Bose gas

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Bose_gas 

An ideal Bose gas is a quantum-mechanical phase of matter, analogous to a classical ideal gas. It is composed of bosons, which have an integer value of spin, and abide by Bose–Einstein statistics. The statistical mechanics of bosons were developed by Satyendra Nath Bose for a photon gas, and extended to massive particles by Albert Einstein who realized that an ideal gas of bosons would form a condensate at a low enough temperature, unlike a classical ideal gas. This condensate is known as a Bose–Einstein condensate.

Introduction and examples

Bosons are quantum mechanical particles that follow Bose–Einstein statistics, or equivalently, that possess integer spin. These particles can be classified as elementary: these are the Higgs boson, the photon, the gluon, the W/Z and the hypothetical graviton; or composite like the atom of hydrogen, the atom of ¹⁶O, the nucleus of deuterium, mesons etc. Additionally, some quasiparticles in more complex systems can also be considered bosons like the plasmons (quanta of charge density waves).

The first model that treated a gas with several bosons, was the photon gas, a gas of photons, developed by Bose. This model leads to a better understanding of Planck's law and the black-body radiation. The photon gas can be easily expanded to any kind of ensemble of massless non-interacting bosons. The phonon gas, also known as Debye model, is an example where the normal modes of vibration of the crystal lattice of a metal, can be treated as effective massless bosons. Peter Debye used the phonon gas model to explain the behaviour of heat capacity of metals at low temperature.

An interesting example of a Bose gas is an ensemble of helium-4 atoms. When a system of ⁴He atoms is cooled down to temperature near absolute zero, many quantum mechanical effects are present. Below 2.17 kelvins, the ensemble starts to behave as a superfluid, a fluid with almost zero viscosity. The Bose gas is the most simple quantitative model that explains this phase transition. Mainly when a gas of bosons is cooled down, it forms a Bose–Einstein condensate, a state where a large number of bosons occupy the lowest energy, the ground state, and quantum effects are macroscopically visible like wave interference.

The theory of Bose-Einstein condensates and Bose gases can also explain some features of superconductivity where charge carriers couple in pairs (Cooper pairs) and behave like bosons. As a result, superconductors behave like having no electrical resistivity at low temperatures.

The equivalent model for half-integer particles (like electrons or helium-3 atoms), that follow Fermi–Dirac statistics, is called the Fermi gas (an ensemble of non-interacting fermions). At low enough particle number density and high temperature, both the Fermi gas and the Bose gas behave like a classical ideal gas.^[Macroscopic limit

The thermodynamics of an ideal Bose gas is best calculated using the grand canonical ensemble. The grand potential for a Bose gas is given by:

${\displaystyle \mathrm{\Omega }=-\ln (\mathcal{Z})=\sum _i{g}_i\ln \left(1-z{e}^{-\beta {ϵ}_i}\right).}$

where each term in the sum corresponds to a particular single-particle energy level ε_i ; g_i  is the number of states with energy ε_i ; z  is the absolute activity (or "fugacity"), which may also be expressed in terms of the chemical potential μ by defining:

${\displaystyle z(\beta ,\mu )=e^{\beta \mu }}$

and β defined as:

${\displaystyle \beta =\frac{1}{k_{\mathrm{B}}T}}$

where k_B  is Boltzmann's constant and T  is the temperature. All thermodynamic quantities may be derived from the grand potential and we will consider all thermodynamic quantities to be functions of only the three variables z , β (or T ), and V . All partial derivatives are taken with respect to one of these three variables while the other two are held constant.

The permissible range of z is from negative infinity to +1, as any value beyond this would give an infinite number of particles to states with an energy level of 0 (it is assumed that the energy levels have been offset so that the lowest energy level is 0).

Macroscopic limit, result for uncondensed fraction

Pressure vs temperature curves of classical and quantum ideal gases (Fermi gas, Bose gas) in three dimensions. The Bose gas pressure is lower than an equivalent classical gas, especially below the critical temperature (marked with ★) where particles begin moving en masse into the zero-pressure condensed phase.

Following the procedure described in the gas in a box article, we can apply the Thomas–Fermi approximation which assumes that the average energy is large compared to the energy difference between levels so that the above sum may be replaced by an integral. This replacement gives the macroscopic grand potential function ${\displaystyle {\mathrm{\Omega }}_m}$, which is close to ${\displaystyle \mathrm{\Omega }}$:

${\displaystyle {\mathrm{\Omega }}_{\mathrm{m}}={\int }_0^{\mathrm{\infty }}\ln \left(1-z{e}^{-\beta E}\right)dg\approx \mathrm{\Omega }.}$

The degeneracy dg  may be expressed for many different situations by the general formula:

${\displaystyle dg=\frac{1}{\mathrm{\Gamma }(\alpha )}\frac{E^{\alpha -1}}{E_{\mathrm{c}}^{\alpha }}dE}$

where α is a constant, E_c is a critical energy, and Γ is the Gamma function. For example, for a massive Bose gas in a box, α=3/2 and the critical energy is given by:

${\displaystyle \frac{1}{(\beta E_{\mathrm{c}}{)}^{\alpha }}=\frac{Vf}{{\mathrm{\Lambda }}^3}}$

where Λ is the thermal wavelength, and f is a degeneracy factor (f=1 for simple spinless bosons). For a massive Bose gas in a harmonic trap we will have α=3 and the critical energy is given by:

${\displaystyle \frac{1}{(\beta E_c{)}^{\alpha }}=\frac{f}{(\hslash \omega \beta {)}^3}}$

where V(r)=mω²r²/2  is the harmonic potential. It is seen that E_c  is a function of volume only.

This integral expression for the grand potential evaluates to:

${\displaystyle {\mathrm{\Omega }}_{\mathrm{m}}=-\frac{{\text{Li}}_{\alpha +1}(z)}{{\left(\beta E_c\right)}^{\alpha }},}$

where Li_s(x) is the polylogarithm function.

The problem with this continuum approximation for a Bose gas is that the ground state has been effectively ignored, giving a degeneracy of zero for zero energy. This inaccuracy becomes serious when dealing with the Bose–Einstein condensate and will be dealt with in the next sections. As will be seen, even at low temperatures the above result is still useful for accurately describing the thermodynamics of just the un-condensed portion of the gas.

Limit on number of particles in uncondensed phase, critical temperature

The total number of particles is found from the grand potential by

${\displaystyle N_{\mathrm{m}}=-z\frac{\mathrm{\partial }{\mathrm{\Omega }}_m}{\mathrm{\partial }z}=\frac{{\text{Li}}_{\alpha }(z)}{(\beta E_c{)}^{\alpha }}.}$

This increases monotonically with z (up to the maximum z = +1). The behaviour when approaching z = 1 is however crucially dependent on the value of α (i.e., dependent on whether the gas is 1D, 2D, 3D, whether it is in a flat or harmonic potential well).

