Patterning of the neural tube
The anterior / posterior pattern
Initially, in Xenopus, after the anterior endoderm and prechordal plate have migrated beneath the prospective neural tissue the neural plate cells induced are of completely anterior fate. Other signals are required to transform the posterior part of the neural tube so that it differs from the anterior cells. This is known as the active transformation model of neural induction and is vital in the anterior / posterior patterning of neural cell fates. The inducing properties of the organiser change over time, transplanting an early Xenopus organiser onto a second embryo leads to the induction of a complete secondary nervous system however transplanting an older organiser will only induce more posterior neural structures. It is therefore likely that the chordamesoderm produces factors that induce posterior neural tube fate.
Wnt signals have been implicated in this process as well as fibroblast growth factors (FGFs) that can induce posterior gene expression in ectoderm that has undergone neural induction. However the most prominent posteriorising factor appears to be retinoic acid (RA). RA is a small, non-polar molecule that can diffuse across cell membranes and bind to cytoplasmic receptors exerting an affect on gene expression. It can specifically induce a class of homeobox genes known as the Hox genes which confer segmental identity on the neural tube hindbrain and spinal cord. After neural tube closure as the A/P pattern develops a rostral / caudal (R/C) axis develops initially with the prospective forebrain most rostral and the spinal cord most caudal with the prospective hindbrain in between. A gradient of RA with its source in the posterior neural tube acts to induce different Hox genes along the A/P axis which pattern the future spinal cord and hindbrain. This segmental identity can clearly be seen in the hindbrain which becomes divided into eight rhombomeres based on a specific pattern of paralogous groups of Hox genes. As the Hox gene expression is continuous, the loss of a specific Hox gene therefore leads to a homeotic transfer by which loss of one Hox gene is masked by the expression of a more anterior hox gene. For example loss of Hoxa 1 leads to the partial transformation of rhombomere 4/5 identity to that of 2/3. 
The prospective forebrain region of the neural tube is patterned by many transcription factors which subdivide the future forebrain into distinct prosomeres. The Pax genes are vital in the patterning of the future forebrain. Cross repression between Otx 2 (a transcription factor from the forebrain region) and Gbx 2 (a transcription factor from the hindbrain region) establishes a secondary organiser centre between the two, the isthmus. Wnt, engrailed (En) and (FGF) signals from this organiser establish the future midbrain and produce the cerebellum and the pons to complete the hindbrain and establish a midbrain / hindbrain barrier.
The dorsal / ventral pattern
Sonic Hedgehog (SHh), bone morphogenetic protein (BMP) and RA are all vital in dorsal / ventral (D/V) patterning. After neural induction production of RA by the paraxial mesoderm (lies either side of the notochord (nc)) leads to the down regulation of FGF signals in the neural tube which initially helped specify the neuroepithelium and maintains dividing caudal progenitors. This is vital to allow differentiation to occur as FGFs represses ventral neural genes e.g. Pax 6. However the ventral inducing properties of RA only applies to a subset of ventral genes, the others are induced by SHh. As soon as the nc is established it begins to express SHh which in turn diffuses away from the nc and acts on the ventral most region of the neural tube in which it induces specialised floor plate cells.
SHh is a morphogen as it acts directly on cells of the neural tube at distance in a concentration dependant manner to induce specific ventral cell fates. Once induced the floor plate also expresses SHh which establishes a concentration gradient in the ventral half of the neural tube patterning this area. There are two main classes of ventral neural genes, class 1 genes are induced by RA but repressed by high levels of SHh and these are therefore expressed in the dorsal part of the ventral neural tube. Class 2 genes, e.g. Nkx 2.2, are expressed at high levels of SHh and are found in the ventral areas of the ventral neural tube near to the source of SHh signalling, the floor plate. Class 1 and 2 transcription factors cross repress each other to establish sharp domains of gene expression producing a characteristic pattern in the vertebrate neural tube. Dorsally BMP signalling molecules from the non-neuronal ectoderm induce the roof plate in the most dorsal neural tube cells ( an equivalent structure to the floor plate). BMPs act in a concentration dependant manner to induce dorsal cell markers e.g. Pax 7.
SHh and BMPs establish D/V patterning
Both SHh and BMPs induce homeotic genes which provide neural tube cells with positional identity depending on the position they occupy in the D/V axis. Over expression of SHh leads to the ectopic expansion of ventral neural tube domains at the expense of dorsal domains and increasing BMP signalling has the opposite affects. SHh and BMP relfect a common theme throughout all neural tube development in that the actions of external signals, in a concentration dependant manner establishs specific regions of gene expression that both specify the neural tube to begin with and dictate its regional identity. The development of the neural tube, like other developmental processes is dependant on signalling molecules altering specific cell gene expression patterns to dictate cell fate. The sequential action of these signalling molecules in the correct temporal and spatial regions is vital in order to develop a functional adult nervous system.