Single Chain Cyclized/Knotted Polymers are a new class of polymer architecture with a general structure consisting of multiple intramolecularcyclization units within a single polymer chain.
Such a structure was synthesized via the controlled polymerization of
multivinyl monomers, which was first reported in Dr. Wenxin Wang's
research lab. These multiple intramolecular cyclized/knotted units mimic
the characteristics of complex knots found in proteins and DNA which
provide some elasticity to these structures. Of note, 85% of elasticity in natural rubber is due to knot-like structures within its molecular chain.
An intramolecular cyclization reaction is where the growing polymer chain reacts with a vinylfunctional group
on its own chain, rather than with another growing chain in the
reaction system. In this way the growing polymer chain covalently links
to itself in a fashion similar to that of a knot
in a piece of string. As such, single chain cyclized/knotted polymers
consist of many of these links (intramolecularly cyclized), as opposed
to other polymer architectures including branched and crosslinked polymers that are formed by two or more polymer chains in combination.
Figure 1. Single chain cyclized/knotted polymer, analogous to a Celtic knot.
Linear polymers can also fold into knotted topologies via
non-covalent linkages. Knots and slipknots have been identified in
naturally evolved polymers such as proteins as well. Circuit topology and knot theory formalise and classify such molecular conformations.
Synthesis
Deactivation enhanced ATRP
A simple modification to atom transfer radical polymerization (ATRP) was introduced in 2007 to kinetically control the polymerization by increasing the ratio of inactive copper(II) catalyst
to active copper(I) catalyst. The modification to this strategy is
termed deactivation enhanced ATRP, whereby different ratios of
copper(II)/copper(I) are added. Alternatively a copper(II) catalyst may
be used in the presence of small amounts of a reducing agent such as ascorbic acid to produce low percentages of copper(I) in situ and to control the ratio of copper (II)/copper (I). Deactivation enhanced ATRP features the decrease of the instantaneous kinetic chain length ν as defined by:,
meaning an average number of monomer units are added to a propagating chain end during each activation/deactivation cycle,
The resulting chain growth rate is slowed down to allow sufficient
control over the reaction thus greatly increasing the percentage of
multi-vinyl monomers in the reaction system (even up to 100 percent
(homopolymerization)).
Polymerization process
Typically,
single chain cyclized/knotted polymers are synthesized by deactivation
enhanced ATRP of multivinyl monomers via kinetically controlled
strategy. There are several main reactions during this polymerization
process: initiation, activation, deactivation, chain propagation,
intramolecular cyclization and intermolecular crosslinking. The
polymerization process is explained in Figure 2.
Figure 2. Single chain cyclized/knotted polymers synthesis approach.
In a similar way to normal ATRP, the polymerization is started by initiation to produce a free radical, followed by chain propagation
and reversible activation/deactivation equilibrium. Unlike the
polymerization of single vinyl monomers, for the polymerization of
multivinyl monomers, the chain propagation occurs between the active
centres and one of the vinyl groups from the free monomers. Therefore,
multiple unreacted pendent vinyl groups are introduced into the linear
primary polymer chains, resulting in a high local/spatial vinyl
concentration. As the chain grows, the propagating centre reacts with
their own pendent vinyl groups to form intramolecular cyclized rings
(i.e. intramolecular cyclization). The unique alternating chain
propagation/intramolecular cyclization process eventually leads to the
single chain cyclized/knotted polymer architecture.
Intramolecular cyclization or intermolecular crosslinking
It
is worthy to note that due to the multiple reactive sites of the
multivinyl monomers, plenty of unreacted pendent vinyl groups are
introduced to linear primary polymer chains. These pendent vinyl groups
have the potential to react with propagating active centres either from
their own polymer chain or others. Therefore, both of the intramolecular
cyclization and intermolecular crosslinking might occur in this
process.
Using the deactivation enhanced strategy, a relatively small
instantaneous kinetic chain length limits the number of vinyl groups
that can be added to a propagating chain end during each
activation/deactivation cycles and thus keeps the polymer chains growing
in a limited space. In this way, unlike what happens in free radical polymerization (FRP),
the formation of huge polymer chains and large-scale combinations at
early reaction stages is avoided. Therefore, a small instantaneous
kinetic chain length is the prerequisite for further manipulation of
intramolecular cyclization or intermolecular crosslinking. Based on the
small instantaneous kinetic chain length, regulation of different chain
dimensions and concentrations would lead to distinct reaction types. A
low ratio of initiator to monomer would result in the formation of
longer chains but of a lower chain concentration, This scenario would no
doubt increases the chances of intramolecular cyclization due to the
high local/spatial vinyl concentration within the growth boundary.
Although the opportunity for intermolecular reactions can increase as
the polymer chains grow, the likelihood of this occurring at the early
stage of reactions is minimal due to the low chain concentration, which
is why single chain cyclized/knotted polymers can form. However, in
contrast, a high initiator concentration not only diminishes the chain
dimension during the linear-growth phase thus suppressing the
intramolecular cyclization, but it also increases the chain
concentration within the system so that pendent vinyl groups in one
chain are more likely to fall into the growth boundary of another chain.
Once the monomers are converted to short chains, the intermolecular
combination increases and allows the formation of hyperbranched
structures with a high density of branching and vinyl functional groups.
Note
The
monomer concentration is important for the synthesis of single chain
cyclized/knotted polymers, but the kinetic chain length is the key
determining factor for synthesis.
Applications
Single
chain cyclized polymers consist of multiple cyclized rings which afford
them some unique properties, including high density, low intrinsic viscosity, low translational friction coefficients, high glass transition temperatures, and excellent elasticity of the formed network.
In particular, an abundance of internal space makes the single chain
cyclized polymers ideal candidates as efficient cargo-carriers.
