## mFold Documentation

Structure Drawing Mode | Structure annotation | Energy dot plot | Exterior Loop

Image width - png & jpg files | Ionic Conditions | Structure numbering frequency

Max asymmetry of a bulge/interior loop | Max distance between paired bases

Max number of foldings | Max size of a bulge/interior loop | Structure format

Sequence numbering offset | Percent suboptimality | Regularization angle (in degrees)

Structure rotation | ss-count | Window

*Structure Drawing Mode*- In natural mode, bases in a loop are placed on a circle, with a uniform distance between them. (Exceptions are small bulge and interior loops. In these cases, the two stems are coaxial.) Stems that branch from the loop are orthogonal to the tangent of the circle at the closing base pair on the circle. This determines all of the relative angles of helices. The structure plot may intersect itself. The untangle modes determine relative angles to ensure non-ovelap. In addition, the loop fix extension enlarges and/or modifies the shape of multi-branch loops to avoid drawing bases on top of one another and to separate stems.

When "default" is chosen, structures with lengths up to 120 are drawn with natural angles and otherwise with the loop fix untangle option. Structures may be recomputed using different parameters after they have been computed.

*Structure annotation*- Individual structures may be annotated using colored base characters, colored dots, or both. Usually, the annotation is based on either p-num or ss-count information. The color scheme is given here. ss-count coloring follows the reverse scheme as p-num coloring. (red: most likely to be single stranded; high value of ss-count) See article by Zuker and Jacobson. The "high-light" feature allows the user to specify multiple ranges of bases, separated by commas (as in 3-9, 13-20,
*etc.*). The high-lighted regions will be in green, while the other regions will be drawn in black.

*Energy dot plot*- In the upper triangular region, a dot in row
*i*and column*j*represents a base pair between the*i*and^{th}*j*bases. The dots represent the superposition of all possible foldings within^{th}*p%*of ΔG_{mfe}, the minimum free energy, where*p*is the maximium percent deviation from ΔG_{mfe}. Different colors are used to indicate varying levels of suboptimality. The number of colors ranges from two to eight (the default). If n colors are used, the first color indicates base pairs in optimal foldings. These base pairs are also plotted in the lower left triangle (reversing row and column) for emphasis. The remaining n-1 colors are used for base pairs in suboptimal foldings. If ΔG_{i.j}is the minimum of the free energies of all possible structures containing base pair*i.j*, and if ΔG_{mfe}+(k-2)pΔG/(n-1) < ΔG_{i.j}≤ ΔG_{mfe}+(k-1)pΔG/(n-1), then color*k*is used for base pair*i.j*, for 2 ≤ k ≤ n. When n is 8 (the default), the optimal base pairs are colored in red and black colors base pairs that are least likely to form.

*Exterior loop*- Single-stranded bases that are not in a hairpin, bulge, interior or multi-branch loop are called "free bases". Similarly, a base pair at the end of a helix is called a "free base pair" if it is not in a hairpin, bulge, interior or multi-branch loop. Free bases and base pairs comprise the "exterior loop". The default option draws the exterior loop as if it were a regular loop, except that the 5' and 3' ends are not joined (for linear molecules). The "Flat" option places the exterior bases and base pairs on a straight line. The helices associated with the external base pairs are all placed on the same side of the line. The "Flat_Alt" option draws these helices on both sides of the line. Odd numbered helices appear on one side and even number helices appear on the other side.

*Image width - png & jpg files*- The default value is 935 pixels (13 in / 33 cm). Longer sequences with complicated folds require larger widths. Small sequences with simple folds require smaller widths. Pdf and PostScripts images may be enlarged at will without loss in resolution. For png and jpg format, the "domain" option should be used to plot selected parts of very large foldings.

*Ionic conditions*-
The corrections for [Na
^{+}] and [Mg^{++}] have been empirically derived. They are currently being used only for DNA folding, where the conditions under which free energy measurements were made, [Na^{+}] = 1 M and [Mg^{++}] = 0 M, are far from reasonable physiological conditions.__Oligomer correction:__[Na^{+}] should be kept between 0.01 M and 1 M, and [Mg^{++}] should be no larger than 0.1 M. This correction is most likely valid for foldings that result in stems of up to 20 base pairs, including bulges and interior loops. It is certainly not valid for a long stretch of perfect Watson-Crick base pairs.__Polymer correction:__[Mg^{++}] must be 0. The combined effect of [Na^{+}] and [Mg^{++}] in polymers is still not understood. This correction should be used when long stems form. A "long stem" contains about 20 or more consecutive nucleotides that are base paired or in bulge/interior loops .

