent discoveries, each requiring more evidence: i. The particles of the Standard Model, SU(3) x SU(2) x U(1), are formally capable of collective autocatalysis. This leads us to ask what roles such autocatalysis may have played in Cosmogenesis, and in trying to answer, Why our Laws? Why our Constants? A capacity of the particles of SU(3) x SU(2) x U(1) for collective autocatalysis may be open to experimental test, stunning if confirmed. ii. Reasonable evidence now suggests that matter can expand spacetime. The first issue is to establish this claim at or beyond 5 sigma if that can be done. If true, this process may elucidate Dark Matter, Dark Energy and Inflation and require alteration of Einstein's Field Equations. Cosmology would be transformed. iii. Evidence at 6.49 Sigma suggests that mind can alter the outcome of the two-slit experiment. If widely and independently verified, the foundations of quantum mechanics must be altered. Mind plays a role in the universe. That role may include Cosmic Mind.

Our considerations concern

1. Ontologically Real Potentia and the Unmanifest; 2. Nonlocality as Fundamental; 3. Res potentia, Res extensa, and Actualization; 4. Mind and Qualia, Mind is not in Spacetime; 5. Quantum Vacuum = Potentia not in Spacetime = Mind not in Spacetime; 6. Mind can Actualize Potentia; 7. The emergence of the classical world; 8. Co-evolution of evermore complex matter; 9. Why “My Mind”?; 10. Each embodied mind is coupled bilaterally to the Quantum Vacuum that is Cosmic Mind; 11. Responsible Free Will.

在本文中,我们试图提出一个概念性的、可检验的框架,将宇宙、心灵和物质编织成一个整体。我们以最近的三个发现为基础,每个发现都需要更多的证据: i. 标准模型的粒子,即 SU(3) x SU(2) x U(1) ,在形式上能够进行集体自催化。这让我们不禁要问,这种自催化作用在宇宙生成过程中可能扮演了什么角色,并试图回答:为什么是我们的定律?为什么是我们的常数?苏(3)x 苏(2)x 乌(1)粒子的集体自催化能力可能有待实验检验,如果得到证实,将令人惊叹。现在有合理的证据表明,物质可以扩展时空。首先要做的是在 5 西格玛或更高水平上证实这一说法。如果属实,这一过程可能会阐明暗物质、暗能量和膨胀,并要求改变爱因斯坦的场方程。宇宙学将发生变革。6.49 西格玛的证据表明,意念可以改变双缝实验的结果。如果得到广泛和独立的验证,量子力学的基础就必须改变。心灵在宇宙中扮演着某种角色。这个角色可能包括宇宙心灵。心灵可以实现潜能;7.经典世界的出现;8.越来越复杂的物质的共同进化;9.为什么是 "我的心灵";10.每个具身的心灵都与量子真空(即宇宙心灵)双向耦合;11.负责任的自由意志。
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引用次数: 0
Machine-learning-based structural analysis of interactions between antibodies and antigens 基于机器学习的抗体与抗原相互作用结构分析。
IF 2 4区 生物学 Q2 BIOLOGY Pub Date : 2024-07-02 DOI: 10.1016/j.biosystems.2024.105264
Grace Zhang , Xiaohan Kuang , Yuhao Zhang , Yunchao Liu , Zhaoqian Su , Tom Zhang , Yinghao Wu

Computational analysis of paratope-epitope interactions between antibodies and their corresponding antigens can facilitate our understanding of the molecular mechanism underlying humoral immunity and boost the design of new therapeutics for many diseases. The recent breakthrough in artificial intelligence has made it possible to predict protein-protein interactions and model their structures. Unfortunately, detecting antigen-binding sites associated with a specific antibody is still a challenging problem. To tackle this challenge, we implemented a deep learning model to characterize interaction patterns between antibodies and their corresponding antigens. With high accuracy, our model can distinguish between antibody-antigen complexes and other types of protein-protein complexes. More intriguingly, we can identify antigens from other common protein binding regions with an accuracy of higher than 70% even if we only have the epitope information. This indicates that antigens have distinct features on their surface that antibodies can recognize. Additionally, our model was unable to predict the partnerships between antibodies and their particular antigens. This result suggests that one antigen may be targeted by more than one antibody and that antibodies may bind to previously unidentified proteins. Taken together, our results support the precision of antibody-antigen interactions while also suggesting positive future progress in the prediction of specific pairing.