Gene delivery
It
is well established that the macromolecular structure of nonviral gene
delivery vectors alters their transfection efficacy and cytotoxicity.
The cyclized structure has been proven to reduce cytotoxicity and increase circulation time for drug and gene delivery applications.
The unique structure of cyclizing chains provides the single chain
cyclized polymers a different method of interaction between the polymer
and plasmid DNA, and results in a general trend of higher transfection
capabilities than branched polymers.
Moreover, due to the nature of the single chain structure, this
cyclized polymer can “untie” to a linear chain under reducing
conditions. Transfection profiles on astrocytes comparing 25 kDa-PEI, SuperFect® and Lipofectamine®2000
and cyclized polymer showed greater efficiency and cell viability
whilst maintaining neural cell viability above 80% four days post
transfections.
Pervasive throughout the Eastern Mediterranean and Western Asia until late antiquity and beyond, mágos (μάγος) was influenced by (and eventually displaced) Greek goēs (γόης), the older word for a practitioner of magic, with a meaning expanded to include astronomy, astrology, alchemy, and other forms of esoteric knowledge. This association was in turn the product of the Hellenistic fascination for Pseudo-Zoroaster, who was perceived by the Greeks to be the Chaldean
founder of the Magi and inventor of both astrology and magic, a meaning
that still survives in the modern-day words "magic" and "magician".
In the Gospel of Matthew, "μάγοι" (magoi) from the east do homage to the Christ Child, and the transliterated plural "magi" entered English from Latin
in this context around 1200 CE (this particular use is also commonly
rendered in English as "kings" and more often in recent times as "wise
men"). The singular "magus" appears considerably later, when it was borrowed from Old French in the late 14th century with the meaning magician.
Hereditary Zoroastrian priesthood has survived in India and Iran. They are termed Herbad, Mobad (Magupat, i.e. chief of the Maga), and Dastur depending on the rank.
The term only appears twice in Iranian texts from before the 5th
century BC, and only one of these can be dated with precision. This one
instance occurs in the trilingual Behistun inscription of Darius the Great, and which can be dated to about 520 BC. In this trilingual text, certain rebels have magian as an attribute; in the Old Persian portion as maγu- (generally assumed to be a loan word from Median). The meaning of the term in this context is uncertain.
The other instance appears in the texts of the Avesta, the sacred literature of Zoroastrianism. In this instance, which is in the Younger Avestan portion, the term appears in the hapaxmoghu.tbiš, meaning "hostile to the moghu", where moghu does not (as was previously thought) mean "magus", but rather "a member of the tribe" or referred to a particular social class in the proto-Iranian language and then continued to do so in Avestan.
An unrelated term, but previously assumed to be related, appears in the older Gathic Avestan language texts. This word, adjectival magavan meaning "possessing maga-", was once the premise that Avestan maga- and Median (i.e. Old Persian) magu- were coeval (and also that both these were cognates of Vedic Sanskritmagha-). While "in the Gathas
the word seems to mean both the teaching of Zoroaster and the community
that accepted that teaching", and it seems that Avestan maga- is related to Sanskrit magha-, "there is no reason to suppose that the western Iranian form magu (Magus) has exactly the same meaning" as well. But it "may be, however", that Avestan moghu (which is not the same as Avestan maga-) "and Medean magu
were the same word in origin, a common Iranian term for 'member of the
tribe' having developed among the Medes the special sense of 'member of the (priestly) tribe', hence a priest."
Some examples of the use of magi in Persian poetry, are present in the poems of Hafez. There are two frequent terms used by him, first one is Peer-e Moghan (literally "the old man of the magi") and second one is Deyr-e Moghan (literally "the monastery of the magi").
Greco-Roman sources
Classical Greek
The oldest surviving Greek reference to the magi – from Greek μάγος (mágos, plural: magoi) – might be from 6th century BC Heraclitus (apud ClemensProtrepticus 2.22.2), who curses the magi for their "impious" rites and rituals.
A description of the rituals that Heraclitus refers to has not
survived, and there is nothing to suggest that Heraclitus was referring
to foreigners.
Better preserved are the descriptions of the mid-5th century BC Herodotus, who in his portrayal of the Iranian expatriates living in Asia Minor uses the term "magi" in two different senses. In the first sense (Histories 1.101), Herodotus speaks of the magi as one of the tribes/peoples (ethnous) of the Medes. In another sense (1.132), Herodotus uses the term "magi" to generically refer to a "sacerdotal caste", but "whose ethnic origin is never again so much as mentioned." According to Robert Charles Zaehner, in other accounts, "we hear of Magi not only in Persia, Parthia, Bactria, Chorasmia, Aria, Media, and among the Sakas, but also in non-Iranian lands like Samaria, Ethiopia, and Egypt.
Their influence was also widespread throughout Asia Minor. It is,
therefore, quite likely that the sacerdotal caste of the Magi was
distinct from the Median tribe of the same name."
As early as the 5th century BC, Greek magos had spawned mageia and magike to describe the activity of a magus, that is, it was his or her art and practice. But almost from the outset the noun for the action and the noun for the actor parted company. Thereafter, mageia
was used not for what actual magi did, but for something related to the
word 'magic' in the modern sense, i.e. using supernatural means to
achieve an effect in the natural world, or the appearance of achieving
these effects through trickery or sleight of hand. The early Greek texts typically have the pejorative meaning, which in turn influenced the meaning of magos to denote a conjurer and a charlatan. Already in the mid-5th century BC, Herodotus identifies the magi as interpreters of omens and dreams (Histories 7.19, 7.37, 1.107, 1.108, 1.120, 1.128).