For α > 1, the number of particles only increases up to a finite maximum value, i.e., ${\displaystyle N_{\mathrm{m}}}$ is finite at z = 1:

${\displaystyle N_{\mathrm{m},\mathrm{m}\mathrm{a}\mathrm{x}}=\frac{\zeta (\alpha )}{(\beta E_{\mathrm{c}}{)}^{\alpha }},}$

where ζ(α) is the Riemann zeta function (using Li_α(1) = ζ(α)). Thus, for a fixed number of particles ${\displaystyle N_{\mathrm{m}}}$, the largest possible value that β can have is a critical value β_c. This corresponds to a critical temperature T_c=1/k_Bβ_c, below which the Thomas–Fermi approximation breaks down (the continuum of states simply can no longer support this many particles, at lower temperatures). The above equation can be solved for the critical temperature:

${\displaystyle T_{\mathrm{c}}={\left(\frac{N}{\zeta (\alpha )}\right)}^{1/\alpha }\frac{E_{\mathrm{c}}}{k_{\mathrm{B}}}}$

For example, for the three-dimensional Bose gas in a box (${\displaystyle \alpha =3/2}$ and using the above noted value of $E_{\mathrm{c}}$) we get:

${\displaystyle T_{\mathrm{c}}={\left(\frac{N}{Vf\zeta (3/2)}\right)}^{2/3}\frac{h^2}{2\pi m{k}_{\mathrm{B}}}}$

For α ≤ 1, there is no upper limit on the number of particles (${\displaystyle N_{\mathrm{m}}}$ diverges as z approaches 1), and thus for example for a gas in a one- or two-dimensional box (${\displaystyle \alpha =1/2}$ and ${\displaystyle \alpha =1}$ respectively) there is no critical temperature.

Inclusion of the ground state

The above problem raises the question for α > 1: if a Bose gas with a fixed number of particles is lowered down below the critical temperature, what happens? The problem here is that the Thomas–Fermi approximation has set the degeneracy of the ground state to zero, which is wrong. There is no ground state to accept the condensate and so particles simply 'disappear' from the continuum of states. It turns out, however, that the macroscopic equation gives an accurate estimate of the number of particles in the excited states, and it is not a bad approximation to simply "tack on" a ground state term to accept the particles that fall out of the continuum:

${\displaystyle N=N_0+N_{\mathrm{m}}=N_0+\frac{{\text{Li}}_{\alpha }(z)}{(\beta E_{\mathrm{c}}{)}^{\alpha }}}$

where N₀ is the number of particles in the ground state condensate.

Thus in the macroscopic limit, when T < T_c, the value of z is pinned to 1 and N₀ takes up the remainder of particles. For T > T_c there is the normal behaviour, with N₀ = 0. This approach gives the fraction of condensed particles in the macroscopic limit:

${\displaystyle \frac{N_0}{N}=\{\begin{array}{ll}1-{\left(\frac{T}{T_{\mathrm{c}}}\right)}^{\alpha }& \text{if }\alpha >1\text{ and }T<T_{\mathrm{c}},\\ 0& \text{otherwise}.\end{array}}$

Limitations of the macroscopic Bose gas model

The above standard treatment of a macroscopic Bose gas is straight-forward, but the inclusion of the ground state is somewhat inelegant. Another approach is to include the ground state explicitly (contributing a term in the grand potential, as in the section below), this gives rise to an unrealistic fluctuation catastrophe: the number of particles in any given state follow a geometric distribution, meaning that when condensation happens at T < T_c and most particles are in one state, there is a huge uncertainty in the total number of particles. This is related to the fact that the compressibility becomes unbounded for T < T_c. Calculations can instead be performed in the canonical ensemble, which fixes the total particle number, however the calculations are not as easy.

Practically however, the aforementioned theoretical flaw is a minor issue, as the most unrealistic assumption is that of non-interaction between bosons. Experimental realizations of boson gases always have significant interactions, i.e., they are non-ideal gases. The interactions significantly change the physics of how a condensate of bosons behaves: the ground state spreads out, the chemical potential saturates to a positive value even at zero temperature, and the fluctuation problem disappears (the compressibility becomes finite).

Approximate behaviour in small gases

Figure 1: Various Bose gas parameters as a function of normalized temperature τ. The value of α is 3/2. Solid lines are for N=10,000, dotted lines are for N=1000. Black lines are the fraction of excited particles, blue are the fraction of condensed particles. The negative of the chemical potential μ is shown in red, and green lines are the values of z. It has been assumed that k =ε_c=1.

For smaller, mesoscopic, systems (for example, with only thousands of particles), the ground state term can be more explicitly approximated by adding in an actual discrete level at energy ε=0 in the grand potential:

${\displaystyle \mathrm{\Omega }=g_0\ln (1-z)+{\mathrm{\Omega }}_{\mathrm{m}}}$

which gives instead ${\displaystyle N_0=\frac{g_{0}z}{1-z}}$. Now, the behaviour is smooth when crossing the critical temperature, and z approaches 1 very closely but does not reach it.

This can now be solved down to absolute zero in temperature. Figure 1 shows the results of the solution to this equation for α=3/2, with k=ε_c=1 which corresponds to a gas of bosons in a box. The solid black line is the fraction of excited states 1-N₀/N  for N =10,000 and the dotted black line is the solution for N =1000. The blue lines are the fraction of condensed particles N₀/N  The red lines plot values of the negative of the chemical potential μ and the green lines plot the corresponding values of z . The horizontal axis is the normalized temperature τ defined by

${\displaystyle \tau =\frac{T}{T_{\mathrm{c}}}}$

It can be seen that each of these parameters become linear in τ^α in the limit of low temperature and, except for the chemical potential, linear in 1/τ^α in the limit of high temperature. As the number of particles increases, the condensed and excited fractions tend towards a discontinuity at the critical temperature.

The equation for the number of particles can be written in terms of the normalized temperature as:

${\displaystyle N=\frac{g_{0}z}{1-z}+N\frac{{\text{Li}}_{\alpha }(z)}{\zeta (\alpha )}{\tau }^{\alpha }}$

For a given N  and τ, this equation can be solved for τ^α and then a series solution for z  can be found by the method of inversion of series, either in powers of τ^α or as an asymptotic expansion in inverse powers of τ^α. From these expansions, we can find the behavior of the gas near T =0 and in the Maxwell–Boltzmann as T  approaches infinity. In particular, we are interested in the limit as N  approaches infinity, which can be easily determined from these expansions.

This approach to modelling small systems may in fact be unrealistic, however, since the variance in the number of particles in the ground state is very large, equal to the number of particles. In contrast, the variance of particle number in a normal gas is only the square-root of the particle number, which is why it can normally be ignored. This high variance is due to the choice of using the grand canonical ensemble for the entire system, including the condensate state.

Thermodynamics

Expanded out, the grand potential is:

${\displaystyle \mathrm{\Omega }=g_0\ln (1-z)-\frac{{\text{Li}}_{\alpha +1}(z)}{{\left(\beta E_{\mathrm{c}}\right)}^{\alpha }}}$

All thermodynamic properties can be computed from this potential. The following table lists various thermodynamic quantities calculated in the limit of low temperature and high temperature, and in the limit of infinite particle number. An equal sign (=) indicates an exact result, while an approximation symbol indicates that only the first few terms of a series in ${\displaystyle {\tau }^{\alpha }}$ is shown.

