FUNNELLING

For these sequences the value of Gj, is less than a certain small value g. For such sequences the folding occurs directly from the ensemble of unfolded states to the NBA. The free energy surface is dominated by the NBA (or a funnel) and the volume associated with NBA is very large. The partition factor <6 is near unify so that these sequences reach the native state by two-state kinetics. The amplitudes in (C2.5.7) are nearly zero. There are no intennediates in the pathways from the denatured state to the native state. Fast folders reach the native state by a nucleation-collapse mechanism which means that once a certain number of contacts (folding nuclei) are fonned then the native state is reached very rapidly [25, 26]. The time scale for reaching the native state for fast folders (which are nonnally associated with those sequences for which topological fmstration is minimal) is found to be... 

Dill K A and Chan H S 1997 From Levinthal to pathways to funnels Natur. Struct. Biot. 4 10-19... 

Bryngelson J D, Onuchic J N, Socci N D and Wolynes P G 1995 Funnels, pathways, and the energy landscape of protein folding a synthesis Profe/ns 21 167-95... 

Conical intersections, introduced over 60 years ago as possible efficient funnels connecting different elecbonically excited states [1], are now generally believed to be involved in many photochemical reactions. Direct laboratory observation of these subsurfaces on the potential surfaces of polyatomic molecules is difficult, since they are not stationary points . The system is expected to pass through them veiy rapidly, as the transition from one electronic state to another at the conical intersection is very rapid. Their presence is sunnised from the following data [2-5] ... 

Arsenic present only in traces (in any form) can be detected by reducing it to arsine and then applying tests for the latter. In Marsh s test, dilute sulphuric acid is added dropwise through a thistle funnel to some arsenic-free zinc in a flask hydrogen is evolved and led out of the flask by a horizontal delivery tube. The arsenic-containing compound is then added to the zinc-acid solution, and the delivery tube heated in the middle. If arsenic is present, it is reduced to arsine by the zinc-acid reaction, for example ... 

In a way, the limit set is thus the entire funnel between the two extreme cases qlc, and g o, Fig. 5. This effect is called Takens-chaos, [21, 5, 7]. As a consequence of this theorem each momentum uncertainty effects a kind of disintegration" process at the crossing. Thus, one can reasonably expect to reproduce the true excitation process by using QCMD trajectory bundles for sampling the funnel. To realize this idea, we have to study the full quantum solution and compare it to suitable QCMD trajectory bundles. 

Pig. 5. Comparison of the qi expectation value of the uncoupled QCMD bundle ([g]e o) and full QD ( q)qd) for the test system for e = 1/100 (pictures on top) and e = 1/500 (below). Initial data as in Fig. 3. The shaded domain indicates the funnel between the two curves Qbo and geo (cf. Thm. 5). The light dashed line shows Hagedorn s limit solution qna and the dense lines (q )Qo (left hand pictures) and [ ]e s (right hand pictures). 

Bryngelson J D, J N Onuchic, N D Socci and P G Wolynes 1995. Funnels, Pathways, and the Energy Landscape of Protein Folding A Synthesis. Proteins Structure, Function and Genetics 21 167-195. 

This type of filtration is almost invariably performed with the aid of a Buchner flask and funnel, by means of which a rapid and almost complete separation can be obtained. The Buchner flask A (Fig. 4) consists of a simple thick-walled conical flask with a short side-arm for connection to a water-pump. Into the neck of the flask is fitted the Buchner funnel B which consists usually of a cylindrical porcelain funnel, the bed of which is pierced by a... 

When only a small quantity of solid material has to be filtered from a liquid, the small conical funnel C, usually known as a Hirsch funnel, is used in order to collect and drain the material on a very small filter-paper (see p. 68). 

A hot-water funnel is a slower and less efficient apparatus for filtering hot solutions. A satisfactory form of the apparatus is shown in Fig. 6, in which the double-walled funnel is heated... 

For the filtration of small quantities of dilute solution, it is often possible to dispense with the outer heater, and use the ordinary glass funnel which has been heated above a flame immediately before use. 

The filtration of any solution through the ordinary conical funnel may be hastened considerably by the use of a fluted filter-paper, instead of one folded into quarters in the usual way. The folding of a fluted paper may be learnt far more readily by a demonstration in the laboratory than by any written description. 