Other Greek sources from before the Hellenistic period include the gentleman-soldier Xenophon, who had first-hand experience at the Persian Achaemenid court. In his early 4th century BC Cyropaedia, Xenophon depicts the magians as authorities for all religious matters (8.3.11), and imagines the magians to be responsible for the education of the emperor-to-be. Apuleius, a NumidianPlatonist philosopher, describes magus to be considered as a "sage and philosopher-king" based on its Platonic notion.
Once the magi had been associated with "magic" – Greek magikos – it was but a natural progression that the Greeks' image of Zoroaster would metamorphose into a magician too. The first century Pliny the Elder names "Zoroaster" as the inventor of magic (Natural History
xxx.2.3), but a "principle of the division of labor appears to have
spared Zoroaster most of the responsibility for introducing the dark
arts to the Greek and Roman worlds. That dubious honor went to another
fabulous magus, Ostanes, to whom most of the pseudepigraphic magical literature was attributed." For Pliny, this magic was a "monstrous craft" that gave the Greeks not only a "lust" (aviditatem) for magic, but a downright "madness" (rabiem) for it, and Pliny supposed that Greek philosophers – among them Pythagoras, Empedocles, Democritus, and Plato – traveled abroad to study it, and then returned to teach it (xxx.2.8–10).
"Zoroaster"
– or rather what the Greeks supposed him to be – was for the Hellenists
the figurehead of the 'magi', and the founder of that order (or what
the Greeks considered to be an order). He was further projected as the author of a vast compendium of "Zoroastrian" pseudepigrapha,
composed in the main to discredit the texts of rivals. "The Greeks
considered the best wisdom to be exotic wisdom" and "what better and
more convenient authority than the distant – temporally and
geographically – Zoroaster?" The subject of these texts, the authenticity of which was rarely challenged, ranged from treatises on nature to ones on necromancy. But the bulk of these texts dealt with astronomical speculations and magical lore.
One factor for the association with astrology was Zoroaster's
name, or rather, what the Greeks made of it. His name was identified at
first with star-worshiping (astrothytes "star sacrificer") and, with the Zo-, even as the living star. Later, an even more elaborate mytho-etymology evolved: Zoroaster died by the living (zo-) flux (-ro-) of fire from the star (-astr-) which he himself had invoked, and even that the stars killed him in revenge for having been restrained by him. The second, and "more serious" factor for the association with astrology was the notion that Zoroaster was a Chaldean. The alternate Greek name for Zoroaster was Zaratas / Zaradas / Zaratos (cf.Agathias 2.23–5, ClementStromata I.15), which – according to Bidez and Cumont – derived from a Semitic form of his name. The Suda's chapter on astronomia notes that the Babylonians learned their astrology from Zoroaster. Lucian of Samosata (Mennipus 6) decides to journey to Babylon "to ask one of the magi, Zoroaster's disciples and successors", for their opinion.
Byzantine depiction of the Three Magi in a 6th-century mosaic at Basilica of Sant'Apollinare NuovoConventional post-12th century depiction of the Biblical magi (Adoração dos Magos by Vicente Gil). Balthasar, the youngest magus, bears frankincense and represents Africa. To the left stands Caspar, middle-aged, bearing gold and representing Asia. On his knees is Melchior, oldest, bearing myrrh and representing Europe.
The word mágos (Greek) and its variants appear in both the Old and New Testaments.
Ordinarily this word is translated "magician" or "sorcerer" in the
sense of illusionist or fortune-teller, and this is how it is translated
in all of its occurrences (e.g. Acts 13:6) except for the Gospel of Matthew, where, depending on translation, it is rendered "wise man" (KJV, RSV) or left untranslated as Magi, typically with an explanatory note (NIV). However, early church fathers, such as St. Justin, Origen, St. Augustine and St. Jerome, did not make an exception for the Gospel, and translated the word in its ordinary sense, i.e. as "magician". The Gospel of Matthew states that magi visited the infant Jesus to do him homage shortly after his birth (2:1–2:12). The gospel describes how magi from the east were notified of the birth of a king in Judaea by the appearance of his star. Upon their arrival in Jerusalem, they visited King Herod to determine the location of the king of the Jews's birthplace. Herod, disturbed, told them that he had not heard of the child, but informed them of a prophecy that the Messiah would be born in Bethlehem.
He then asked the magi to inform him when they find the child so that
he himself may also pay homage to the child. Guided by the Star of Bethlehem,
the wise men found the child Jesus in a house. They paid homage to him,
and presented him with "gifts of gold and of frankincense and of
myrrh." (2.11) In a dream they are warned not to return to Herod, and
therefore return to their homes by taking another route. Since its
composition in the late 1st century, numerous apocryphal stories have
embellished the gospel's account. Matthew 2:16 implies that Herod learned from the wise men that up to two years had passed since the birth, which is why all male children two years or younger were slaughtered.
In addition to the more famous story of Simon Magus found in chapter 8, the Book of Acts (13:6–11) also describes another magus who acted as an advisor of Sergius Paulus, the Roman proconsul at Paphos on the island of Cyprus. He was a Jew named Bar-Jesus (son of Jesus), or alternatively Elymas. (Another Cypriot magus named Atomos is referenced by Josephus, working at the court of Felix at Caesarea.)
One of the non-canonical Christian sources, the Syriac Infancy Gospel,
provides, in its third chapter, a story of the wise men of the East
which is very similar to much of the story in Matthew. This account
cites Zoradascht (Zoroaster) as the source of the prophecy that
motivated the wise men to seek the infant Jesus.
Jewish tradition
In the Talmud, instances of dialogue between the Jewish sages
and various magi are recorded. The Talmud depicts the Magi as sorcerers
and in several descriptions, they are negatively described as
obstructing Jewish religious practices.