Quantity	General	${\displaystyle T\ll T_c}$	${\displaystyle T\gg T_c}$
${\displaystyle z}$		${\displaystyle \approx \frac{\zeta (\alpha )}{{\tau }^{\alpha }}-\frac{{\zeta }^2(\alpha )}{2^{\alpha }{\tau }^{2\alpha }}}$	${\displaystyle =1}$
Vapor fraction ${\displaystyle 1-\frac{N_0}{N}}$	${\displaystyle =\frac{{\text{Li}}_{\alpha }(z)}{\zeta (\alpha )}{\tau }^{\alpha }}$	${\displaystyle ={\tau }^{\alpha }}$	${\displaystyle =1}$
Equation of state ${\displaystyle \frac{PV\beta }{N}=-\frac{\mathrm{\Omega }}{N}}$	${\displaystyle =\frac{{\text{Li}}_{\alpha +1}(z)}{\zeta (\alpha )}{\tau }^{\alpha }}$	${\displaystyle =\frac{\zeta (\alpha +1)}{\zeta (\alpha )}{\tau }^{\alpha }}$	${\displaystyle \approx 1-\frac{\zeta (\alpha )}{2^{\alpha +1}{\tau }^{\alpha }}}$
Gibbs Free Energy ${\displaystyle G=\ln (z)}$	${\displaystyle =\ln (z)}$	${\displaystyle =0}$	${\displaystyle \approx \ln \left(\frac{\zeta (\alpha )}{{\tau }^{\alpha }}\right)-\frac{\zeta (\alpha )}{2^{\alpha }{\tau }^{\alpha }}}$

It is seen that all quantities approach the values for a classical ideal gas in the limit of large temperature. The above values can be used to calculate other thermodynamic quantities. For example, the relationship between internal energy and the product of pressure and volume is the same as that for a classical ideal gas over all temperatures:

${\displaystyle U=\frac{\mathrm{\partial }\mathrm{\Omega }}{\mathrm{\partial }\beta }=\alpha PV}$

A similar situation holds for the specific heat at constant volume

${\displaystyle C_V=\frac{\mathrm{\partial }U}{\mathrm{\partial }T}=k_{\mathrm{B}}(\alpha +1)U\beta }$

The entropy is given by:

${\displaystyle TS=U+PV-G}$

Note that in the limit of high temperature, we have

${\displaystyle TS=(\alpha +1)+\ln \left(\frac{{\tau }^{\alpha }}{\zeta (\alpha )}\right)}$

which, for α=3/2 is simply a restatement of the Sackur–Tetrode equation. In one dimension bosons with delta interaction behave as fermions, they obey Pauli exclusion principle. In one dimension Bose gas with delta interaction can be solved exactly by Bethe ansatz. The bulk free energy and thermodynamic potentials were calculated by Chen-Ning Yang. In one dimensional case correlation functions also were evaluated. In one dimension Bose gas is equivalent to quantum non-linear Schrödinger equation.

Boson

From Wikipedia, the free encyclopedia

For other uses, see Boson (disambiguation).

Bosons form one of the two fundamental classes of subatomic particle, the other being fermions. All subatomic particles must be one or the other. A composite particle (hadron) may fall into either class depending on its composition

In particle physics, a boson is a subatomic particle whose spin quantum number has an integer value (0, 1, 2, ...). Bosons form one of the two fundamental classes of subatomic particle, the other being fermions, which have odd half-integer spin (1⁄2, 3⁄2, 5⁄2, ...). Every observed subatomic particle is either a boson or a fermion.

Some bosons are elementary particles occupying a special role in particle physics, distinct from the role of fermions (which are sometimes described as the constituents of "ordinary matter"). Certain elementary bosons (e.g. gluons) act as force carriers, which give rise to forces between other particles, while one (the Higgs boson) contributes to the phenomenon of mass. Other bosons, such as mesons, are composite particles made up of smaller constituents.

Outside the realm of particle physics, multiple identical composite bosons (in this context sometimes known as 'bose particles') behave at high densities or low temperatures in a characteristic manner described by Bose–Einstein statistics: for example a gas of helium-4 atoms becomes a superfluid at temperatures close to absolute zero. Similarly, superconductivity arises because some quasiparticles, such as Cooper pairs, behave in the same way.

Name

The name boson was coined by Paul Dirac to commemorate the contribution of Satyendra Nath Bose, an Indian physicist, when he was a reader (later professor) at the University of Dhaka, Bengal (now in Bangladesh), he developed, in conjunction with Albert Einstein, the theory characterising such particles, now known as Bose–Einstein statistics and Bose-Einstein condensate.

Elementary bosons

See also: List of particles § Bosons

All observed elementary particles are either bosons (with integer spin) or fermions (with odd half-integer spin). Whereas the elementary particles that make up ordinary matter (leptons and quarks) are fermions, elementary bosons occupy a special role in particle physics. They act either as force carriers which give rise to forces between other particles, or in one case give rise to the phenomenon of mass.

According to the Standard Model of Particle Physics there are five elementary bosons:

• One scalar boson (spin = 0)
  • 
    H⁰
    Higgs boson – the particle that contributes to the phenomenon of mass via the Higgs mechanism
• Four vector bosons (spin = 1) that act as force carriers. These are the gauge bosons:
  • 
    γ
      Photon – the force carrier of the electromagnetic field
  • 
    g
      Gluons (eight different types) – force carriers that mediate the strong force
  • 
    Z
      Neutral weak boson – the force carrier that mediates the weak force
  • 
    W^±
      Charged weak bosons (two types) – also force carriers that mediate the weak force

A second order tensor boson (spin = 2) called the graviton (G) has been hypothesised as the force carrier for gravity, but so far all attempts to incorporate gravity into the Standard Model have failed.

Composite bosons

See also: List of particles § Composite particles

Composite particles (such as hadrons, nuclei, and atoms) can be bosons or fermions depending on their constituents. Since bosons have integer spin and fermions odd half-integer spin, any composite particle made up of an even number of fermions is a boson.

Composite bosons include:

• All types of meson
• Stable nuclei of even mass number such as deuterium, helium-4 (the alpha particle), carbon-12 and lead-208.

As quantum particles, the behaviour of multiple indistinguishable bosons at high densities is described by Bose–Einstein statistics. One characteristic which becomes important in superfluidity and other applications of Bose–Einstein condensates is that there is no restriction on the number of bosons that may occupy the same quantum state. As a consequence, when for example a gas of helium-4 atoms is cooled to temperatures very close to absolute zero and the kinetic energy of the particles becomes negligible, it condenses into a low-energy state and becomes a superfluid.

Quasiparticles

Certain quasiparticles are observed to behave as bosons and to follow Bose–Einstein statistics, including Cooper pairs, plasmons and phonons.