*Stucture numbering frequency*-
Individual structures are numbered, starting at some number
**N**, and continuing with every multiple of**N**. When**N**=0, there is no structure numbering. If the user does not choose a value, it will be taken from the table below.*Default numbering increment for structures.*Sequence length Numbering increment 1-50 10 51-300 20 > 300 50

*Maximum asymmetry of a bulge/interior loop*- The
*upper bound*on the asymmetry of a bulge/interior loop. This parameter is the maximum size of a bulge loop. For interior loops, if the number of single-stranded bases on the two sides are n_{1}and n_{2}, then |n_{1}- n_{2}| ≤ this limit.

*Maximum distance between paired bases*- If this parameter is set to
*max*, then a base pair between bases numbered*i*to*j*will not be allowed if*j-i > max*. In a sequence of 1000 nucleotides, setting*max*to 50, for example, will force the server to compute foldings involving only short range base pairs. Please note that in circular sequences, a base pair*i.j*will be disallowed if and only if*min{j-i,N+i-j} > max*. This takes into account the circular nature of the molecule.

*Maximium number of foldings*- The
*upper bound*on the number of foldings that are computed is not necessary. The folding algorithm automatically computes a selection of secondary structures within the prescribed energy increment and stops when no more*sufficiently different*foldings can be found. See also the definition of the*window*parameter (below).

*Maximium size of a bulge/interior loop*- The
*upper bound*on the total number of single-stranded bases that are allowed in a bulge or interior loop. The default value is 30. The user may select any smaller value.

*Structure format*- The PostScript, png & jpg plots of secondary structure have 2 formats. In the first format, individual bases are shown and base pairs are depicted by colored dots. This is the "Bases" option. Otherwise, only an outline of the secondary structure is drawn, and base pairs become colored line segments. This is the "Outline" option. The default "Automatic" option draws bases when sequence length is less than 800, and an outline otherwise.

*Sequence numbering offset*- This number will be added to the base labels. If you wish, for example, your sequence to begin with base
**N**, then set OFFSET to**N-1**. The default is 0, or no offset.

*Percent suboptimality*- If this number is set to
*p*, then only foldings within*p%*from the minimum free energy will be computed. The*energy dot plot*contains the superposition of all possible foldings within*p%*of the minimum energy. An energy increment of**less than**1 kcal/mol is rounded up to 1 kcal/mol. Similarly, an increment of more than 12.0 kcal/mol is rounded down to 12.0 kcal/mol.

*Regularization angle (in degrees)*- This non-negative number is not used if 0. If it is > 0 and if the drawing mode is untangle (simple or loop fix), then angles between any two stems are always an integral multiple of this regularization angle. Users are encouraged to experiment with this (and other) parameters. Predicted secondary structures may be drawn over and over again without refolding the sequence.

*Structure rotation*- Plotted structures may be rotated through a user selected angle (in degrees). The default value is 'auto', which means that the angle is chosen by the structure drawing program, sir_graph. Otherwise, any positive or negative integer may be chosen for counterclockwise or clockwise rotation, respectively.

*ss-count**ss-count*is the propensity of a base to be single stranded, as measured by the number of times it is single stranded in a group of predicted foldings. The*ss-count*file gives the number of predicted foldings on the first line. The i^{th}subsequent line contains*i*and the number of foldings in which the i^{th}base was single stranded. The plotting option gives plots of*ss-count*values averaged over a user selected window.

*Window*-
The
*window parameter*controls how many foldings will be automatically computed and how different they will be from one another. It takes on positive whole number values. A smaller value of this parameter will usually result in more computed foldings that may be quite similar to one another. A larger value will result in fewer foldings that are very different from one another. If this parameter is not chosen by the user, a default value will be selected from the table below according to the sequence size.*Default window parameters depending on sequence length. The user is encouraged to experiment with this parameter.*Sequence length Default window size 0-29 0 30-49 1 50-119 2 120-199 3 200-299 5 300-399 7 400-499 8 500-599 10 600-699 11 700-799 12 800-1199 15 1200-1999 20 > 1999 25