Tuesday, December 22, 2015

dnagr01 electrons scatter very strongly from water Visible light ranges has a wavelength ranging from 650 nm (red) through 350 nm (violet). the electron microscope only works on samples in vacuum

http://www.uic.edu/classes/phys/phys461/phys450/MARKO/N003.html

Basic Physical Scales Relevant to Cells and Molecules 

Relevant Length Scales

Cells are roughly microns in size (1 micron = 10-3 millimeters = 10-6 meters)
E. coli cells are usually around 1 x 1 x 3 microns
Yeast cells are little balls around 2 microns in diameter
Most human cells are roughly 20 microns across, with roughly nuclei about 10 microns in diameter.
Newt cells have 40 micron-diameter nuclei, and the cells are around 60 microns across. Specialized cells in eukaryotes can be much longer (the long axons of neuron cells can be a meter or so in length), or larger (eggs of amphibians and birds are good examples) The basic length scale used to describe molecules is a nanometer (1 nanometer = 1 nm = 10-9 meters) Many biomolecules are made out of chemical units (e.g. nucleotides, amino acids) which are around 1 nm in size, meaning that they are a few atoms across.  Other `small' molecules such as lipids and sugars are also roughly on this length scale.  Most folded up proteins are a few nm in diameter.  So, the nanometer is really useful as a basic yardstick of biomolecules.
Another commonly used unit of length is the Angstrom (1 Angstrom = 10-10 m = 0.1 nanometer).  Atoms are roughly Angstroms in size (a hydrogen atom is about 1 A in diameter, a carbon atom is about 2 A in diameter).  You might read about Angstroms, and you should just immediately think of them as a tenth of a nanometer. What is remarkable about biomolecules is that they can be made of many nm-size units, strung together to make long, linear polymers. For example, the genetic DNAs in human cells are roughly 108 nucleotides in length; each nucleotide contributes a fraction of a nm, making the whole DNA a few centimeters long! The wavelength of light is a bit shorter than one micron Visible light ranges has a wavelength ranging from 650 nm (red) through 350 nm (violet).  As you know from your introductory physics courses, the light microscope can only be used to image details in cells down to at the very best, about 1/2 of the wavelength being used.  This means that we can't directly observe the structure of cells at scales smaller than about 100 nm. In practice things are usually worse - usual white-light microscopes can't resolve detail smaller than about 250 nm, and heroic measures must be taken to observe with 100 nm detail. This is important since it implies that all information about the molecular-scale operation of live cells must be gathered indirectly. One important tool for looking at cells with higher resolution is the electron microscope, which uses electrons with sub-nm wavelengths to image at down to sub-nm resolution.   Unfortunately at present, the electron microscope only works on samples in vacuum, and therefore on dead (and usually `fixed' or cross-linked) cells.   In any case, because electrons scatter very strongly from water, the electron microscope can't be even conceivably be used at present to look into cells at the depths needed to observe their workings. A way to image inside live cells at  10-nanometer spatial resolution would be an extremely useful tool for someone to invent.

Thermal Energy

Each microscopic degree of freedom has an energy kBT associated with it
At room temperature, molecules are jiggling around continually due to thermal motion.  In cells, everything is surrounded by water and so everything is being bumped continuously by neighboring molecules.  All of this random motion gives rise to diffusion of individual molecules, which will be one of the topics discussed in detail later. The energy associated with a single molecular degree of freedom, e.g. the linear motion of a molecule, or the energy of stretching of a chemical bond, is a fundamental physical quantity:     kBT = (Boltzmann's constant) x  (absolute temperature) Here Boltzmann's constant is kB = 1.38 x 10-23 Joules/Kelvin, and is a fundamental constant determined experimentally. Remember that room temperature (25 C) in absolute terms is around 300 Kelvin (25 + 273.1 = 298.1 K to be more precise). So  kBT = 4.1 x 10-21 J  is the relevant thermal energy of single molecular degrees of freedom (note that there is not much change over the range from around 270 K to 330 K relevant to most living things). So now we can roughly estimate the velocity with which a water molecule is moving in a glass of water (or in a cell) at 300 K.
Between collisions, a water molecule has kinetic energy which will be about the thermal energy:
m v2 
2
= kB T
 
which means that the velocity will be about
v = æ 
ç 
è 		2 kB T 
m 		ö 
÷ 
ø 		1/2    = æ 
ç 
è 		2 ×4 ×10-21     J 
18 ×1.6 ×10-27     kg 		ö 1/2 
÷ 
ø 		=   530    m/sec
 
Make sure you understand where the factor of 18 comes from.