Base pair

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Base_pair 

The chemical structure of DNA base-pairs

A base pair (bp) is a fundamental unit of double-stranded nucleic acids consisting of two nucleobases bound to each other by hydrogen bonds. They form the building blocks of the DNA double helix and contribute to the folded structure of both DNA and RNA. Dictated by specific hydrogen bonding patterns, "Watson–Crick" (or "Watson–Crick–Franklin") base pairs (guanine–cytosine and adenine–thymine) allow the DNA helix to maintain a regular helical structure that is subtly dependent on its nucleotide sequence. The complementary nature of this based-paired structure provides a redundant copy of the genetic information encoded within each strand of DNA. The regular structure and data redundancy provided by the DNA double helix make DNA well suited to the storage of genetic information, while base-pairing between DNA and incoming nucleotides provides the mechanism through which DNA polymerase replicates DNA and RNA polymerase transcribes DNA into RNA. Many DNA-binding proteins can recognize specific base-pairing patterns that identify particular regulatory regions of genes.

Intramolecular base pairs can occur within single-stranded nucleic acids. This is particularly important in RNA molecules (e.g., transfer RNA), where Watson–Crick base pairs (guanine–cytosine and adenine–uracil) permit the formation of short double-stranded helices, and a wide variety of non–Watson–Crick interactions (e.g., G–U or A–A) allow RNAs to fold into a vast range of specific three-dimensional structures. In addition, base-pairing between transfer RNA (tRNA) and messenger RNA (mRNA) forms the basis for the molecular recognition events that result in the nucleotide sequence of mRNA becoming translated into the amino acid sequence of proteins via the genetic code.

The size of an individual gene or an organism's entire genome is often measured in base pairs because DNA is usually double-stranded. Hence, the number of total base pairs is equal to the number of nucleotides in one of the strands (with the exception of non-coding single-stranded regions of telomeres). The haploid human genome (23 chromosomes) is estimated to be about 3.2 billion bases long and to contain 20,000–25,000 distinct protein-coding genes. A kilobase (kb) is a unit of measurement in molecular biology equal to 1000 base pairs of DNA or RNA. The total number of DNA base pairs on Earth is estimated at 5.0×10³⁷ with a weight of 50 billion tonnes. In comparison, the total mass of the biosphere has been estimated to be as much as 4 TtC (trillion tons of carbon).

Hydrogen bonding and stability

Top, a G.C base pair with three hydrogen bonds. Bottom, an A.T base pair with two hydrogen bonds. Non-covalent hydrogen bonds between the bases are shown as dashed lines. The wiggly lines stand for the connection to the pentose sugar and point in the direction of the minor groove.

Hydrogen bonding is the chemical interaction that underlies the base-pairing rules described above. Appropriate geometrical correspondence of hydrogen bond donors and acceptors allows only the "right" pairs to form stably. DNA with high GC-content is more stable than DNA with low GC-content. But, contrary to popular belief, the hydrogen bonds do not stabilize the DNA significantly; stabilization is mainly due to stacking interactions.

The bigger nucleobases, adenine and guanine, are members of a class of double-ringed chemical structures called purines; the smaller nucleobases, cytosine and thymine (and uracil), are members of a class of single-ringed chemical structures called pyrimidines. Purines are complementary only with pyrimidines: pyrimidine–pyrimidine pairings are energetically unfavorable because the molecules are too far apart for hydrogen bonding to be established; purine–purine pairings are energetically unfavorable because the molecules are too close, leading to overlap repulsion. Purine–pyrimidine base-pairing of AT or GC or UA (in RNA) results in proper duplex structure. The only other purine–pyrimidine pairings would be AC and GT and UG (in RNA); these pairings are mismatches because the patterns of hydrogen donors and acceptors do not correspond. The GU pairing, with two hydrogen bonds, does occur fairly often in RNA (see wobble base pair).

Paired DNA and RNA molecules are comparatively stable at room temperature, but the two nucleotide strands will separate above a melting point that is determined by the length of the molecules, the extent of mispairing (if any), and the GC content. Higher GC content results in higher melting temperatures; it is, therefore, unsurprising that the genomes of extremophile organisms such as Thermus thermophilus are particularly GC-rich. On the converse, regions of a genome that need to separate frequently — for example, the promoter regions for often-transcribed genes — are comparatively GC-poor (for example, see TATA box). GC content and melting temperature must also be taken into account when designing primers for PCR reactions.

Examples

The following DNA sequences illustrate pair double-stranded patterns. By convention, the top strand is written from the 5′-end to the 3′-end; thus, the bottom strand is written 3′ to 5′.

A base-paired DNA sequence:

ATCGATTGAGCTCTAGCG

TAGCTAACTCGAGATCGC

The corresponding RNA sequence, in which uracil is substituted for thymine in the RNA strand:

AUCGAUUGAGCUCUAGCG

UAGCUAACUCGAGAUCGC

Base analogs and intercalators

Main article: Nucleic acid analogue

Chemical analogs of nucleotides can take the place of proper nucleotides and establish non-canonical base-pairing, leading to errors (mostly point mutations) in DNA replication and DNA transcription. This is due to their isosteric chemistry. One common mutagenic base analog is 5-bromouracil, which resembles thymine but can base-pair to guanine in its enol form.

Other chemicals, known as DNA intercalators, fit into the gap between adjacent bases on a single strand and induce frameshift mutations by "masquerading" as a base, causing the DNA replication machinery to skip or insert additional nucleotides at the intercalated site. Most intercalators are large polyaromatic compounds and are known or suspected carcinogens. Examples include ethidium bromide and acridine.

Mismatch repair

Mismatched base pairs can be generated by errors of DNA replication and as intermediates during homologous recombination. The process of mismatch repair ordinarily must recognize and correctly repair a small number of base mispairs within a long sequence of normal DNA base pairs. To repair mismatches formed during DNA replication, several distinctive repair processes have evolved to distinguish between the template strand and the newly formed strand so that only the newly inserted incorrect nucleotide is removed (in order to avoid generating a mutation). The proteins employed in mismatch repair during DNA replication, and the clinical significance of defects in this process are described in the article DNA mismatch repair. The process of mispair correction during recombination is described in the article gene conversion.

Length measurements

Schematic karyogram of a human. The blue scale to the left of each nuclear chromosome pair (as well as the mitochondrial genome at bottom left) shows its length in terms of mega–base-pairs.

Further information: Karyotype

The following abbreviations are commonly used to describe the length of a D/RNA molecule:

• bp = base pair—one bp corresponds to approximately 3.4 Å (340 pm) of length along the strand, and to roughly 618 or 643 daltons for DNA and RNA respectively.
• kb (= kbp) = kilo–base-pair = 1,000 bp
• Mb (= Mbp) = mega–base-pair = 1,000,000 bp
• Gb (= Gbp) = giga–base-pair = 1,000,000,000 bp

For single-stranded DNA/RNA, units of nucleotides are used—abbreviated nt (or knt, Mnt, Gnt)—as they are not paired. To distinguish between units of computer storage and bases, kbp, Mbp, Gbp, etc. may be used for base pairs.

The centimorgan is also often used to imply distance along a chromosome, but the number of base pairs it corresponds to varies widely. In the human genome, the centimorgan is about 1 million base pairs.

Unnatural base pair (UBP)

See also: Artificial gene synthesis, Expanded genetic code, Nucleic acid analogue, and Synthetic genomics

An unnatural base pair (UBP) is a designed subunit (or nucleobase) of DNA which is created in a laboratory and does not occur in nature. DNA sequences have been described which use newly created nucleobases to form a third base pair, in addition to the two base pairs found in nature, A-T (adenine – thymine) and G-C (guanine – cytosine). A few research groups have been searching for a third base pair for DNA, including teams led by Steven A. Benner, Philippe Marliere, Floyd E. Romesberg and Ichiro Hirao. Some new base pairs based on alternative hydrogen bonding, hydrophobic interactions and metal coordination have been reported.