Several references include the sages criticizing practices performed by
various magi. One instance is a description of the Zoroastrian priests
exhuming corpses for their burial practices which directly interfered
with the Jewish burial rites. Another instance is a sage forbidding learning from the magi.
In Arabic, "Magians" (majus) is the term for Zoroastrians. The term is mentioned in the Quran, in sura 22 verse 17, where the "Magians" are mentioned alongside the Jews, the Sabians and the Christians in a list of religions who will be judged on the Day of Resurrection.
In the 1980s, Saddam Hussein's Ba'ath Party used the term majus during the Iran–Iraq War as a generalization of all modern-day Iranians. "By referring to the Iranians in these documents as majus,
the security apparatus [implied] that the Iranians [were] not sincere
Muslims, but rather covertly practice their pre-Islamic beliefs. Thus,
in their eyes, Iraq's war took on the dimensions of not only a struggle
for Arab nationalism, but also a campaign in the name of Islam."
Indian tradition
Brihat Samhita of Varahamihira, 1279 CE palm leaf manuscript, Pratima lakshana, Sanskrit
In India, the Sakaldwipiya Brahmins are considered to be the descendants of the ten Maga (Sanskrit मग) priests who were invited to conduct worship of Mitra (Surya) at Mitravana (Multan), as described in the Samba Purana, Bhavishya Purana and the Mahabharata. Their original home was a mythological region called Śākadvīpa. According to Varahamihira
(c. 505 – c. 587), the statue of the Sun god (Mitra), is represented as
wearing the "northern" (Central Asian) dress, specifically with horse
riding boots. Some Brahmin
communities of India trace their descent from the Magas. Some classical
astronomers and mathematicians of India such are Varahamihira are
considered to be the descendants of the Magas.
Varahamihira specifies that installation and consecration of the Sun images should be done by the Magas. al-Biruni
mentions that the priests of the Sun Temple at Multan were Magas. The
Magas had colonies in a number of places in India, and were the priests
at Konark, Martanda and other sun temples.
Victor H. Mair (1990) suggested that Chinese wū (巫 "shaman; witch, wizard; magician") may originate as a loanword from Old Persian *maguš "magician; magi". Mair reconstructs an Old Chinese *myag. The reconstruction of Old Chinese forms is somewhat speculative. The velar final -g in Mair's *myag (巫) is evident in several Old Chinese reconstructions (Dong Tonghe's *mywag, Zhou Fagao's *mjwaγ, and Li Fanggui's *mjag), but not all (Bernhard Karlgren's *mywo and Axel Schuessler's *ma).
Mair adduces the discovery of two figurines with unmistakably
Caucasoid or Europoid features dated to the 8th century BC, found in a
1980 excavation of a Zhou dynasty palace in Fufeng County, Shaanxi Province. One of the figurines is marked on the top of its head with an incised ☩ graph.
Mair's suggestion is based on a proposal by Jao Tsung-I (1990), which connects the "cross potent" bronzeware script glyph for wu巫
with the same shape found in Neolithic West Asia, specifically a cross
potent carved in the shoulder of a goddess figure of the Halaf period.
The argument is a play on the notion of a "tornado sweeping through a junkyard to assemble a Boeing 747" employed to decry abiogenesis and evolution as vastly unlikely and better explained by the existence of a creator god (although this quote is first attributed to Fred Hoyle, who used it to argue for panspermia, not creationism). According to Dawkins, this logic is self-defeating as the theist
must now account for the god's existence and explain whether or how the
god was created. In his view, if the existence of highly complex life
on Earth is the equivalent of the implausible junkyard Boeing 747, the
existence of a highly complex god is the "ultimate Boeing 747" that
truly does require the seemingly impossible to explain its existence.
Richard Dawkins begins The God Delusion by making it clear that the God he talks about is the Abrahamic concept of a personal god
who is susceptible to worship. He considers the existence of such an
entity to be a scientific question, because a universe with such a god
would be significantly different from a universe without one, and he
says that the difference would be empirically
discernible. Therefore, Dawkins concludes, the same kind of reasoning
can be applied to the God hypothesis as to any other scientific
question.
After discussing some of the most common arguments for the existence of God in chapter 3, Dawkins concludes that the argument from design
is the most convincing. The extreme improbability of life and a
universe capable of hosting it requires explanation, but Dawkins
considers the God hypothesis inferior to evolution by natural selection as an explanation for the complexity of life. As part of his efforts to refute intelligent design, he redirects the argument from complexity
in order to show that God must have been designed by a superintelligent
designer, then presents his argument for the improbability of God's
existence.
Dawkins' name for the statistical demonstration that God almost
certainly does not exist is the "Ultimate Boeing 747 gambit". This is an
allusion to the junkyard tornado. AstrophysicistFred Hoyle, who was an atheist, anti-theist and advocate of the panspermia theory of life,
is reported as having stated that the "probability of life originating
on Earth is no greater than the chance that a hurricane, sweeping
through a scrapyard, would have the luck to assemble a Boeing 747."
Arguments against empirically based theism date back at least as far as the eighteenth-century philosopher David Hume, whose objection can be paraphrased as the question "Who designed the designer?" According to philosopher Daniel Dennett, however – one of Dawkins' fellow "brights" –
the innovation in Dawkins' argument is twofold: to show that where
design fails to explain complexity, evolution by natural selection
succeeds as the only workable solution; and to argue how this should
illuminate the confusion surrounding the anthropic principle.
Dawkins's statement
Dawkins summarizes his argument as follows; the references to "crane" and "skyhook" are two notions from Daniel Dennett's book Darwin's Dangerous Idea.
One of the greatest challenges to the human intellect, over the
centuries, has been to explain how the complex, improbable appearance of
design in the universe arises.
The natural temptation is to attribute the appearance of design to actual design itself. In the case of a man-made artefact
such as a watch, the designer really was an intelligent engineer. It is
tempting to apply the same logic to an eye or a wing, a spider or a
person.