对抗体及其相应抗原之间的副位点-表位相互作用进行计算分析,有助于我们了解体液免疫的分子机制,并促进许多疾病的新疗法的设计。人工智能领域的最新突破使预测蛋白质-蛋白质相互作用并建立其结构模型成为可能。遗憾的是,检测与特定抗体相关的抗原结合位点仍然是一个具有挑战性的问题。为了应对这一挑战,我们采用了一种深度学习模型来描述抗体与其相应抗原之间的相互作用模式。我们的模型可以高精度地区分抗体-抗原复合物和其他类型的蛋白质-蛋白质复合物。更有趣的是,即使只有表位信息,我们也能从其他常见的蛋白质结合区域识别抗原,准确率超过 70%。这表明抗原表面有抗体可以识别的明显特征。此外,我们的模型无法预测抗体与其特定抗原之间的伙伴关系。这一结果表明,一种抗原可能被不止一种抗体靶向,而且抗体可能与之前未识别的蛋白质结合。综上所述,我们的研究结果支持了抗体与抗原相互作用的精确性,同时也预示着未来在预测特定配对方面将取得积极进展。
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引用次数: 0
Quantum-like environment adaptive model for creation of phenotype 创造表型的类量子环境适应模型
IF 2 4区 生物学 Q2 BIOLOGY Pub Date : 2024-07-02 DOI: 10.1016/j.biosystems.2024.105261
Andrei Khrennikov , Satoshi Iryama , Irina Basieva , Keiko Sato

The textbook conceptualization of phenotype creation, “genotype (G) + environment (E) + genotype & environment interactions (GE) phenotype (Ph)”, is modeled with open quantum systems theory (OQST) or more generally with adaptive dynamics theory (ADT). The model is quantum-like, i.e., it is not about quantum physical processes in biosystems. Generally such modeling is about applications of the quantum formalism and methodology outside of physics. Macroscopic biosystems, in our case genotypes and phenotypes, are treated as information processors which functioning matches the laws of quantum information theory. Phenotypes are the outputs of the E-adaptation processes described by the quantum master equation, Gorini–Kossakowski–Sudarshan–Lindblad equation (GKSL). Its stationary states correspond to phenotypes. We highlight the class of GKSL dynamics characterized by the camel-like graphs of (von Neumann) entropy: in the process of E-adaptation phenotype’s state entropy (disorder) first increases and then falls down — a stable and well-ordered phenotype is created. Traits, an organism’s phenotypic characteristics, are modeled within the quantum measurement theory, as generally unsharp observables given by positive operator valued measures (POVMs. This paper is also a review on the methods and mathematical apparatus of quantum information biology.

教科书中关于表型产生的概念,即 "基因型(G)+环境(E)+基因型与环境相互作用(GE)↦表型(Ph)",是用开放量子系统理论(OQST)或更广义的自适应动力学理论(ADT)来建模的。该模型是类量子模型,即与生物系统中的量子物理过程无关。一般来说,这种建模是关于量子形式主义和方法论在物理学之外的应用。宏观生物系统,在我们的例子中是基因型和表型,被视为信息处理器,其运作符合量子信息论的规律。表型是量子主方程戈里尼-科萨科夫斯基-苏达山-林德布拉德方程(GKSL)所描述的电子适应过程的输出。其静止状态与表型相对应。我们强调了一类以(冯-诺依曼)熵的骆驼状图为特征的 GKSL 动力学:在 E 适应过程中,表型的状态熵(无序)先是增加,然后下降--一个稳定而有序的表型就产生了。生物体的表型特征--性状,是量子测量理论中的模型,一般是由正算子有值量度(POVMs)给出的非锐利观测值。本文也是对量子信息生物学方法和数学装置的综述。
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引用次数: 0
Quantum Brain Dynamics and Virtual Reality 量子大脑动力学与虚拟现实
IF 2 4区 生物学 Q2 BIOLOGY Pub Date : 2024-06-25 DOI: 10.1016/j.biosystems.2024.105259
Akihiro Nishiyama , Shigenori Tanaka , Jack A. Tuszynski