In 1989 Steven Benner (then working at the Swiss Federal Institute of Technology in Zurich) and his team led with modified forms of cytosine and guanine into DNA molecules in vitro. The nucleotides, which encoded RNA and proteins, were successfully replicated in vitro. Since then, Benner's team has been trying to engineer cells that can make foreign bases from scratch, obviating the need for a feedstock.

In 2002, Ichiro Hirao's group in Japan developed an unnatural base pair between 2-amino-8-(2-thienyl)purine (s) and pyridine-2-one (y) that functions in transcription and translation, for the site-specific incorporation of non-standard amino acids into proteins. In 2006, they created 7-(2-thienyl)imidazo[4,5-b]pyridine (Ds) and pyrrole-2-carbaldehyde (Pa) as a third base pair for replication and transcription. Afterward, Ds and 4-[3-(6-aminohexanamido)-1-propynyl]-2-nitropyrrole (Px) was discovered as a high fidelity pair in PCR amplification. In 2013, they applied the Ds-Px pair to DNA aptamer generation by in vitro selection (SELEX) and demonstrated the genetic alphabet expansion significantly augment DNA aptamer affinities to target proteins.

In 2012, a group of American scientists led by Floyd Romesberg, a chemical biologist at the Scripps Research Institute in San Diego, California, published that his team designed an unnatural base pair (UBP). The two new artificial nucleotides or Unnatural Base Pair (UBP) were named d5SICS and dNaM. More technically, these artificial nucleotides bearing hydrophobic nucleobases, feature two fused aromatic rings that form a (d5SICS–dNaM) complex or base pair in DNA. His team designed a variety of in vitro or "test tube" templates containing the unnatural base pair and they confirmed that it was efficiently replicated with high fidelity in virtually all sequence contexts using the modern standard in vitro techniques, namely PCR amplification of DNA and PCR-based applications. Their results show that for PCR and PCR-based applications, the d5SICS–dNaM unnatural base pair is functionally equivalent to a natural base pair, and when combined with the other two natural base pairs used by all organisms, A–T and G–C, they provide a fully functional and expanded six-letter "genetic alphabet".

In 2014 the same team from the Scripps Research Institute reported that they synthesized a stretch of circular DNA known as a plasmid containing natural T-A and C-G base pairs along with the best-performing UBP Romesberg's laboratory had designed and inserted it into cells of the common bacterium E. coli that successfully replicated the unnatural base pairs through multiple generations. The transfection did not hamper the growth of the E. coli cells and showed no sign of losing its unnatural base pairs to its natural DNA repair mechanisms. This is the first known example of a living organism passing along an expanded genetic code to subsequent generations. Romesberg said he and his colleagues created 300 variants to refine the design of nucleotides that would be stable enough and would be replicated as easily as the natural ones when the cells divide. This was in part achieved by the addition of a supportive algal gene that expresses a nucleotide triphosphate transporter which efficiently imports the triphosphates of both d5SICSTP and dNaMTP into E. coli bacteria. Then, the natural bacterial replication pathways use them to accurately replicate a plasmid containing d5SICS–dNaM. Other researchers were surprised that the bacteria replicated these human-made DNA subunits.

The successful incorporation of a third base pair is a significant breakthrough toward the goal of greatly expanding the number of amino acids which can be encoded by DNA, from the existing 20 amino acids to a theoretically possible 172, thereby expanding the potential for living organisms to produce novel proteins. The artificial strings of DNA do not encode for anything yet, but scientists speculate they could be designed to manufacture new proteins which could have industrial or pharmaceutical uses. Experts said the synthetic DNA incorporating the unnatural base pair raises the possibility of life forms based on a different DNA code.

Non-canonical base pairing

Main article: Non-canonical base pairing

 

Wobble base pairs

 

Comparison of Hoogsteen to Watson–Crick base pairs.

In addition to the canonical pairing, some conditions can also favour base-pairing with alternative base orientation, and number and geometry of hydrogen bonds. These pairings are accompanied by alterations to the local backbone shape.

The most common of these is the wobble base pairing that occurs between tRNAs and mRNAs at the third base position of many codons during transcription and during the charging of tRNAs by some tRNA synthetases. They have also been observed in the secondary structures of some RNA sequences.

Additionally, Hoogsteen base pairing (typically written as A•U/T and G•C) can exist in some DNA sequences (e.g. CA and TA dinucleotides) in dynamic equilibrium with standard Watson–Crick pairing. They have also been observed in some protein–DNA complexes.

In addition to these alternative base pairings, a wide range of base-base hydrogen bonding is observed in RNA secondary and tertiary structure. These bonds are often necessary for the precise, complex shape of an RNA, as well as its binding to interaction partners.

Synaptic pruning

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Synaptic_pruning 

A model view of the synapse

Synaptic pruning, a phase in the development of the nervous system, is the process of synapse elimination that occurs between early childhood and the onset of puberty in many mammals, including humans. Pruning starts near the time of birth and continues into the late-20s. During pruning, both the axon and dendrite decay and die off. It was traditionally considered to be complete by the time of sexual maturation, but this was discounted by MRI studies.

The infant brain will increase in size by a factor of up to 5 by adulthood, reaching a final size of approximately 86 (± 8) billion neurons. Two factors contribute to this growth: the growth of synaptic connections between neurons and the myelination of nerve fibers; the total number of neurons, however, remains the same. After adolescence, the volume of the synaptic connections decreases again due to synaptic pruning.

Pruning is influenced by environmental factors and is widely thought to represent learning.

Variations

Regulatory pruning

At birth, the neurons in the visual and motor cortices have connections to the superior colliculus, spinal cord, and pons. The neurons in each cortex are selectively pruned, leaving connections that are made with the functionally appropriate processing centers. Therefore, the neurons in the visual cortex prune the synapses with neurons in the spinal cord, and the motor cortex severs connections with the superior colliculus. This variation of pruning is known as large-scaled stereotyped axon pruning. Neurons send long axon branches to appropriate and inappropriate target areas, and the inappropriate connections are eventually pruned away.

Regressive events refine the abundance of connections, seen in neurogenesis, to create a specific and mature circuitry. Apoptosis and pruning are the two main methods of severing the undesired connections. In apoptosis, the neuron is killed and all connections associated with the neuron are also eliminated. In contrast, the neuron does not die in pruning, but requires the retraction of axons from synaptic connections that are not functionally appropriate.

It is believed that the purpose of synaptic pruning is to remove unnecessary neuronal structures from the brain; as the human brain develops, the need to understand more complex structures becomes much more pertinent, and simpler associations formed at childhood are thought to be replaced by complex structures.

Despite the fact it has several connotations with regulation of cognitive childhood development, pruning is thought to be a process of removing neurons which may have become damaged or degraded in order to further improve the "networking" capacity of a particular area of the brain. Furthermore, it has been stipulated that the mechanism not only works in regard to development and reparation, but also as a means of continually maintaining more efficient brain function by removing neurons by their synaptic efficiency.