The temptation is a false one, because the designer hypothesis
immediately raises the larger problem of who designed the designer. The
whole problem we started out with was the problem of explaining
statistical improbability. It is obviously no solution to postulate
something even more improbable. We need a "crane", not a "skyhook"; for
only a crane can do the business of working up gradually and plausibly
from simplicity to otherwise improbable complexity.
The most ingenious and powerful crane so far discovered is Darwinian
evolution by natural selection. Darwin and his successors have shown
how living creatures, with their spectacular statistical improbability
and appearance of design, have evolved by slow, gradual degrees from
simple beginnings. We can now safely say that the illusion of design in
living creatures is just that – an illusion.
We don't yet have an equivalent crane for physics. Some kind of
multiverse theory could in principle do for physics the same explanatory
work as Darwinism does for biology. This kind of explanation is
superficially less satisfying than the biological version of Darwinism,
because it makes heavier demands on luck. But the anthropic principle entitles us to postulate far more luck than our limited human intuition is comfortable with.
We should not give up hope of a better crane arising in physics,
something as powerful as Darwinism is for biology. But even in the
absence of a strongly satisfying crane to match the biological one, the
relatively weak cranes we have at present are, when abetted by the
anthropic principle, self-evidently better than the self-defeating
skyhook hypothesis of an intelligent designer.
A central thesis of the argument is that compared to supernatural
abiogenesis, evolution by natural selection requires the supposition of
fewer hypothetical processes; according to Occam's razor, therefore, it is a better explanation. Dawkins cites a paragraph where Richard Swinburne
agrees that a simpler explanation is better but reasons that theism is
simpler because it only invokes a single substance (God) as a cause and
maintainer of every other object. This cause is seen as omnipotent, omniscient
and totally "free". Dawkins argues that an entity that monitors and
controls every particle in the universe and listens to all thoughts and
prayers cannot be simple. Its existence would require a "mammoth
explanation" of its own. The theory of natural selection is much simpler
– and thus preferable – than a theory of the existence of such a
complex being.
Dawkins then turns to a discussion of Keith Ward's views on divine simplicity
to show the difficulty "the theological mind has in grasping where the
complexity of life comes from." Dawkins writes that Ward is sceptical of
Arthur Peacocke's
ideas that evolution is directed by other forces than only natural
selection and that these processes may have a propensity toward
increasing complexity. Dawkins says that this scepticism is justified,
because complexity does not come from biased mutations. Dawkins writes:
[Natural selection], as far as we know, is the only process
ultimately capable of generating complexity out of simplicity. The
theory of natural selection is genuinely simple. So is the origin from
which it starts. That which it explains, on the other hand, is complex
almost beyond telling: more complex than anything we can imagine, save a
God capable of designing it.
Assessment and criticism
Theist authors have presented extensive opposition, most notably by theologian Alister McGrath (in The Dawkins Delusion?) and philosophers Alvin Plantinga and Richard Swinburne. Another negative review, by biologist H. Allen Orr, sparked heated debate, prompting, for example, the mathematician Norman Levitt to ask why theologians are assumed to have the exclusive right to write about who "rules" the universe. Daniel Dennett also took exception to Orr's review, leading to an exchange of open letters between himself and Orr. The philosopher Sir Anthony Kenny also considers this argument to be flawed. Cosmologist Stephen Barr responded as follows: "Paley finds a watch and asks how
such a thing could have come to be there by chance. Dawkins finds an
immense automated factory that blindly constructs watches, and feels
that he has completely answered Paley's point."
Simplicity of God and materialist assumptions
Both
Alvin Plantinga and Richard Swinburne raise the objection that God is
not complex. Swinburne gives two reasons why a God that controls every
particle can be simple: first, a person, as indicated by phenomena such
as split-brains,
is not the same as their highly complex brain but "is something
simpler" that can "control" that brain; and second, simplicity is a quality that is intrinsic to a hypothesis, not related to its empirical consequences.
Plantinga writes:
So first, according to classical
theology, God is simple, not complex. More remarkable, perhaps, is that
according to Dawkins's own definition of complexity, God is not complex.
According to his definition (set out in The Blind Watchmaker),
something is complex if it has parts that are "arranged in a way that
is unlikely to have arisen by chance alone." But of course God is a
spirit, not a material object at all, and hence has no parts. A fortiori
(as philosophers like to say) God doesn't have parts arranged in ways
unlikely to have arisen by chance. Therefore, given the definition of
complexity Dawkins himself proposes, God is not complex."
He continues:
"But second, suppose we concede,
at least for purposes of argument, that God is complex. Perhaps we think
the more a being knows, the more complex it is; God, being omniscient, would then be highly complex. Given materialism
and the idea that the ultimate objects in our universe are the
elementary particles of physics, perhaps a being that knew a great deal
would be improbable – how could those particles get arranged in such a
way as to constitute a being with all that knowledge? Of course we
aren't given materialism.
In other words, Plantinga concludes that this argument, to be valid,
would require materialism to be true; but, as materialism is not
compatible with traditional theology, the argument begs the question by requiring its premise to assume God's non-existence.
In an extensive analysis published in Science and Christian Belief,
Patrick Richmond suggests that "Dawkins is right to object to
unexplained organised complexity in God" but that God is simply
specified and lacks the sort of composition and limitations found in
[physical] creatures; hence the theist can explain why nature exists
without granting unexplained organised complexity or the extreme
improbability of God.
Some respondents, such as Stephen Law, have suggested that God is or would indeed be complex if responsible for creating and sustaining the universe; According to Law, God's omniscience would require the retention of and ability to use all knowledge. Richard Carrier also argued that God's mind is extremely complex.
