Nematoplexus aspects
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The nematophyte Nematoplexus, discovered by
A.G. Lyon [1] in one piece of Rhynie chert and since then found in poorer quality only a very few times more, seemed to be characterized by rather well defined structure parameters, as pointed out in Rhynie Chert News 29:
(1) The tubes are wound into a rather regular
screw-like thread ...
(2)   ... which is always right-handed ...
(3)   ... with diameters of 0.08 - 0.12 mm.
(4)   ... whose pitch seems to roughly equal its diameter.

A sample found in 2003 confirmed this, except for the diameters of tubes and threads:
(3)   ... with thread diameters of 0.14 - 0.20 mm.
Closer inspection of the raw surface of this sample has revealed another patch of 3mm width with the usual curled tubes and, surprisingly, a few tube sections curved and wound so slightly that it is uncertain whether they are parts of bigger threads, wound otherwise, or flat (Fig.1, left).

Nematoplexus uncurledFig.1: Nematoplexus, thread-like tubes and weakly curved ones. Width 2.6mm.
Fig.2: Detail of Fig.1. Width 0.62mm.

Apparently they are rather evenly curved but their radius of curvature is difficult to estimate owing to the uneven surface of the raw sample and limited visual depth. Some of the slightly curved tubes are near an edge of the sample so that by visual inspection from various sides an osculating plane to the tube fragment can be defined. By turning the sample such that the osculating plane is made the picture plane of the photograph, the radius of curvature
is easily found as 0.75mm for one of the tube fragments. It would not much differ from the half diameter of the thread (if this tube were wound, which cannot be ascertained with the available fragment). 
So it appears that Nematoplexus offers more enigmas: In addition to the small regular threads, it brings forth evenly curved objects with
diameters nearly ten times larger but made of tubes of about the same thickness of 10...15Ám, also slighty curved thinner tubes of 7-8Ám (Fig.2, two thin tubes running parallel with only a small gap in between).

This contribution has shown structures which distinguish Nematoplexus from other nematophytes. The following is about one feature which Nematoplexus has in common with other nematophytes: the so-called branch knots (Fig.3). Since nobody seems to know what nematophytes are, one need not wonder why nobody knows what the branch knots are for. They look as if they produce the tubes. Other silicified nematophyte samples seem to indicate that the branch knots also contain a tangle of tubes which are much thinner than the conspicuous larger ones seen here.

Nematoplexus branch knot
Fig.3: Nematoplexus branch knot amidst spiralling tubes. Nematoplexus branch knot

Width of the picture 1.6mm.

Fig.4 (right): Solitary branch knot of Nematoplexus with short tubes attached but no spirals nearby. Same chert sample, width of the picture 0.25mm.

The solitary knot of about 0.12mm in Fig.4 resembles the one pictured in [2] under "another branch knot" (as the images are not numbered there), with the difference that the diameter of the tubes is less than half that in [2]. The similarity of the pictures (except sizes) of solitary knots here and in [2] suggests that they are no incidental formations but represent another type of knot or another stage of development without the spiralling tubes as in Fig.3.

It appears that Nematoplexus is a subject more difficult to handle than originally thought, for quite different reasons:
 - The sample containing the type specimen first described in [1] had been shattered by A.G. Lyon unawares of the unique content of the sample, with a hammer, and only some fragments had been recovered. (Fossiliferous chert should never be hit.)
 - Tube sizes differ distinctly between specimens: [1,2] and Rhynie Chert News 29.
 - The smooth tubes of one specimen may differ in their radius of curvature by a factor of about ten: Fig.1.
 - The available information is scarce, published size data are contradictory or questionable: [3] differs from [1,2].

In particular, the scale bar of Fig. 6.9 in [3] should be 18Ám instead of 100Ám, which follows from comparison with [2]. What is offered as a branch knot in [3], Fig. 6.10, differs much from any Nematoplexus branch knot pictured here and in [1,2], which raises the suspicion that a wrong picture has been placed in [3] by mistake. The suspicion is confirmed by the presence of several more mistakes and errors concerning Rhynie Chert fossils in [3], Chapter 8.
Considering that the rugged outline of the branch knots is poorly defined, it is quite unreasonable to quantify a lower size boundary as 99Ám, as done in [2].

The characteristic feature of Nematoplexus, the spirally wound tubes, is ascribed in [2] to all nematophytes: "Nematophytes appear to generally comprise networks of intertwined spirally coiled tubular cells."  This is utterly wrong: No other nematophyte has got spirally wound tubes.

According to present knowledge, Nematoplexus is very rare but less rare in mm-size patches than in larger aggregates. Hence there is reason for hope that more specimens will be discovered by carefully inspecting the Rhynie chert samples stored in collections.
The chert sample pictured here was found by Sieglinde Weiss in 2003.
Addendum 2015: Another chert sample with similar fossil content is described in Rhynie Chert News 71.  

H.-J. Weiss  
    emended 2014, 2015

[1]  A.G. Lyon: On the fragmentary remains of an organism referable to the nematophytales, from the Rhynie chert, Nematoplexus rhyniensis
      Trans. Roy. Soc. Edinburgh 65(1961-62), 79-87, 2 plates.   
(Scale error on Plate I Fig.1: not x19 but x1.5)
[3] T.N. Taylor, E.L. Taylor, M. Krings: Paleobotany, Elsevier 2009.
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