In this paper we propose a control theory of manipulating holograms in Quantum Brain Dynamics (QBD) involving our subjective experiences, i.e. qualia. We begin with the Lagrangian density in QBD and extend our theory to a hierarchical model involving multiple layers covering the neocortex. We adopt reservoir computing approach or morphological computation to manipulate waveforms of holograms involving our subjective experiences. Numerical simulations performed indicate that the convergence to target waveforms of holograms is realized by external electric fields in QBD in a hierarchy. Our theory can be applied to non-invasive neuronal stimulation of the neocortex and adopted to check whether or not our brain adopts the language of holography. In case the protocol in a brain is discovered and the brain adopts the language of holography, our control theory will be applied to develop virtual reality devices by which our subjective experiences provided by the five senses in the form of qualia are manipulated non-invasively. Then, the information content of qualia might be directly transmitted into our brain without passing through sensory organs.

在本文中,我们提出了一种在量子脑动力学(QBD)中操纵全息图的控制理论,其中涉及我们的主观体验,即质点。我们从 QBD 中的拉格朗日密度入手,将理论扩展到涉及覆盖新皮层的多层次模型。我们采用水库计算方法或形态学计算来处理涉及我们主观体验的全息图波形。数值模拟表明,全息图目标波形的收敛是通过分层 QBD 中的外部电场实现的。我们的理论可应用于对新皮层神经元的非侵入性刺激,并用于检查我们的大脑是否采用了全息语言。如果发现了大脑中的协议,并且大脑采用了全息语言,那么我们的控制理论将被应用于开发虚拟现实设备,通过这种设备,我们可以非侵入性地操纵由五官提供的以 "质点"(qualia)形式存在的主观体验。届时,"质点 "的信息内容可能会不经感觉器官直接传入我们的大脑。
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引用次数: 0
Contrasting philosophical and scientific views in the long history of studying the generation of form in development 在研究发展过程中形式产生的漫长历史中,哲学和科学观点的对立。
IF 2 4区 生物学 Q2 BIOLOGY Pub Date : 2024-06-24 DOI: 10.1016/j.biosystems.2024.105260
Ute Deichmann

Focusing on the opposing ways of thinking of philosophers and scientists to explain the generation of form in biological development, I show that today's controversies over explanations of early development bear fundamental similarities to the dichotomy of preformation theory versus epigenesis in Greek antiquity. They are related to the acceptance or rejection of the idea of a physical form of what today would be called information for the generating of the embryo as a necessary pre-requisite for specific development and heredity.

As a recent example, I scrutinize the dichotomy of genomic causality versus self-organization in 20th and 21st century theories of the generation of form. On the one hand, the generation of patterns and form, as well as the constant outcome in development, are proposed to be causally related to something that is "preformed" in the germ cells, the nucleus of germ cells, or the genome. On the other hand, it is proposed that there is no pre-existing form or information, and development is seen as a process where genuinely new characters emerge from formless matter, either by immaterial "forces of life," or by physical-chemical processes of self-organization.

I also argue that these different ways of thinking and the research practices associated with them are not equivalent, and maintain that it is impossible to explain the generation of form and constant outcome of development without the assumption of the transmission of pre-existing information in the form of DNA sequences in the genome. Only in this framework of "preformed" information can "epigenesis" in the form of physical and chemical processes of self-organization play an important role.