Sometimes the crude substance may contain an insoluble impurity, and on cooling the solution it may be difficult to judge how much of the solid matter is merely undissolved impurity and how much is solute which has subsequently crystallised from solution. To avoid this difficulty, the hot solution should be filtered, and should thus always be absolutely clear before cooling is attempted. Therefore filter the hot solution into a clean tube through a very small fluted filter-paper contained in a correspondingly small glass funnel, which should have had its stem cut off as that shown in Fig. 6, p. 12 (and for the same reason). Unless the upper part of the filter is cut awav to reduce its size to a minimum, a large proportion of the solution will remain held mechanically in the pores of the paper itself and only a few drops of clear filtrate will be obtained. 

When crystallisation is complete, the mixture of crystals and crude mother-liquor is filtered at the pump, again using a Buchner funnel and flask as described on p. 10, and the crystals remaining in the funnel are then pressed well down with a spatula whilst continual suction of the pump is applied, in order to drain the mother-liquor from the crystals as effectively as possible. If it has been found in the preliminary tests that the crystalline material is almost insoluble in the cold solvent, the crystals in the... 

The basin A is then gently heated by a small Bunsen flame, which should be carefully protected from side draughts by screens, so that the material in A receives a steady uniform supply of heat. The material vaporises, and the vapour passes up through the holes into the cold funnel C. Here it cools and condenses as fine crystals on the upper surface of the paper B and on the walls of C. When almost the whole of the material in A has vaporised, the heating is stopped and the pure sublimed material collected. In using such an apparatus, it is clearly necessary to adjust the supply of heat so that the crude material in A is being steadily vaporised, while the funnel C does not become more than luke warm. 

To extract the substance, the aqueous solution or suspension is placed in a separating-funnel, which may be either cylindrical. Fig. i6(a), or (better) pear-shaped, Fig. i6(b). Ether is then... 

Fig. 23(B) shows a modification of the reflux assembly to allow a gas to be passed through the boiling liquid cf. Fischer-Speier esterification, p. 104). The inlet-tube A fits into a three-necked adaptor shown in Fig. 22(J). The stopper B can be replaced by a dropping-funnel, etc.

Fig. 23(E) shows a distillation assembly particularly useful for distilling ether from an ethereal extract. When all the ether has distilled over, the drop-ping-funnel may be replaced by a thermometer for distillation of the residual liquid the adaptor A and the receiver B can then be replaced by the simple adaptor shown in Fig. 23(D) and a flask or bottle of suitable size.

Mix 100 g. of active alumina with dry benzene until a suspension or slurry of suitable consistency is obtained, and pour this carefully into the tube. Clamp a dropping-funnel just above the top of the tube and Fig 2 benzene to run slowly down as the alumina... 

For the separation of immiscible liquids a small separating funnel of the conventional type should be used whenever practicable, a pear-shaped funnel (Fig. 16, p. 35) of 5-10 ml. capacity being particularly... 

The filtration of crystals is carried outusing a small conical Buchner funnel (C, Fig. 4, p. 10) or a funnel of similar design but having a sintered filtration plate. Alternatively an ordinary conical funnel in which is placed a circular perforated plate can be used. 

The complete filtration apparatus is shown in Fig. 5, p. 11. A simpler and cheaper apparatus is shown in Fig. 45. This consists of a boiling-tube A having a side-arm for connection to the pump the tube A is conveniently held in a wooden or cork block B or in a clamp. The funnel F may be fitted into A through a pliable rubber disc D the latter is more useful than a cork since it covers tubes of various diameters. The filtrate is collected in the centrifuge-tube T. 

For the filtration of very small quantities of crystals, the simple apparatus shown in Fig. 46 is often used. It consists of a fine glass rod (sometimes termed a filtration nail ) which is flattened at one end, the flattened surface being preferably roughened. It fits as shown into a small funnel which replaces F (Fig. 45). A circular piece of filter-paper is cut e-g.y with a clean sharp cork-borer) so as to fit completely and snugly over the flat end. After draining, the nail is raised and the filter-paper and crystals are removed with forceps and dried. 

Fit a 500 ml. bolt-head flask F with a well-fitting cork which is free from flaws, and which carries a dropping-funnel D and a delivery tube (or knee-tube ) T, the latter being connected to a water-condenser C (Fig. 52). Attach an adaptor A to the lower end of the condenser. (Alternatively, use a ground-glass flask (Fig. 22(a), p. 43) with a distillation-head (Fig. 22(F)) the dropping-funnel can be fitted into the distillation-head, the side-arm of which is connected to a condenser as in Fig. 23(0), p. 45.)... 

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