Necessity of external explanations
There are many variations on how to express this objection. William F. Vallicella
holds that organized complexity as such does not need explanation,
because when in search of an ultimate explanation, one must in the end
accept an entity whose complexity has no external explanation.
Dawkins has stated that we should search for simple beginnings for
explanations, like in evolution which moves from simple to complex, and
so what we ultimately accept with no external explanation must be simple
for it to be a good explanation. And Plantinga writes that when not
in search for an ultimate explanation of organized complexity, it is
perfectly fine to explain one kind of complexity, that of terrestrial
life, in terms of another kind of complexity, namely divine activity. Dawkins addresses this point in his debate with John Lennox over The God Delusion,
saying that it would be perfectly reasonable to infer from artifacts on
earth or another planet that an intelligence existed, but that you
would still need to explain that intelligence, which evolution does,
while for God's existence there is no such explanation.
Alister McGrath suggests that the leap from the recognition of
complexity to the assertion of improbability is problematic, as a theory of everything
would be more complex than the theories it would replace, yet one would
not conclude that it is less probable. Dawkins has responded to this
point in his debate with Lennox and at other times, saying that while
physics is hard to understand, fundamentally, unlike biology, it is
simple.
McGrath then argues that probability is not relevant to the question of
existence: life on earth is highly improbable and yet we exist. The
important question in his view is not whether God is probable, but whether God is actual. In interviewing McGrath for The Root of All Evil,
Dawkins responds that the existence of life on Earth is indeed highly
improbable, but this is exactly why a theory such as evolution is
required to explain that improbability. In the case of God, Dawkins says, there is no such satisfactory explanation.
On the point of probability, Alvin Plantinga claims that if God is a necessary being,
as argued by classical theism, God is, by definition, maximally
probable; thus an argument that there is no necessary being with the
qualities attributed to God is required to demonstrate God's
improbability.
Eric MacDonald has pointed out that theists assume the coherence of
their position when they make arguments for God when, by Plantinga's
standards, they would have to present an argument that the concept of
God is not logically incoherent before discussing other arguments.
Plantinga's objection would seem to apply to all atheist arguments that
contend that God is improbable, such as evidential arguments about the problem of evil and the argument from nonbelief.
But the reason why theists and atheists do not usually address this
prior to making their arguments is because they want to go beyond merely
discussing whether God is maximally probable or impossible.
Dawkins's response to criticism in The God Delusion
Dawkins writes about his attendance at a conference in Cambridge sponsored by the Templeton Foundation,
where he challenged the theologians present to respond to the argument
that a creator of a complex universe would have to be complex and
improbable. He reports the strongest response as the claim he was imposing a scientific epistemology
on a question that lies beyond the realm of science. When theologians
hold God to be simple, who is a scientist like Dawkins "to dictate to
theologians that their God had to be complex?"
Dawkins writes that he did not feel that those employing this "evasive"
defence were being "wilfully dishonest", but that they were "defining
themselves into an epistemological safe-zone where rational argument
could not reach them because they had declared by fiat that it could not."
Theologians, Dawkins writes, demand that there be a first cause
named "God". Dawkins responds that it must have been a simple cause and
contends that unless "God" is divested of its normal associations, it
is not an appropriate name. Postulating a prime mover
that is capable of indulging in intelligent design is, in Dawkins's
opinion, "a total abdication of the responsibility to find an
explanation"; instead, he seeks a "self-bootstrapping crane" (see above)
that can "lift" the universe into more complex states. This, he states,
does not necessitate a scientific explanation, but does require a
"crane" rather than a "skyhook" (ibid.) if it is to account for the complexity of the natural world.
In philosophy, the problem of the creator of God is the controversy regarding the hypothetical cause responsible for the existence of God, on the assumption God exists. It contests the proposition that the universe cannot exist without a creator by asserting that the creator of the Universe must have the same restrictions. This, in turn, may lead to a problem of infinite regress wherein each new presumed creator of a creator is itself presumed to have its own creator. A common challenge to theistic propositions of a creator deity as a necessary first-cause explanation for the universe is the question: "Who created God?" Some faith traditions have such an element as part of their doctrine. Jainism posits that the universe is eternal and has always existed. Isma'ilism rejects the idea of God as the first cause, due to the doctrine of God's incomparability and source of any existence including abstract objects.
No, don't ask that. That's what all
the religions say – don't ask who created God. But this is strange –
why not? If the question is valid about existence, why does it become
invalid when it is applied to God? And once you ask who created God, you
are falling into a regress absurdum.
John Humphreys writes:
... if someone were able to provide
the explanation, we would be forced to embark upon what philosophers
call an infinite regress. Having established who created God, we would
then have to answer the question of who created God's creator.
Alan Lurie writes:
In response to one of my blogs
about God's purpose in the creation of the universe, one person wrote,
"All you've done is divert the question. If God created the Universe,
who created God? That is a dilemma that religious folks desperately try
to avoid." The question, "Who created God?", has been pondered by
theologians for millennia, and the answer is both surprisingly obvious
and philosophically subtle... whatever one
thinks about the beginnings of the Universe, there is "something" at the
very origin that was not created. This is an inescapable given, a
cosmic truth.
God himself was once as we are now,
and is an exalted man, and sits enthroned in yonder heavens! That is
the great secret. If the veil were rent today, and the great God who
holds this world in its orbit, and who upholds all worlds and all things
by His power, was to make himself visible—I say, if you were to see him
today, you would see him like a man in form—like yourselves in all the
person, image, and very form as a man... it
is necessary we should understand the character and being of God and
how He came to be so; for I am going to tell you how God came to be God.
We have imagined and supposed that God was God from all eternity. I
will refute that idea, and take away the veil...