Relevant Time Scales

The time between collisions of small molecules in a liquid is about a picosecond
The preceeding calculation puts us in good shape to understand a basic time scale associated with water and other small molecules - the typical time between successive collisions of a water molecule with its neighbors.   We simply have
Dx 
Dt 		= v 
 
 where  Dx = 0.2 nm is the rough size of a water molecule, and where v = 500 m/sec.  Rearranging and solving for the time interval gives Dt = 0.4 x 10-12 sec, about half a picosecond.
Over times longer than one collision time, molecules undergo random-walk or diffusive motion After one collision, the direction of our water molecule will be changed in an difficult-to-predict way.  After a few collisions there will be no chance to predict its direction of motion, or even where it is.  This process is called diffusion, and we will discuss it in detail later.  Diffusive motion is totally different from the straight-line motion we just considered.  We'll see that a diffusing molecule has a relation between distance covered Dx and time interval Dt which is
(Dx)2 
Dt
= D
 
where D is the diffusion constant, with units length-squared per time, for that molecule.  For a water molecule in water we can estimate its diffusion constant very roughly as
D = (0.2 nm)2 
0.4 x 10-12 sec
= 1 x 10-3  (cm)2/sec 
 
A key point about diffusion is that the time you have to wait to go a distance Dx grows as the square of that distance.    So diffusion is increasingly slow at longer and longer distances.
Similarly, motion of larger molecules (e.g. large proteins or nucleic acids) occurs essentially by diffusion, in the absence of other forces.  Biomolecules which are flexible additionally undergo random shape changes.  We'll see that even moderately long molecules - a few thousand repeat units - can take microseconds to milliseconds to move. Relevant time scales for us will include the time that it takes chemical reaction to occur, which if there are large energy barriers to cross, can be seconds or longer. 

Stored Energy in Cells

Cells don't rely on thermal energy or thermal motion to move molecules around.  Instead, they harvest energy from their surroundings, and then store it until it is needed.  One of the molecules used to store energy for the short term is ATP, which can be converted to ADP in an exothermic reaction which liberates about 20 kBT under cellular conditions.   Very roughly ATP -> ADP conversion steps are used to liberate energy to drive other chemical reactions in the cell.
So - cells use units of energy which are appreciably larger than single thermal excitations.  This is crucial to avoid having thermal motion simply bring the contents of a cell to thermal equilibrium - meaning death.

Forces in Cells

A force is developed when work (with a change in energy) is done over a distance:
f =DE 
Dx
 
We can use this to estimate the forces experienced by molecules during thermal fluctuations, and during biological processes.
Generally we will be worried about energies on the order of a kBT, and distance over which such energies are transferred of a nm.  So we can see that the rough forces that we will be talking about will be
f =4x 10-21 J 
10-9 m
= 4 x 10-12 N = 4 piconewtons = 4 pN
 
For random thermal motions, we already saw that the energy of a water molecule can change by a fraction of kBT over a distance comparable to its size of 0.1 nm, so water molecules are subject to random forces that instantaneously may be a few tens of pN.
For directed motions generated by e.g. burning of ATP in the cell, the steps will be a nm or so, and the energy used per step will be a few kBT, again giving forces in the few pN range. So at the molecular scale, we will be worried about forces of around a pN.


