To introduce the vector pAKE 604 from a donor(S17) to recipient (Rhodococcus) in order to insert a gene (with mutation) by homologous recombination in the genome of recipient.
Conjugation realization is fondamentally different in gram + and gram - bacteria. One is based on chimiotactism and physical contact between cells (gram +), the other one is based on physical connection through the production of pili (gram -).
You should probably try to extract your plasmid from E. coli with a plasmid preparation method :
We have used S17-1 for transfer to different Bacilli (not Rhodococcus) species frequently. May also work for your strain:
http://dx.doi.org/10.1007/s00253-010-2503-9
It is based on the paper from deMuro and Priest:
http://dx.doi.org/10.1016/S0923-2508(00)00224-2
The techniques described are difficult to establish. And dirty.
here a simplyfied Protocol:
1. Be prepared for FRESH selection plates (Polymixin as counterselect for E. coli works well) and place a 2,3 (or bigger) cm filter-paper on it, 450 nm Nirtocellulose is our Standard.
2. Grow S17-1 and your strain simultanious (may by difficult) near to the stationary phase. Watch the cell numbers.
3. Wash Media away and resuspend in the same Buffer (be quick).
4. Mix Cells by number (not OD) , 1:1 gave best results in our test.
5. CO-Centrifuge both strains in the same tube at max speed. Remove supernatant and try to spread the pellet on the filter with a minimum of buffer and pipette strokes.
6. Play a CD, Barry White is recommended.
7. Go to Bed.
8. If your strain in growing in strains or clusters, a short bath in Lysosyme-Puffer is recommended after washing the filter.
9. Plate as usual.
0. At all Steps: Have a Microscope at your hands to see what happens and which steps went right or not.
E. coli strain S17-1 is probably identical to the E. coli strain SM10, both of which are obtainable from Ecoli Genetic Stock Center at Yale: https://cgsc.biology.yale.edu/StrainQuery.php
I don't know anything about your vector or why you wish to use conjugation to transfer DNA to your grave +ve bacterial host, but I presume you wish to do this because your DNA when cloned into your vector is very large (so might be too fragile for transformation).
You might be able to do an interspecies conjugative transfer from S17-1 only if you first introduce a conjugative plasmid into this strain (E. coli S17-1 is F–) or make it a Hfr. Note that rate of transfer from E. coli to a gram-positive bacteria will be very low, as has been pointed out above by a commentator that the two kinds of bacteria use very different processes for conjugation, but it might be possible, given that E. coli can transfer plasmid DNA even into a eukaryote like yeast (doi: 10.3390/ijms20205212, Nature. 1989 Jul 20;340(6230):205-9.)
**I wrote the above in a haste...I now realize that E. coli S17-1 listed in the stock center has a broad host range conjugative plasmid RK4 in it, so it should be possible for you to directly transfer from this strain into your bacterial species through inter-species transfer (without having to introduce another conjugative plasmid into it). See here: Article RP4-based plasmids for conjugation between Escherichia coli ...