Pruning in the maturing brain

The pruning that is associated with learning is known as small-scale axon terminal arbor pruning. Axons extend short axon terminal arbors toward neurons within a target area. Certain terminal arbors are pruned by competition. The selection of the pruned terminal arbors follow the "use it or lose it" principle seen in synaptic plasticity. This means synapses that are frequently used have strong connections while the rarely used synapses are eliminated. Examples seen in vertebrate include pruning of axon terminals in the neuromuscular junction in the peripheral nervous system and the pruning of climbing fiber inputs to the cerebellum in the central nervous system.

In terms of humans, synaptic pruning has been observed through the inference of differences in the estimated numbers of glial cells and neurons between children and adults, which differs greatly in the mediodorsal thalamic nucleus.

In a study conducted in 2007 by Oxford University, researchers compared 8 newborn human brains with those of 8 adults using estimates based upon size and evidence gathered from stereological fractionation. They showed that, on average, estimates of adult neuron populations were 41% lower than those of the newborns in the region they measured, the mediodorsal thalamic nucleus.

However, in terms of glial cells, adults had far larger estimates than those in newborns; 36.3 million on average in adult brains, compared to 10.6 million in the newborn samples. The structure of the brain is thought to change when degeneration and deafferentation occur in postnatal situations, although these phenomena have not been observed in some studies. In the case of development, neurons which are in the process of loss via programmed cell death are unlikely to be re-used, but rather replaced by new neuronal structures or synaptic structures, and have been found to occur alongside the structural change in the sub-cortical gray matter.

Synaptic pruning is classified separately from the regressive events seen during older ages. While developmental pruning is experience dependent, the deteriorating connections that are synonymous with old age are not. The stereotyped pruning can be compared to the process of chiseling and molding of stone into a statue. Once the statue is complete, the weather will begin to erode the statue and this represents the experience-independent deletion of connections.

Forgetting problems with learning through pruning

All attempts to construct artificial intelligence systems that learn by pruning connections that are disused have the problem that every time they learn something new, they forget everything they learned before. Since biological brains follow the same laws of physics as artificial intelligences, as all physical objects do, these researchers argue that if biological brains learned by pruning they would face the same catastrophic forgetting issues. This is pointed out as an especially severe problem if the learning is supposed to be part of a developmental process since retention of older knowledge is necessary for developmental types of learning, and as such it is argued that synaptic pruning cannot be a mechanism of mental development. It is argued that developmental types of learning must use other mechanisms that do not rely on synaptic pruning.

Energy saving for reproduction and discontinuous differences

One theory of why many brains are synaptically pruned when a human or other primate grows up is that maintenance of synapses consume nutrients which may be needed elsewhere in the body during growth and sexual maturation. This theory presupposes no mental function of synaptic pruning. The empirical observation that human brains fall into two distinct categories, one that reduces synaptic density by about 41% while growing up and another synaptically neotenic type in which there is very little to no reduction of synaptic density, but no continuum between them, is explainable by this theory as an adaptation to physiologies with different nutritional needs in which one type needs to free up nutrients to get through puberty while the other can mature sexually by other redirections of nutrients that do not involve reducing the brain's consumption of nutrients. Citing that most of the nutrient costs in the brain are in maintaining the brain cells and their synapses, rather than the firing itself, this theory explains the observation that some brains appear to continue pruning years after sexual maturation as a result of some brains having more robust synapses, allowing them to take years of neglect before the synaptic spines finally disintegrate. Another hypothesis that can explain the discontinuity is that of limited functional genetic space restricted by the fact that most of the human genome needs to lack sequence-specific functions to avoid too many deleterious mutations, predicting that evolution proceeds by a few of the mutations happening to have large effects while most mutations do not have any effects at all.

Mechanisms

The three models explaining synaptic pruning are axon degeneration, axon retraction, and axon shedding. In all cases, the synapses are formed by a transient axon terminal, and synapse elimination is caused by the axon pruning. Each model offers a different method in which the axon is removed to delete the synapse. In small-scale axon arbor pruning, neural activity is thought to be an important regulator, but the molecular mechanism remains unclear. Hormones and trophic factors are thought to be the main extrinsic factors regulating large-scale stereotyped axon pruning.

Axon degeneration

In Drosophila, there are extensive changes made to the nervous system during metamorphosis. Metamorphosis is triggered by ecdysone, and during this period, extensive pruning and reorganization of the neural network occurs. Therefore, it is theorized that pruning in Drosophila is triggered by the activation of ecdysone receptors. Denervation studies at the neuromuscular junction of vertebrates have shown that the axon removal mechanism closely resembles Wallerian degeneration. However, the global and simultaneous pruning seen in Drosophilia differs from the mammalian nervous system pruning, which occurs locally and over multiple stages of development.

Axon retraction

Axon branches retract in a distal to proximal manner. The axonal contents that are retracted are thought to be recycled to other parts of the axon. The biological mechanism with which axonal pruning occurs still remains unclear for the mammalian central nervous system. However, pruning has been associated with guidance molecules in mice. Guidance molecules serve to control axon pathfinding through repulsion, and also initiate pruning of exuberant synaptic connections. Semaphorin ligands and the receptors neuropilins and plexins are used to induce retraction of the axons to initiate hippocampo-septal and infrapyramidal bundle (IPB) pruning. Stereotyped pruning of the hippocampal projections have been found to be significantly impaired in mice that have a Plexin-A3 defect. Specifically, axons that are connected to a transient target will retract once the Plexin-A3 receptors are activated by class 3 semaphorin ligands. In IPB, the expression of mRNA for Sema3F is present in the hippocampus prenatally, lost postnatally and returns in the stratum oriens. Coincidentally, onset IPB pruning occurs around the same time. In the case of the hippocampal-septal projections, expression of mRNA for Sema3A was followed by the initiation of pruning after 3 days. This suggests that pruning is triggered once the ligand reaches threshold protein levels within a few days after detectable mRNA expression. Pruning of axons along the visual corticospinal tract (CST) is defective in neuropilin-2 mutants and plexin-A3 and plexin-A4 double mutant mice. Sema3F is also expressed in the dorsal spinal cord during the pruning process. There is no motor CST pruning defect observed in these mutants.

Stereotyped pruning has also been observed in the tailoring of overextended axon branches from the retinotopy formation. Ephrin and the ephrin receptors, Eph, have been found to regulate and direct retinal axon branches. Forward signaling between ephrin-A and EphA, along the anterior-posterior axis, has been found to inhibit retinal axon branch formation posterior to a terminal zone. The forward signaling also promotes pruning of the axons that have reached into the terminal zone. However, it remains unclear whether the retraction mechanism seen in IPB pruning is applied in retinal axons.

Reverse signaling between ephrin-B proteins and their Eph receptor tyrosine kinases have been found to initiate the retraction mechanism in the IPB. Ephrin-B3 is observed to transduce tyrosine phosphorylation-dependent reverse signals into hippocampal axons that trigger pruning of excessive IPB fibers. The proposed pathway involves EphB being expressed on the surface of target cells that results in tyrosine phosphorylation of ephrin-B3. Ensuing binding of ephrin-B3 to the cytoplasmic adaptor protein, Grb4, leads to the recruitment and binding of Dock180 and p21 activated kinases (PAK). The binding of Dock180 increases Rac-GTP levels, and PAK mediates the downstream signaling of active Rac that leads to the retraction of the axon and eventual pruning.