Basic Physical Scales Relevant to Cells and Molecules
www.uic.edu/classes/phys/.../N003.html

University of Illinois at Chicago
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Unfortunately at present, the electron microscope only works on samples in vacuum, and therefore on dead (and usually `fixed' or cross-linked) cells. In any case ...

http://zhs.4truth.net/fourtruthzhspb.aspx?pageid=8589981747


http://www.mikeblaber.org/oldwine/BCH4053/Lecture10/Lecture10.htm
蛋白质、核糖核酸和脱氧核糖核酸都是长链聚合物。“聚合物”中的 “ 物 ”指装配块，“聚合”指许多。蛋白质分子是典型的聚合物分子，由一百到三百个小装配块(或物) 组成，称为氨基酸。在蛋白质中，共有二十个不同类型的氨基酸装配块，图1列出了其中五个的示意图。这些氨基酸起化学反应，形成聚合物长链，然后再折叠起来形成三维结构（如图2所示）。正是这种独特结构使不同的蛋白质能够起到催化作用，使化学反应在生物系统内的速度快一百万倍。

生命的起源

作者：沃尔特•布拉德利
简介
安东尼•孚卢是英国哲学教授，也是半个多世纪以来无神论的主要拥护者。但他在81岁高龄时突然改变了想法，成为了自然神论信仰者。在二十04年12月9月接受美国广播公司新闻频道的电话采访时，他表示：“超理智是解释生命起源和自然复杂性的唯一好的解释。” 尼古拉斯?威德在二十00年6月13日的《纽约时报》中将现在关于生命起源事件的状态归纳如下：“解释第一个生命的化学反应就是场噩梦。迄今为止，就最初生命（有人认为是核糖核酸）如何从无机化学物质（无机化学物质可能在早期地球中就已存在）构造了它自己这一点，还没有人找到令人信服的解释。在原始地球上小小的核糖核酸分子自发装配“几乎就是一个奇迹”。两位这方面的专家去年曾说过有益的话：“生命的起源究竟是什么？它困惑了科学家这么多年，让无神论者变成了自然神论信仰者或有神论者。为什么生命的起源是“最伟大、未解决的科学奇事” 之一？”（《探索频道》，1993年）
生命系统所需的最低功能要求包括:能源加工、信息存储及复制。莱拉?加特林捕捉到了问题的本质，意识到生命可从操作的角度定义，作为一种信息处理系统，能够为自己的繁殖存储并处理信息。非常复杂的分子，例如，脱氧核糖核酸、核糖核酸及蛋白质等使这些生物操作可能。在这篇文章中，我想就对生命而言必须的分子复杂性进行综述，并说明为何对于不能控制的自然规则（有时以偶然和必须为特点）很难解释这些生命分子的起源问题，通过这两点来探究“生命起源的秘密”。
信息及生命的分子
蛋白质、核糖核酸和脱氧核糖核酸都是长链聚合物。“聚合物”中的 “ 物 ”指装配块，“聚合”指许多。蛋白质分子是典型的聚合物分子，由一百到三百个小装配块(或物) 组成，称为氨基酸。在蛋白质中，共有二十个不同类型的氨基酸装配块，图1列出了其中五个的示意图。这些氨基酸起化学反应，形成聚合物长链，然后再折叠起来形成三维结构（如图2所示）。正是这种独特结构使不同的蛋白质能够起到催化作用，使化学反应在生物系统内的速度快一百万倍。