我着重探讨了哲学家和科学家在解释生物发育过程中形式的产生时所采用的截然相反的思维方式,并指出,当今关于早期发育解释的争论与古希腊时期形成前理论和表观遗传学的对立有着根本的相似之处。它们都与接受或拒绝这样一种观点有关,即今天被称为胚胎生成信息的物理形式是特定发育和遗传的必要前提。作为最近的一个例子,我仔细研究了 20 世纪和 21 世纪形式生成理论中基因组因果关系与自组织的二分法。一方面,模式和形式的产生以及发育过程中的恒定结果被认为与生殖细胞、生殖细胞核或基因组中 "预先形成 "的东西有因果关系。另一方面,有人认为不存在预先存在的形式或信息,发育被视为从无形物质中产生真正新特征的过程,或者是通过非物质的 "生命力量",或者是通过物理化学的自组织过程。我还认为,这些不同的思维方式以及与之相关的研究实践并不等同,并坚持认为,如果不假定基因组中以 DNA 序列形式存在的先在信息的传递,就不可能解释形式的产生和发展的恒定结果。只有在这种 "预先形成的 "信息框架内,以物理和化学自组织过程为形式的 "表观成因 "才能发挥重要作用。
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引用次数: 0
Size matters in metabolic scaling: Critical role of the thermodynamic efficiency of ATP synthesis and its dependence on mitochondrial H+ leak across mammalian species 新陈代谢规模的大小很重要:ATP 合成的热力学效率的关键作用及其对不同哺乳动物线粒体 H+ 泄漏的依赖性
IF 1.6 4区 生物学 Q2 BIOLOGY Pub Date : 2024-06-19 DOI: 10.1016/j.biosystems.2024.105255
Sunil Nath
<div><p>In this last article of the trilogy, the unified biothermokinetic theory of ATP synthesis developed in the previous two papers is applied to a major problem in comparative physiology, biochemistry, and ecology—that of metabolic scaling as a function of body mass <em>across</em> species. A clear distinction is made between intraspecific and interspecific relationships in energy metabolism, clearing up confusion that had existed from the very beginning since Kleiber first proposed his mouse-to-elephant rule almost a century ago. It is shown that the overall mass exponent of basal/standard metabolic rate in the allometric relationship <span><math><mrow><mi>P</mi><mo>=</mo><msub><mi>P</mi><mn>0</mn></msub><msup><mi>M</mi><mrow><msup><mi>b</mi><mo>′</mo></msup><mo>+</mo><mi>b</mi></mrow></msup></mrow></math></span> is composed of two parts, one emerging from the relative intraspecific <em>constancy</em> of the slope (<span><math><mrow><mi>b</mi></mrow></math></span>), and the other (<span><math><mrow><msup><mi>b</mi><mo>′</mo></msup></mrow></math></span>) arising from the interspecific <em>variation</em> of the mass coefficient, <span><math><mrow><mi>a</mi><mrow><mo>(</mo><mi>M</mi><mo>)</mo></mrow></mrow></math></span> with body size. Quantitative analysis is shown to reveal the hidden underlying relationship followed by the interspecific mass coefficient, <span><math><mrow><mi>a</mi><mrow><mo>(</mo><mi>M</mi><mo>)</mo></mrow><mo>=</mo><msub><mi>P</mi><mn>0</mn></msub><msup><mi>M</mi><mn>0.10</mn></msup></mrow></math></span>, and a universal value of <span><math><mrow><msub><mi>P</mi><mn>0</mn></msub><mo>=</mo><mn>3.23</mn></mrow></math></span> watts, <span><math><mrow><mi>W</mi></mrow></math></span> is derived from empirical data on mammals from mouse to cattle. The above relationship is shown to be understood only within an evolutionary biological context, and provides a physiological explanation for Cope's rule. The analysis also helps in fundamentally understanding how variability and a diversity of scaling exponents arises in allometric relations in biology and ecology. Next, a <em>molecular-level</em> understanding of the scaling of metabolism across mammalian species is shown to be obtained by consideration of the thermodynamic efficiency of ATP synthesis <em>η</em>, taking mitochondrial proton leak as a major determinant of basal metabolic rate in biosystems. An iterative solution is obtained by solving the mathematical equations of the biothermokinetic ATP theory, and the key thermodynamic parameters, e.g. the degree of coupling <span><math><mrow><mi>q</mi></mrow></math></span>, the operative <span><math><mrow><mi>P</mi><mo>/</mo><mi>O</mi></mrow></math></span> ratio, and the metabolic efficiency of ATP synthesis <em>η</em> are quantitatively evaluated for mammals from rat to cattle. Increases in <em>η</em> (by <span><math><mrow><mo>∼</mo><mn>15</mn><mo>%</mo></mrow></math></span>) over a <span><math><mrow><mn>2000</mn><mo>−</mo></mr
在这三部曲的最后一篇文章中,前两篇论文中提出的统一的 ATP 合成生物热动力学理论被应用于比较生理学、生物化学和生态学中的一个主要问题--即作为体重函数的跨物种新陈代谢比例。论文明确区分了能量代谢中的种内关系和种间关系,澄清了自近一个世纪前克莱伯首次提出小鼠对大象规则以来一直存在的混淆。研究表明,在异速关系 P=P0Mb′+b 中,基础/标准代谢率的总体质量指数由两部分组成,一部分来自斜率(b)在种内的相对恒定性,另一部分(b′)来自质量系数 a(M)随体型的种间变化。定量分析显示,种间质量系数 a(M)=P0M0.10 和 P0=3.23 瓦特的普遍值 W 是由从小鼠到牛的哺乳动物的经验数据得出的。上述关系只有在生物进化的背景下才能被理解,并为科普规则提供了生理学解释。该分析还有助于从根本上理解生物学和生态学中的异速关系是如何产生变异性和比例指数多样性的。接下来,通过考虑 ATP 合成的热力学效率 η,并将线粒体质子泄漏作为生物系统中基础代谢率的主要决定因素,可以从分子层面理解哺乳动物物种间新陈代谢的比例关系。通过求解生物热动力学 ATP 理论的数学方程,得到了一个迭代解,并定量评估了从大鼠到牛等哺乳动物的关键热力学参数,如耦合度 q、工作 P/O 比率和 ATP 合成代谢效率 η。从大鼠到牛,在 2000 倍的体型范围内,η 的增加(增加 ∼15%)主要源于线粒体 H+ 泄漏率降低了 ∼3 倍,统一 ATP 理论对此进行了量化。详细讨论了解释基础代谢的生物化学和机理后果,以及由此产生的各种分子影响。这些结果被扩展到最大代谢率,并作为一般 ATP 理论的极限情况进行数学解释。指出了分析的局限性。总之,基于 ATP 合成的统一生物热动力学理论的全面定量分析,解决了生物学、生理学和生态学中关于能量代谢与体型比例的核心问题。
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引用次数: 0
Biological thermodynamics: Bridging the gap between physics and life 生物热力学:弥合物理学与生命之间的鸿沟。
IF 2 4区 生物学 Q2 BIOLOGY Pub Date : 2024-06-14 DOI: 10.1016/j.biosystems.2024.105258
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引用次数: 0
Use of directed quasi-metric distances for quantifying the information of gene families 利用定向准计量距离量化基因家族的信息。
IF 2 4区 生物学 Q2 BIOLOGY Pub Date : 2024-06-12 DOI: 10.1016/j.biosystems.2024.105256