Axon shedding

Time-lapse imaging of retreating axons in neuromuscular junctions of mice have shown axonal shedding as a possible mechanism of pruning. The retreating axon moved in a distal to proximal order and resembled retraction. However, there were many cases in which remnants were shed as the axons were retracting. The remnants, named axosomes, contained the same organelles seen in the bulbs attached to the end of axons and were commonly found around the proximity of the bulbs. This indicates that axosomes are derived from the bulbs. Furthermore, axosomes did not have electron-dense cytoplasms or disrupted mitochondria indicating that they were not formed through Wallerian degeneration.

Potential role in schizophrenia

Synaptic pruning has been suggested to have a role in the pathology of neurodevelopmental disorders such as schizophrenia, as well as in autism spectrum disorder. 

Microglia have been implicated in synaptic pruning, as they have roles in both the immune response as macrophages as well as in neuronal upkeep and synaptic plasticity in the CNS during fetal development, early postnatal development, and adolescence, in which they engulf unneeded or redundant synapses via phagocytosis.  Microglial synapse engulfment and uptake has been specifically observed to be upregulated in the isolated synaptosomes of male patients with schizophrenia compared to healthy controls, suggesting upregulated microglia-induced synaptic pruning in these individuals. Microglia-mediated synaptic pruning has also been observed to be upregulated during late adolescence and early adulthood, which could also account for the age of onset for schizophrenia often being reported around this time in development (late teens to early 20s for men, and mid-to-late 20s for women)  The drug minocycline, a semisynthetic brain-penetrant tetracycline antibiotic, has been found to somewhat reverse these changes made to patient synaptosomes by downregulating synaptic pruning.

Genes in the Complement Component 4 (C4) locus of the major histocompatibility complex (MHC), which encode for complement factors, have also been tied to schizophrenia risk through gene linkage studies. The fact that some of these complement factors are involved in signaling during synaptic pruning also seems to suggest that schizophrenia risk may be linked to synaptic pruning. Specifically, complement factors C1q and C3 have been found to have a role in microglia-mediated synaptic pruning.  Carriers of C4 risk variants have also been found to be tied to this kind of synapse overpruning in microglia. The proposed mechanism for this interaction is increased complement factor C3 deposition onto synaptosomes as a consequence of increased C4A expression in these risk variant carriers.

Romanticism in philosophy

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Romanticism_in_philosophy 

The philosophical ideas and thoughts of Edmund Burke, Thomas Carlyle, Johann Gottlieb Fichte, Friedrich Wilhelm Joseph Schelling, Søren Kierkegaard, Arthur Schopenhauer and Richard Wagner have been frequently described as Romantic.

German idealism

Immanuel Kant's criticism of rationalism is thought to be a source of influence for early Romantic thought. The third volume of the History of Philosophy edited by G. F. Aleksandrov, B. E. Bykhovsky, M. B. Mitin and P. F. Yudin (1943) assesses that "From Kant originates that metaphysical isolation and opposition of the genius of everyday life, on which later the Romantics asserted their aesthetic individualism."

Hamann's and Herder's philosophical thoughts were influential on both the proto-Romantic Sturm und Drang movement and on Romanticism itself. The History of Philosophy stresses: "As a writer, Hamann stood close to the Sturm und Drang literary movement with his cult of genius personality and played a role in the preparation of German Romanticism."

The philosophy of Fichte was of pivotal importance for the Romantics. The founder of German Romanticism, Friedrich Schlegel, identified the "three sources of Romanticism": the French Revolution, Fichte's philosophy and Goethe's novel Wilhelm Meister.

In the words of A. Lavretsky:

In the person of Fichte, German idealism put forward its most militant figure, and German Romanticism found the philosophy of its revolutionary period. Fichte’s system in the sphere of German thought is a bright lightning of a revolutionary storm in the West. His entire frame of mind is full of the stormy energy of revolutionary epochs, his entire spiritual appearance amazes with his conscious class purposefulness. Never before or after have sounded such harsh notes of the class struggle in German idealist philosophy. This creator of the most abstract system knew how to put problems on a practical basis. When he speaks about morality, he does not convince us, like Kant, that human nature is fundamentally corrupted, but notes: “people are the worse, the higher their class.” When he talks about the state, he knows how not to ask, but to demand as a true plebeian their rights to equality in this state.

Schelling, who was associated with the Schlegel brothers in Jena, took many of his philosophical and aesthetical ideas from the Romantics, and also influenced them on their own views. According to the History of Philosophy, "In his philosophy of art, Schelling emerged from the subjective boundaries in which Kant concluded aesthetics, referring it only to features of judgment. Schelling's aesthetics, understanding the world as an artistic creation, has adopted a universal character and served as the basis for the teachings of the Romantic school." It is argued that Friedrich Schlegel's subjectivism and his glorification of the superior intellect as property of a select elite influenced Schelling's doctrine of intellectual intuition, which György Lukács called "the first manifestation of irrationalism". As much as Early Romanticism influenced the young Schelling's Naturphilosophie (his interpretation of nature as an expression of spiritual powers), so did Late Romanticism influence the older Schelling's mythological and mysticist worldview (Mysterienlehre).

Kierkegaard

Also according to Lukács, Kierkegaard's views on philosophy and aesthetics were an offshoot of Romanticism:

We can see, despite all Kierkegaard's polemical digressions, an enduring and living legacy of Romanticism. With regard to this, the basic problem in his philosophy, he came very close in methodology to the moral philosopher of early Romanticism, the Schleiermacher of the Talks on Religion and Intimate Letters on Friedrich Schlegel's Lucinde. Certainly the resemblance of the propositions is limited to the fact that, as a result of the passing of Romantic aesthetics into an aesthetically determined 'art of living' on the one hand, and of a religion founded purely on subjective experience on the other, the two areas were bound to mesh all the time. But just that was the young Schleiermacher's intention: it was just by that route that he sought to lead his Romantic-aesthetically oriented generation back to religion and to encourage the Romantic aesthetic and art of living to sprout into religiosity. If, then, the resemblance and the structural closeness of the two spheres were of advantage to Schleiermacher's arguments, the self-same factors gave rise to the greatest intellectual difficulties for Kierkegaard.

Schopenhauer

Schopenhauer also owed certain features of his philosophy to Romantic pessimism: "Since salvation from suffering associated with the will is available through art only to a select few, Schopenhauer proposed another, more accessible way of overcoming the "I" - Buddhist Nirvana. In essence, Schopenhauer, although he was confident in the innovation of his revelations, did not give anything original here in comparison with the idealization of the Eastern world outlook by reactionary Romantics - it was indeed Friedrich Schlegel who introduced this idealization in Germany with his Über die Sprache und Weisheit der Indier (About the language and wisdom of the Indians)."