图1.不同氨基酸的五个图表

图2.高分子链折叠成三维结构的蛋白质
二十种不同的氨基酸序列决定了三维结构。在氨基酸可能的序列中，只有极少的一部分能够生成有生物效用的三维结构。事实上，蛋白质氨基酸（例如，细胞色素C）能够有正确序列的概率约为1：1060。这一点无论是在理论预测还是在实验中都已得到证实。那么活细胞中的氨基酸如何始终成功地装配蛋白质呢？
蛋白质中的氨基酸在活细胞中提供重要的生物功能，要取得这些氨基酸的序列关键在于脱氧核糖核酸和核糖核酸分子。脱氧核糖核酸的编码信息可用来为某有机体内不同蛋白质的氨基酸排序。信使核糖核酸(m-核糖核酸)分子从脱氧核糖核酸接到这一编码信息，然后作为模板为超过三百种的功能蛋白质取得绝对正确的氨基酸序列。我们可以把脱氧核糖核酸看作每个细胞的“电脑”，它控制着三百个甚至更多个不同蛋白质中的氨基酸序列，这些氨基酸依次控制着每个细胞生命所需的化学反应。化学家为大肠杆菌制作有正确编码信息的脱氧核糖核酸分子需要460万道指令，相当于800页的资料。因此，尽管解决了不同蛋白质序列所需信息的来源问题，却并没有解决如此庞大信息的来源问题，而只是又把它转给了脱氧核糖核酸（在第一生命系统中可能是核糖核酸）。脱氧核糖核酸中的庞大信息的来源（这一点体现在生命所需的分子复杂性中）是生命起源的关键之迷。
在生命起源前的条件下制造脱氧核糖核酸，核糖核酸及蛋白质
脱氧核糖核酸分子在蛋白质的帮助下复制自身，再通过核糖核酸，给各种氨基酸序列编码，从而使生物系统中能量的有效利用成为可能。因此，脱氧核糖核酸、核糖核酸及蛋白质提供了生命的必要功能，即：信息存储、复制及有效地利用能源。但第一个脱氧核糖核酸、核糖核酸及蛋白质是如何产生的呢?关于生命起源的研究50多年来一直试图解答这个问题。我们究竟知道了什么?
关于生命起源的研究始于二十世纪50年代，当时试图化学合成组成蛋白质、脱氧核糖核酸（包括各种氨基酸、碱基和糖）的基本分子装配块。米勒和尤里在所谓的早期地球条件下做实验制作这些分子装配块取得了成功，但这方面的实验于80年代停止。因为，早期地球的大气中沼气、氨气及氢气的含量绝对不高，而他们在实验中所用的化学气体却与此不同。在所谓的生命起源前的化学环境下，人们只能制作出极少量的氨基酸及核糖。直到今天这些对生命必不可少的装配块的起源仍是个谜。
第二个问题是, 生命起源前的地球的装配块本应被许多其他化学反应物所包围,而这些化学反应物与装配块的反应应该比它们相互之间反应时速度快很多。除非可以避免这种破坏性的交叉反应，否则脱氧核糖核酸、核糖核酸及蛋白质的产生都是不可能的。
第三个问题是将的装配块装配成高分子链。例如，在化学反应中氨基酸可以各种方式装配,但只有一种连接相邻氨基酸分子(即被称为肽的化学键)的方法可以使高分子链有蛋白质的功能（请参见图3）。同样的，3-5需要磷酸二脂键,但2-5键主要作用于多核苷酸聚合中，这是形成脱氧核糖核酸和核糖核酸的主要一步。
图3.形成肽链以便在高分子链中联结氨基酸
第四个难题在于氨基酸和糖是以右旋还是以左旋的版本出现。（关于此参见图4，除非它们是镜像物，否则结构都是相同的)。每种氨基酸与另一版本的化学反应速度都相同，且反应也相同，但生物系统中只有左旋氨基酸和D-糖。我们怎么可能从相同浓度的左旋氨基酸和D-糖的混合物中提取一百种甚至更多种的氨基酸?就该问题，曾进行过广泛的研究，但至尽仍没有解释。

图4.左旋和右旋氨基酸-镜像物
如果能够在生命起源前的条件下制作装配块，成功避开致命的交叉化学反应，并正确组装装配块，得到左旋氨基酸或D-糖，此时就生命起源而言最具挑战性的问题是如何取得蛋白质中氨基酸的正确序列，以及脱氧核糖核酸中给生物功能提供信息的碱基的正确序列。如前所述, 大肠杆菌脱氧核糖核酸中的信息编码相当于800页的资料。尽管有人认为通过一段时间的化学筛选，这可能发生，但对于那些在偶尔出错的情况下不可复制的分子系统及提供优先选择功能的分子系统来说，不可能对其进行筛选。功能脱氧核糖核酸、核糖核酸或蛋白质可在筛选时通过复制错误而逐渐改进，但这对于分子来说是没有意义的，因为这种复杂性甚至还不足以让它承担最小的功能。这就是先有鸡还是先有蛋问题的分子版。
总结
米歇尔•比希曾说过通过自然选择而实现的进化过程有着最为复杂的障碍。例如，多成分系统的同时发展，在每个成分都发展到非常高级的阶段并作为一个系统起作用之前，它们都没有选择优势。生命的起源似乎是对生命系统的起源及发展的元叙述中最复杂障碍的静止例子。这些必要的信息表明分子复杂性不可能是偶然或因需要而发展来的，而是需要智能原因，智能设计师及造物主。