A large hindrance to analyzing information in genetic or protein sequence data has been a lack of a mathematical framework for doing so. In this paper, we present a multinomial probability space X as a general foundation for multicategory discrete data, where categories refer to variants/alleles of biosequences. The external information that is infused in order to generate a sample of such data is quantified as a distance on X between the prior distribution of data and the empirical distribution of the sample. A number of distances on X are treated. All of them have an information theoretic interpretation, reflecting the information that the sampling mechanism provides about which variants that have a selective advantage and therefore appear more frequently compared to prior expectations. This includes distances on X based on mutual information, conditional mutual information, active information, and functional information. The functional information distance is singled out as particularly useful. It is simple and has intuitive interpretations in terms of 1) a rejection sampling mechanism, where functional entities are retained, whereas non-functional categories are censored, and 2) evolutionary waiting times. The functional information is also a quasi-metric on X, with information being measured in an asymmetric, mountainous landscape. This quasi-metric property is also retained for a robustified version of the functional information distance that allows for mutations in the sampling mechanism. The functional information quasi-metric has been applied with success on bioinformatics data sets, for proteins and sequence alignment of protein families.

分析基因或蛋白质序列数据信息的一大障碍是缺乏相关的数学框架。在本文中,我们提出了一个多二项概率空间,作为多类别离散数据的一般基础,其中类别指的是生物序列的变体/等位基因。为生成此类数据样本而注入的外部信息被量化为数据的先验分布与样本的经验分布之间的距离。我们处理了一系列的 "上 "距离。它们都有一个信息论的解释,反映了抽样机制提供的信息,即哪些变体具有选择优势,因此与先前的预期相比出现的频率更高。这包括基于互信息、条件互信息、主动信息和功能信息的距离。功能信息距离尤其有用。它很简单,而且可以从以下两个方面进行直观的解释:1)剔除抽样机制,即保留功能性实体,而剔除非功能性类别;2)进化等待时间。功能信息也是一种准度量,信息是在不对称的多山景观中测量的。功能信息距离的稳健化版本也保留了这一准度量属性,该版本允许采样机制发生突变。功能信息准计量已成功应用于生物信息学数据集、蛋白质和蛋白质族的序列比对。
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