Nietzsche

In the opinion of György Lukács, Friedrich Nietzsche's importance as an irrationalist philosopher lay in that, while his early influences are to be found in Romanticism, he founded a modern irrationalism antithetical to that of the Romantics:

Nietzsche was frequently associated with the Romantic movement. The assumption is correct inasmuch as many motives of Romantic anti-capitalism — e.g., the struggle against the capitalist division of labour and its consequences for bourgeois culture and morals — played a considerable part in his thinking. The setting up of a past age as an ideal for the present age to realize also belonged to the intellectual armoury of Romantic anti-capitalism. Nietzsche’s activity, however, fell within the period after the proletariat’s first seizure of power, after the Paris Commune. Crisis and dissolution, Romantic anti-capitalism’s development into capitalist apologetics, the fate of Carlyle during and after the 1848 revolution — these already lay far behind Nietzsche in the dusty past. Thus the young Carlyle had contrasted capitalism’s cruelty and inhumanity with the Middle Ages as an epoch of popular prosperity, a happy age for those who laboured; whereas Nietzsche began, as we have noted, by extolling as a model the ancient slave economy. And so the reactionary utopia which Carlyle envisioned after 1848 he also found naive and long outdated. Admittedly the aristocratic bias of both had similar social foundations: in the attempt to ensure the leading social position of the bourgeoisie and to account for that position philosophically. But the different conditions surrounding Nietzsche’s work lent to his aristocratic leanings a fundamentally different content and totally different colouring from that of Romantic anti-capitalism. True, remnants of Romanticism (from Schopenhauer, Richard Wagner) are still palpable in the young Nietzsche. But these he proceeded to overcome as he developed, even if — with regard to the crucially important method of indirect apologetics — he still remained a pupil of Schopenhauer and preserved as his basic concept the irrational one of the Dionysian principle (against reason, for instinct); but not without significant modifications, as we shall see. Hence an increasingly energetic dissociation from Romanticism is perceptible in the course of Nietzsche’s development. While the Romantic he identified more and more passionately with decadence (of the bad kind), the Dionysian became a concept increasingly antithetical to Romanticism, a parallel for the surmounting of decadence and a symbol of the ‘good’ kind of decadence, the kind he approved.

Even in his post-Schopenhauerian period, however, Nietzsche paid some tributes to Romanticism, for example borrowing the title of his book The Gay Science (Die fröhliche Wissenschaft, 1882–87) from Friedrich Schlegel's 1799 novel Lucinde.

Pyotr Semyonovich Kogan traced most of the contents of Nietzschean philosophy to Romanticism:

The main sentiments of which [Nietzsche's] philosophy consisted, are already present in the work of many gifted figures anticipating the author of Zarathustra. The rebellious geniuses of the Sturm und Drang era overturned authority and tradition with chaotic energy, longed for boundless space for the development of the human person, despised and hated social bonds. In the German Romantics you can find the will to transvaluation of morals, which found so brilliant substantiation in Nietzsche's paradoxical book. Certainly the author of the book Beyond Good and Evil would have agreed to the words of Friedrich Schlegel: "The first rule of morality is rebellion against positive laws, against the conditions of decency. There is nothing more foolish as moralists when they accuse you of selfishness. They are certainly wrong: what god can a person worship, besides being his own god?" The dream of the Superman already appears in another phrase of the same author: "A real person will become more and more a god. Be man and become a god - two identical manifestations." The same as in Nietzsche, contempt for the fleeting interests of the moment, the same impulse for the eternal and for beauty: "Do not give your love and faith to world politicians," said Schlegel in the 1800s. For the same Schlegel, it was worth "for the divine world of knowledge and art, to sacrifice the deepest feelings of your soul in the sacred, the fiery current of eternal perfection."

Organicism

Lukács also emphasized that the emergence of organicism in philosophy received its impetus from Romanticism:

This view, that only 'organic growth', that is to say change through small and gradual reforms with the consent of the ruling class, was regarded as 'a natural principle', whereas every revolutionary upheaval received the dismissive tag of 'contrary to nature' gained a particularly extensive form in the course of the development of reactionary German romanticism (Savigny, the historical law school, etc.). The antithesis of 'organic growth' and 'mechanical fabrication' was now elaborated: it constituted a defence of 'naturally grown' feudal privileges against the praxis of the French Revolution and the bourgeois ideologies underlying it, which were repudiated as mechanical, highbrow and abstract.

Dilthey

Wilhelm Dilthey, founder (along with Nietzsche, Simmel and Klages) of the intuitionist and irrationalist school of Lebensphilosophie in Germany, is credited with leading the Romantic revival in hermeneutics of the early 20th century. With his Schleiermacher biography and works on Novalis, Hölderlin, etc., he was one of the initiators of the Romantic renaissance in the imperial period. His discovery and annotation of the young Hegel's manuscripts became crucial to the vitalistic interpretation of Hegelian philosophy in the post-war period; his Goethe study likewise ushered in the vitalistic interpretation of Goethe subsequently leading from Simmel and Gundolf to Klages.

Philosophical views of the German Romantics

Passivity was a key element of the Romantic mood in Germany, and it was brought by the Romantics into their own religious and philosophical views. The theologian Schleiermacher argued that the true essence of religion lies not in the active love of one's neighbor, but in the passive contemplation of the infinite; In Schelling’s philosophical system, the creative absolute (God) is immersed in the same passive, motionless state.

The only activity that the Romantics allowed is that in which there is almost no volitional element, that is, artistic creativity. They considered the representatives of art to be the happiest people, and in their works, along with knights chained in armor, poets, painters and musicians usually appear. Schelling considered an artist to be incomparably higher than a philosopher, because the secret of the world can be guessed from his minutia not by systematic logical thinking, but only by direct artistic intuition ("intellectual intuition"). Romantics loved to dream of such legendary countries, where all life with its everyday cares gave way to the eternal holiday of poetry.

The quietist and aestheticist mood of Romanticism, the reflection and idealization of the mood of the aristocracy, again emerges in Schopenhauer’s philosophical system "The World as Will and Representation," ending with a pessimistic chord. Schopenhauer argued that at the heart of the world and man lies the "will to life," which leads them to suffering and boredom, and happiness can be experienced only by those who free themselves from its oppressive domination. Schopenhauer’s ideal human being is, first of all, an artist who, at the moment of aesthetic perception and reproducing the world and life, is in a state, which Kant has already called "weak-willed contemplation," – forgetting in this moment about his personal interests, worries and aspirations. But the artist is freed from the power of the will only temporarily. As soon as he turns into an ordinary mortal, his greedy will again raises its voice and throws him into the embrace of disappointment and boredom. Above the artist stands, therefore, the Hindu sage or the holy ascetic.

In the words of V. M. Fritsche, "just like the views of the Romantics, the philosophy of Schopenhauer, with its purist and aestheticist attitudes, was a product of aristocratic culture, having grown up in the middle of old pompous estates and noble living rooms, and it is not surprising that in Germany, a country so immersed in such an ideology, the bourgeois democratic years began only in the 1840s. The only one of the Romantics who lived to this era, Eichendorff, turned vehemently against democracy, and the revolution of 1848 was met by him and Schopenhauer with the same primal enmity with which the German nobility met it."