为什么量子理论不支持唯物主义

作者：布鲁斯 ·李·戈登
贝勒大学物理学历史和哲学博士
唯物主义（或者物理主义，自然主义）的观点是，一切存在的总和以及实质，都无非是具体的物质形态和演化过程，或者与之伴随的附加因果反应。因此，唯物主义者要提供宇宙运行的解释，只能依赖与有限的物体、原因、事件以及过程。正式由于量子理论被公认为我们科学理解物理现实的基础，才成为唯物主义者支持他们世界观至关重要的理论。但是可惜的是，唯物主义者想为他的教条找一个科学的港湾，却发现量子理论原来消解和挫败了他对世界的唯物理解。
在我们深入探讨这一主张的细节之前，有必要对不是很了解量子理论的人非技术的解释下一些中心概念。首先，什么是量子理论？广义的来讲，它是一种数学理论，在最微小和最基本的层面上描述物理世界的行为。它包含量子力学，量子场理论，还有一些相关的概念和应用程序。
  • 量子力学是在微粒子和亚原子的层面上描述物体的运动。量子力学最重要的是其现象的二元性――电子和质子之类的物体在试验的环境下，既不表现为粒子也不表现为波。类似的，射线，例如光，同时呈现了波和例子的行为。
  • 量子场理论是对系统的量子描述，有无穷的自由度可以发挥。通常很容易通过大量的物体的构成在量子场形式主义中来解释系统――例如金属中的离子和电子或者大原子核中的核子。
  • 相对量子场理论把场理论（例如，电磁场理论），量子力学和特殊相对论融为一个数学结构。它是数学物理的一个重要工具。量子引力理论的研究还在继续完善，希望能够成功的把普遍相对性引入量子场理论。
  • 量子宇宙论把量子场理论运用到宇宙起源和最初形成的问题中，但是一个理论充分的量子宇宙论需要一个完整的量子引力理论。
  • 量子现象的一个主要特征是他们的非定域性和不可定为性。每次一个量子物体或者系统与另一个量子物体或系统相互作用的时候，它们的存在就交织在一起，其中一个发生的变化会立刻反影响另一个，不论它们之间相隔多远。由于局部反应受特别相对性的约束，而且以近似或者等同学光速的速度增加，这种瞬间相关叫做非局部的，相应反应它们的量子系统就展现非定域性。数学物理的结论贝尔定理（经过爱尔兰物理学家证明）指出，量子系统展现出非局部行为，它能够基于局部考虑解释这些瞬间相关关系，这一描述已经没有可以补充的隐藏变量了（无证可考）。
引入这些局部变量时，改进后的理论设想和量子力学中相悖。从1980年左右开始巴黎大学阿莱阿斯派科特设计的试验开始的一系列试验，最后都证实是量子理论促使了正确的设想，而不是修改进一些局部隐藏参数的理论。因此物理世界在本质上是非局部的，而且参杂这瞬间的联系和交错。不可定位性是相对量子力学和量子场理论中的有关现象，这种理论前提下不可能在一个有限的空间区域里隔离开一个看不见的量子物体。如我们将要看到的，非定域性和不可定义性为唯物主义埋下了难题。
有了以上铺垫，可以得出结论，不仅量子理论不支持唯物主义，而且还与唯物主义不相容，这一论点可以表述为下面的前提和结论：
P1.  唯物主义的观点是一切存在都是具体的物质形态，演化过程，或者与之伴随的附加因果反应。
P2.因而唯物主义的解释资源就仅限于物体，原因，事件和过程。
P3.  只要唯物主义的解释缺陷存在，就不能解释非局部量子相关性，也无法解释（基于不可定位性的）物质的真实本质。
P4.  这些量子现象需要一个解释。
 ____________________________________________________________
C   所以，唯物主义/自然主义/物理主义作为世界观都有无可避免的缺陷，是错误和不充分的，所以应当拒绝。
