Profiles:

• Profile1:
  Model with junk domains and no deletions Pretty file Model with deletion and without junk domains pretty file
  This model is obtained by doing the following:
  1. 9 training examples, corresponding to 11 segments were picked.
  2. A profile hidden markov model (one with deletion states) is constructed. The match states corresponds to a strictly hydrophobic column. The rest were treated as insertions. Laplace prior is used to alleviate the problem of overfitting. This model is final.profile1. For the "match" states, the prior is only applied to the hydrophobic symbols. For the insertion states, the prior is applied to every symbol.
  3. This profile hidden markov model then is converted to one which has no deletion states by converting deletion transitions into "skipping transitions". So the transition matrix takes a triangular shape (lower or upper will depend on the structure of the matrix itself). Then two junk modeling states are constructed. Also, to maintain numerical stability, the transition matrix is expressed in the log domain. So is the prior vector. The emission matrix is expressed in the linear domain. Also, the junk domains are appeneded to the ends of this model and some necessary changes was made. The junk domain are the self-looping states using the emission probability from null.model. This model is profile1.model
• Profile2 Model with junk domains and no deletions Pretty file Model with deletion and without junk domains pretty file
  

• initial.model:
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  This is the initial file used to train the hidden markov models with 11 fragments from our family. This initial model is estimated using very rough technique. First, we obtained an output (a multiple alignment) of our family from SuperFamily. Then we marked a few columns with the sheet Prof. Kister provided. Then a few segments with Hydrophobic amino acid residues ONLY in these marked columns are isolated. The transition matrix of the initial hidden markov model is obtained by eye-balling the alignment of THESE SEGMENTS ONLY while assuming an exponential distribution. The emission matrix is estimated in this way: for the "Gap" positions, the distribution is background and for the "critical" positions, the distribution is uniform on HYDROPHOBIC AMINO ACIDS ONLY (Nine: A,C,F,I,L,M,V,W,Y).
• initial-Skip.model:
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  This model is just a slight modification of initial.model, where very slight probability is added to most of the gap states so that critical states can be escaped.
• final.model:
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  The outcome of the EM algorithm, where the training set are the 9 proteins in SWISS-PROT. Here are the 9 proteins: O18835 O77695 O97524 P00722 P00723 P06760 P08236 P12265 P23989. Some of them have multiple domains belonging to our family. The model identified 9 critical positions, which turned out to be TOO SEPCIFIC, i.e. a problem of overfitting. The inital model was hand-crafted. The model has 32 states. This model itself identifies the domain. Nevertheless, two states need to be added -- one in the very beginning and one in the very last (prior to the virtual end state though). These two newly added states should emit symbols with background probablility. This model will later be identified as the identified.model but will do a little more. (The initial model is initial.model).
• final-Skip.model:
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  The outcome of the EM algorithm using inital-Skip.model as initial model. 32 states. No pseudocount is added during and after the training process. It is a little surprising to see that this model and final.model are almost identical, except a 10^-6 difference on the transition vector of the seventh state, despite the fact that we started from a model in which skipping gap is allowed. However, this can be explained by the fact that No training fragments skip a critical state and also the low, discouraging probability of the skipping transition.
• final-SkipPseudo.model:
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  This model is obtained using initial-Skip.model with EM algorithm. However, during each iteration in training, two things are done:
  • Background is added to each gap state.
  • Normalized Hydrophobic background is added to each critical state.
  And of course, after these, normalization is performed. Then 2 states are added to the very beginning and one state prior to the virtual ending state of the model. Therefore, this model has 34 states. A transition from the last state looping back to the second state was also added. Nevertheless, notice again, the 'structure' i.e. the transition matrix of this model and final.model, as well as final-Skip.model are almost identical except some differences between numbers. The impossible transitions remain impossible.
• final-SkipPseudoSkip.model:
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  Obtained by merely adding skipping probability (.01) to final-SkipPseudo.model
• null.model:
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  It is just a single state model (without the virutal end state) which emits symbols according to the background probability.
• critical model:
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  This is a modification of final.model, with 32 states as well. The emitting probability of the first state and the last state has been changed to the background probability, which is intrinsically wrong. The correct way of doing it will be outlined in modified.model
• modified.model:
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  This model is based on final.model. Two states were added, as specified in the section explaining final.model. This first state is added in the very beginning which emits background probability and the second state is added all the way in the end, just before the virtual end state, also emitting background probability. These two states in order to model the other domains that we are not intersted in. The transition probability of the last state (the one which was newly added) has some slight probability of going back to the second state, which encourages the model to identify more than one domain in the family we are interested in.
• mutation.model:
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  This model is based on modified.model. The only difference is that: among all the 9 critical positions that were identified, some slight probability are added to the emission matrix for the hydrophobic amino acid residues. This is in attempt to model mutation. Note that the program need to normalize the emission matrix after reading the model in.
• skipMut.model:
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  Based on mutation.model. However, skipping transitions were added so that, if desirable, critical positions can be skipped. Nevertheless, severe penalty is involved when a critical position is skipped, which discourages the skipping. Note that BOTH transition and the emission probability need to be normalized after the model file is read.
• all-no-pseudo.model:
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  Obtained by using all available instances to train. PseudoCount is not added. Then 2 states are inserted after the training. This model has 34 states. The initial model is initial.model. 43 instances are used for training.
• all-plus-pseudo.model:
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  Obtained by using all available instances to train. PseudoCount is added during each iteration of EM (background to gap states, and normalized hydrophobic background to critical states). Then 2 states are inserted after training. This model has 34 states. The initial model is initial.model. 43 instances are used for training.
• null2.model:
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  Made simply by observing the frequencies of all the amino acids from all 43 fragments.
• all-plus-pseudoFB.model:
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  Obtained using the same method as all-plus-pseudo.model except that now background probability is the one in null2.model.
• null3.model:
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  Obtained by observing the frequencies of all the amino acids from 11 fragments only.
• part-plus-pseudoFB.model:
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  Obtained by training on 11 fragments only and the background probabilities corresponds to those in null3.model.
• flank.model:
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  This model is just a slight modification of the model all-plus-pseudo.model, which has 34 states. States 0 and 32 are the junk-modelling domains. State 33 is the virutal end state. The following describes the modification:
  • First of all, a sequence has the option of directly entering the domain or entering the junk-modelling domain first. The prior vector is set to have 0.5 probability of entering the junk domain and 0.5 probability of entering the first residue in the domain that we are modeling.
  • Originally, state 1 has 2 outgoing probabilities -- a high-probability self-looping transition (0.999999) and a low probability transition that goes to the first residue of the domain we are modeling. Now, let alpha be 0.001. So, the self-looping transition is replaced by (1-alpha) and the low probability transition is replaced by (alpha/2). (N-3) more outgoing transitions are added to state 1 -- all goes to one of the states that models the domain and all have the probability of (alpha/(2*(N-3))).
  • Also, from state 1 to state 30, there is an outgoing probability to state 32, the junk-modeling domain.
  The rationale behind changes 2 and 3 is that in the previous experiments we were forcing all proteins to fit our model. In this representation the idea is that if a protein does not fit the model well, then it should come out of that domain as soon as possible.