It is the first principle of the gospel to know for a certainty the
character of God, and to know that we may converse with Him as one man
converses with another, and that He was once a man like us; yea, that
God himself, the Father of us all, dwelt on an earth, the same as Jesus
Christ Himself did... Is it logic to say
that a spirit is immortal and yet has a beginning? Because if a spirit
has a beginning, it will have an end....
All the fools and learned and wise men from the beginning of creation
who say that man had a beginning prove that he must have an end. If that
were so, the doctrine of annihilation would be true. But if I am right,
I might with boldness proclaim from the house tops that God never did
have power to create the spirit of man at all. God himself could not
create himself. Intelligence exists upon a self-existent principle; it
is a spirit from age to age, and there is no creation about it.
Moreover, all the spirits that God ever sent into the world are
susceptible to enlargement.
Responses
Defenders of religion have countered that, by definition, God is the first cause, and thus that the question is improper:
We ask, "If all things have a
creator, then who created God?" Actually, only created things have a
creator, so it's improper to lump God with his creation. God has
revealed himself to us in the Bible as having always existed.
No person or thing created God. He created "time," and because we dwell in the dimension of time, reason
demands that all things have a beginning and an end. God, however,
dwells outside of the dimension of time. He moves through time as we
flip through a history book...He dwells in "eternity," having no
beginning or end.
Ibn Sina, the preeminent Arabic
philosopher, answered this question a thousand years ago, when he
described G-d as non-contingent, absolute existence. If so, to ask "Why
is there G-d?" is the equivalent of asking, "Why is there is-ness?"
Atheists counter that there is no reason to assume the universe was
created. The question becomes irrelevant if the universe is presumed to
have circular time instead of linear time, undergoing an infinite series
of big bangs and big crunches on its own.
John Lennox, professor of Mathematics at Oxford writes:
Now Dawkins candidly tells us that
he does not like people telling him that they also do not believe in the
God in which he does not believe. But we cannot afford to base our
arguments on his dislikes. For, whether he likes it or not, he openly
invites the charge. After all, it is he who is arguing that God is a
delusion. In order to weigh his argument we need first of all to know
what he means by God. And his main argument is focussed on a created
God. Well, several billion of us would share his disbelief in such a
god. He needn't have bothered. Most of us have long since been convinced
of what he is trying to tell us. Certainly, no Christian would ever
dream of suggesting that God was created. Nor, indeed, would Jews or
Muslims. His argument, by his own admission, has nothing to say about an
eternal God. It is entirely beside the point. Dawkins should shelve it
on the shelf marked 'Celestial Teapots' where it belongs. For the God
who created and upholds the universe was not created – he is eternal. He
was not 'made' and therefore subject to the laws that science
discovered; it was he who made the universe with its laws. Indeed, that
fact constitutes the fundamental distinction between God and the
universe. The universe came to be, God did not.
The rotating view of a smoothed chain of a knotted protein (PDB ID: 1xd3)
Knotted proteins are proteins whose backbones entangle
themselves in a knot. One can imagine pulling a protein chain from both
termini, as though pulling a string from both ends. When a knotted
protein is “pulled” from both termini, it does not get disentangled.
Knotted proteins are very rare, making up only about one percent of the
proteins in the Protein Data Bank,
and their folding mechanisms and function are not well understood.
Although there are experimental and theoretical studies that hint to
some answers, systematic answers to these questions have not yet been
found.
Although number of computational methods have been developed to
detect protein knots, there are still no completely automatic methods to
detect protein knots without necessary manual intervention due to the
missing residues or chain breaks in the X-ray structures or the
nonstandard PDB formats.
Four knot types identified in proteins: the 31 knot (upper left), the 41 knot (upper right), the 52 knots (lower left) and the 61 knot (lower right). These images were produced by KnotPlot. Note that the 31 knot has in fact two distinct forms: left-handed and right-handed. What is shown here is a right-handed 31 knot.
Mathematical interpretation
Mathematically, a knot is defined as a subset of three-dimensional space that is homeomorphic to a circle.
According to this definition, a knot must exist in a closed loop, while
knotted proteins instead exist within open, unclosed chains. In order
to apply mathematical knot theory to knotted proteins, various
strategies can be used to create an artificial closed loop. One such
strategy is to choose a point in space at infinite distance to be
connected to the protein's N- and C-termini through a virtual bond, thus
the protein can be treated as a closed loop. Another such strategy is to use stochastic methods that create random closures.
(A)
A protein is an open chain. (B) To create a closed loop, we pick a
point at an infinite distance, and connect it to the N and C termini,
thus the whole topological structure becomes a closed loop.
Depth of the knot
The
depth of a protein knot relates to the ability of the protein to resist
unknotting. A deep knot is preserved even though the removal of a
considerable number of residues from either end does not destroy the
knot. The higher the number of residues that can be removed without
destroying the knot, the deeper the knot.
Formation of knots
Considering
how knots may be produced with a string, the folding of knotted
proteins should involve first the formation of a loop, and then the
threading of one terminus through the loop. This is the only topological
way that the trefoil knot can be formed. For more complex knots, it is
theoretically possible to have the loop to twist multiple times around
itself, meaning that one end of the chain gets wrapped around at least
once, and then threading to occur. It has also been observed in a
theoretical study that a 61 knot can form by the C-terminus
threading through a loop, and another loop flipping over the first loop,
as well as the C-terminus threading through both the loops which have
previously flipped over each other.
The folding of knotted proteins may be explained by interaction
of the nascent chain with the ribosome. In particular, the affinity of
the chain to the ribosome surface may result in creation of the loop,
which may be next threaded by a nascent chain. Such mechanism was shown
to be plausible for one of the most deeply knotted proteins known.