这个论点的前两个前提是公认的：第一个仅仅是定义，第二个是这一定义的结果。因此前提三、四是论点的关键。一旦明了这些，就可以直接得出结论。因此我们就可以集中精力，证明3.4前提是正确的。
一个粒子要成为物质个体，至少必须有一个确定而独特的特性。这种特性的一个主要方面是时空方位。事物要作为独立的物体存在，必须在特定时间占据一定空间。如果没有，那么不管它是什么－如果它是什么的话－它决不是一个物体。唯物主义的问题在于相对量子力学中的粒子难以定位。
概括来说，杰哈德·黑格菲尔德特和大卫·马勒蒙特已经指出如果（十分合理的）假设单一粒子既无法提供无尽的能源，也不能同时出现在两个地方，那么这个粒子在任何有限空间被找到的几率都是零，不论它有多大！总而言之，“粒子”不存在于任何空间，所以，坦白说，它根本不存在。汉斯·哈沃森和罗伯特·克利夫顿扩充了这些结论，填补了一些漏洞，他们指出杰哈德·黑格菲尔德特的证明的前提甚至更加抽象。他们还特别指出，一旦涉及相对性，就没有物体的微观理解。粒子的讨论在宏观领域有实用性，但是没有微观现实基础（这正是唯物主义基石）。
潜在的问题是：本质上的相关需要因果解释，但是原则上却没有可能的物理解释。此外，场中量子的不可定位性使得这些实体，不管它们是什么，都不符合物质个体的准则。所以，矛盾而又讽刺地，物质世界中最基本的构成和关系实际上却不能通过其实质来理解。既然这些必然需要解释，正确的解释就不得不是非物理的－这与任何唯物主义完全背道而驰。
唯物主义可能这样辩护，主张非局部现象不需要解释，因为虽然认识上有点扰人，它们最终并不成为形而上的问题。大卫·刘易斯用“人类无上”的概念表示了大自然中没有规则需要建立在因果基础上的观点。“人类无上”表示的是大自然决定规律和几率，不受人们想法影响－换句话说，是本体论，而不是认识论。该理论与特别相对性一致，时空式的理解世界本质关系，有本质点－或者点式占据点－和本质特定的局部特点一起。所有其他都附加在地方性质的时空安排中。在这点上，观察的自然规律仅仅在它们是公理推论系统的定理，推论正确，在简单和忠实度间提供可能平衡时，才是法则。
但是这样会导致不连贯。人类无上需要量子结果，非局部相关但是可以通过局部特性理解。这种情况下，需要假设任意设置，空间上和谐隔离，不需要更深的本体解释。可能我能把疑难的微妙这样解释：这种情况下接受似是而非的人类无上，就等于相信坐在世界两极房间同时制造同样的文本的打字员，他们不会进行任何交流。 对世界的量子描述至少在这个背景下的人类无上是不可能的，它附加说，这个系统的历史上既没有共同追求，也没有局部的遗传信息能够解释相关性。这里怀疑不仅成了自然反应，而且是必然反应。一旦抓住了这一概念的内涵，人类无上就成了自身的推论。所以，我重复：量子非定域性缺少深层解释，不可能有物理解释。
所以量子理论形而上理解的困难是如何解释世界，如果世界是一个客观结构，不附加在物质之上。在这个结构中，真正显得似是而非的答案竟然是坚持和解释一个外在的客观结构需要构造一种现象论，我们通过感观信息认识物质世界，使之符合某些结构约束，但是没有物质真实就导致了感官认知。所以剩下是思维的本体，经历和产生精神事件和过程，他们虽然有感官特点，但是有物理理论中基本对称和约束条件的正式结构。说这些感官感知的主观容易倒向唯我论，而且会产生一些形而上和认识论上的迷团：形而上的客观和认识主观性存在于有神论的形而上中，与乔治波克雷和乔纳深爱德华的精神论如出一辙。
简介:布鲁斯戈登在西北大学获取物理哲学历史学博士。他的主要研究兴趣涉及科学哲学，物理哲学，形而上解析，哲学神学以及哲学学科的交叉问题。自1999年他就在贝勒大学做行政，担任哲学副教授。目前他作为学者寄宿在贝勒信仰与学习学院。


http://www.mikeblaber.org/oldwine/BCH4053/Lecture10/Lecture10.htm
Forces influencing protein structure, Primary and secondary structure


Proteins perform many of the functional roles necessary for living systems
  • The function of most proteins is based upon the unique conformation that their polypeptide chain adopts in solution (i.e. the "native" or "folded" conformation)
  • The folded conformation is determined by the primary sequence and the interaction of amino acid side chains with the solvent.
  • The pH, ionic composition and concentration, and the solvent dielectric, can influence the electrostatic interactions that stabilize the folded conformation

Non-covalent interactions stabilizing protein structures:
  • Hydrogen bonds. Structural studies of folded proteins indicate that hydrogen bonding groups almost always find an appropriate partner. Hydrogen bonding groups include the main chain carbonyl and amide groups as well as polar side chains. Polar groups exposed on the surface of proteins often have water as their hydrogen bonding partner. Polar groups within the core region usually form hydrogen bonds with other groups within the protein. Most proteins include at least some buried solvent groups, and these hydrogen bond with side chains and/or main chain groups in the interior of the protein. Mutational studies have shown that elimination of a hydrogen bonding partner is often destabilizing to a protein structure, and hydrogen bonds typically contribute about 12kJ/mol in stabilization energy.
  • Hydrophobic interactions. A primary driving force for protein folding involves the removal of non-polar side chains from solvent exposure. This is accomplished by sequestering them within the core region. Related to this, interior packing (i.e. van der Waals forces) is optimized by appropriate choice of non-polar side chains in the primary sequence. Exposing non-polar groups to solvent is entropically costly (due to water clathrate structure), thus, folding of the polypeptide chain so as to sequester nonpolar sidechains within the core region is "hydrophobically driven". Some non-polar groups are still found on the surface of folded proteins.


This is a "slice" through the center of a small protein known as fibroblast growth factor. Notice that the core region is rich in non-polar amino acids (white atoms are carbons). Polar groups (red oxygen and blue nitrogen) are rich on the surface, and H-bond with solvent. Some polar groups can be found in the interior, and some non-polar groups can be found on the surface, however.
  
  • Electrostatic interactions. These interactions between oppositely charged ionic side chains are also known as "salt-bridges". The main chain amino and carboxyl terminal are fully ionized at physiological pH, as are the side chains Asp (-), Glu (-), Lys (+), and Arg (+). Histidine can also be charged (+) at pH <=6.0. Opposite charge attraction is modulated by the dielectric constant of the environment. Charge groups on the surface experience a dielectric constant of 78.5 (that of water) and are therefore weaker than those in the hydrophobic core (with a dielectric of ~4). Thus, any buried electrostatic interactions are quite strong. The presence of ions in solution can also screen electrostatic charges and weaken them.
  • Van der Waals interactions. Well packed hydrophobic cores of proteins represent optimized van der Waals interactions between non-polar residues. Although individually weak, numerous neighbor interactions in such central cores can contribute a significant stabilization to the native structure.


 This is a "slice" through the center of a small protein known as fibroblast growth factor. Notice that the core packing amino acids (which are primarily hydrophobic) pack closely together with minimal cavity spaces. This maximizes the strength of the van der Waals interactions.

 
Many proteins can reversibly fold (i.e. they unfold at high temperature, and cooling them down allows them to refold to the original structure)
Therefore, all of the information necessary for folding the peptide chain into a unique three-dimensional structure is contained within the primary sequence. But, proteins are "designed" to fold in certain environments (e.g. aqueous, high-salt, non-polar).
Understanding how proteins fold up is a major challenge in modern biochemistry ("The Protein Folding Problem")
  
Secondary structure in proteins

  • While the peptide bond is rigid, there is a single bond between the Ca(1) and C atoms and the N and C(2) which are free to rotate. Thus, while the Ca (1) - C (O) - N (H) - Ca (2) atoms are all planar, this planar peptide bond has two degrees of rotational freedom.
  • These two rotation angles are known by the greek letters F (phi) and Y (psi). Y is the rotation angle about the Ca (1) - C bond and F is the rotation angle about the N - Ca (2) bond. These are also referred to as "main chain" angles.