There have been experimental studies involving YibK
and YbeA, knotted proteins containing trefoil knots. It has been
established that these knotted proteins fold slowly, and that the
knotting in folding is the rate limiting step. In another experimental study, a 91-residue-long protein was attached to the termini of YibK and YbeA.
Attaching the protein to both termini produces a deep knot with about
125 removable residues on each terminus before the knot is destroyed.
Yet it was seen that the resulting proteins could fold spontaneously.
The attached proteins were shown to fold more quickly than YibK and YbeA
themselves, so during folding they are expected to act as plugs at
either end of YibK and YbeA. It was found that attaching the protein to
the N-terminus did not alter the folding speed, but the attachment to
the C-terminus slows folding down, suggesting that the threading event
happens at the C-terminus. The chaperones, although facilitate the
protein knotting, are not crucial in proteins' self-tying.
Other topologically complex structures in proteins
A possible slipknot in a protein. If the terminus is cut from the red line (1), a trefoil knot is created (2).
The class of knotted proteins contains only structures, for which the
backbone, after closure forms a knotted loop. However, some proteins
contain "internal knots" called slipknots, i.e. unknotted structures
containing a knotted subchain. Another topologically complex structure is the link formed by covalent loops, closed by disulfide bridges. Three types of disulfide-based links were identified in proteins: two versions of Hopf link (differing in chirality) and one version of Solomon link.
Another complex structure arising by closing part of the chain with
covalent bridge are complex lasso proteins, for which the covalent loop
is threaded by the chain one or more times. Yet another complex structures arising as a result of the existence of disulfide bridges are the cystine knots,
for which two disulfide bridges form a closed, covalent loop, which is
threaded by third chain. The term "knot" in the name of the motif is
misleading, as the motif does not contain any knotted closed cycle.
Moreover, formation of the cystine knots in general is not different
from the folding of an unknotted protein
Apart from closing only one chain, one may perform also the chain
closure procedure for all the chains present in the crystal structure.
In some cases one obtains the non-trivially linked structures, called
probabilistic links.
One can also consider loops in proteins formed by pieces of the
main chain and the disulfide bridges and interaction via ions. Such
loops can also be knotted of form links even within structures with
unknotted main chain.
First discoveries
Marc L. Mansfield proposed in 1994, that there can be knots in proteins.
He gave unknot scores to proteins by constructing a sphere centered at
the center of mass of the alpha carbons of the backbone, with a radius
twice the distance between the center of mass and the Calpha that is the
farthest away from the center of mass, and by sampling two random
points on the surface of the sphere. He connected the two points by
tracing a geodesic on the surface of the sphere (arcs of great circles),
and then connected each end of the protein chain with one of these
points. Repeating this procedure a 100 times and counting the times
where the knot is destroyed in the mathematical sense yields the unknot
score. Human carbonic anhydrase was identified to have a low unknot
score (22). Upon visually inspecting the structure, it was seen that the
knot was shallow, meaning that the removal of a few residues from
either end destroys the knot.
In 2000, William R. Taylor identified a deep knot in acetohydroxy acid isomeroreductase (PDB ID: 1YVE), by using an algorithm that smooths protein chains and makes knots more visible.
The algorithm keeps both termini fixed, and iteratively assigns to the
coordinates of each residue the average of the coordinates of the
neighboring residues. It has to be made sure that the chains do not pass
through each other, otherwise the crossings and therefore the knot
might get destroyed. If there is no knot, the algorithm eventually
produces a straight line that joins both termini.
Studies about the function of the knot in a protein
Some
proposals about the function of knots have been that it might increase
thermal and kinetic stability. One particular suggestion was that for
the human ubiquitin hydrolase, which contains a 52 knot, the presence of the knot might be preventing it from being pulled into the proteasome.
Because it is a deubiquitinating enzyme, it is often found in proximity
of proteins soon to be degraded by proteasome, and therefore it faces
the danger of being degraded itself. Therefore, the presence of the knot
might be functioning as a plug that prevents it. This notion was
further analyzed on other proteins like YbeA and YibK with computer
simulations.
The knots seem to tighten when they are pulled into a pore, and
depending on the force with which they are pulled in, they either get
stuck and block the pore, the likeliness of which increases with
stronger pulling forces, or in the case of a small pulling force they
might get disentangled as one terminus is pulled out of the knot. For
deeper knots, it is more likely that the pore will be blocked, as there
are too many residues that need to be pulled through the knot. In
another theoretical study,
it was found that the modeled knotted protein was not thermally stable,
but it was kinetically stable. It was also shown that the knot in
proteins creates the places on the verge of hydrophobic and hydrophilic
parts of the chain, characteristic for active sites. This may explain why over 80% of knotted proteins are enzymes.
Another study shows that knotted and slipknotted proteins constitute a
significant number of membrane proteins. They comprise one of the
largest groups of secondary active transporters.
Web servers to extrapolate knotted proteins
Some local programs and a number of web servers
are available, providing convenient query services for knotted
structures and analysis tools for detecting protein knots, including:
Topoly - Python package to analyze topology of polymers
Knot_pull - Python package for biopolymer smoothing and knot detection
KnotProt 2.0 - Database of proteins with knots and other entangled structures
AlphaKnot 2.0 - Database and server to analyze entanglement in structures predicted by AlphaFold methods
![{\displaystyle \nu ={\frac {R_{\text{p}}}{R_{\text{deac}}}}={\frac {k_{\text{p}}[{\text{M}}][{\text{P}}]}{k_{\text{deac}}[{\text{Cu}}^{\text{II}}][{\text{P}}]}}={\frac {k_{\text{p}}[{\text{M}}]}{k_{\text{deac}}[{{\text{Cu}}^{\text{II}}}]}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2059dda9682adfa516f4f9bc3e94ef94ad77a4f8)
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