  • It is these two degrees of rotational freedom that allows polypeptides to fold up into unique conformations

The overall three-dimensional structure of a protein is a consequence of the unique F (phi) and Y (psi) angles that each peptide bond adopts
 Some angles for F (phi) and Y (psi) are prohibited due to steric clashes with other atoms in the adjacent peptide bond:
Here are some VRML files to highlight these steric problems:
 
Ramachandran and coworkers came up with a diagram that shows the allowed regions for main chain F (phi) and Y (psi) angles. It is known as a Ramachandran Plot (dark areas are "low energy", or favored regions for particular combinations of F (phi) and Y (psi) angles):

a-helix and b-sheet secondary structure and the Ramachandran plot
 a-helices and b-sheets are types of secondary structure that have characteristic values for main chain F (phi) and Y (psi) angles that are repeated throughout a region of the polypeptide chain.
a-helix
 
  • The a-helix has typical main chain angles of F (phi) = -60° and Y (psi) = -47°. This does not result in a steric clash of main chain groups (here is a vrml file with a representative structure)
  • This regular arrangement of main chain angles results in the polypeptide backbone folding up into a right-handed helix. All the main chain carbonyl oxygens point "down" the helix, and all the main chain amide nitrogens point "up" the helix.
  • Note that since each peptide bond has a dipole, and that since all the peptide bonds in an a-helix are pointing in the same direction, the peptide dipoles are aligned in an a-helix and reinforce one another, stabilizing the helical structure, and these combined dipole interactions are referred to as the helical macro-dipole
  • The a-helix exhibits an intra-chain hydrogen bonding arrangement between the main chain carbonyl oxygen of group (i) and the main chain amide of group (i+4)
  • The are ~3.6 residues per turn in the a-helix. The "average" helix in a protein comprises about 10 residues, or about 3 turns of the helix

 
  • The amino acid proline will disrupt (put a kink into) an a-helix . Since it is an imino acid, the main chain amide is unavailable to participate in the intrachain hydrogen bond. The main chain carbonyl partner of the intrachain hydrogen bond will point out of the helix to fulfill its hydrogen bonding requirement
  • There are less-common type of helices in proteins with 3.0 residues per turn (310 helix) and 4.4 residues per turn (4.416 helix). The subscript in this nomenclature indicates the number of atoms comprising one turn. The typical a-helix would therefore also be known as a 3.613 helix (13 atoms in one turn, 3.6 residues in one turn)
b-sheet
 
  • Typical main chain angles for b-sheets are F (phi) = -120° and Y (psi) = 120°. This does not result in a steric clash of main chain groups (here is a vrml file with a representative structure)
  • These values for the main chain angles results in an alternating up-down orientation to consecutive side chain functional groups
  • Two polypeptide chains adopting these main chain angles can hydrogen bond together in either a parallel, or anti-parallel orientation (resulting in a parallel b-sheet or an anti-parallel b-sheet ). Note that this requires two strands to get together, therefore, the H-bonds are inter-strand (rather than intra-strand as with the a-helix )

Turns
 Turns are extremely important structures in globular proteins. Without turn structures, the polypeptide secondary structures would simply continue and you would have a fibrous protein. Thus, globular proteins can be described as segments of secondary structure that are interrupted by turns, and this allows a globular tertiary structure to form.
  • A common type of turn is the b-turn.
  • It achieves a 180° turn with three amino acids
  • The main chain amide of the first residue hydrogen bonds with the main chain carbonyl of the third residue, and can connect the ends of an anti-parallel b-sheet
  • Residues such as proline and glycine occur often in turns. They can be readily accommodated in tight turns, and tend to destabilize other types of secondary structure (particularly a-helix )

The characteristic main chain F (phi) and Y (psi) angles for the different types of secondary structure puts them in characteristic locations in the Ramachandran plot:

An example of a Ramachandran plot of a real protein (2,5-diketo-D-gluconate reductase)
  This protein (2,5-DKG for short) is an enzyme involved in carbohydrate biosynthesis. It contains about 270 amino acids, and if we were to plot the location of each amino acid's F (phi) and Y (psi) angles on a Ramachandran plot we would find the following:

  • The plot suggests that the protein contains both a-helices and b-sheets, but it looks like there must be more a-helical secondary structure overall in comparison to b-sheets. It also looks like there may be several b-turns in the protein as well.
The actual tertiary structure of the protein (as diagrammed using a main-chain "ribbon" drawing) looks like this:
 
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