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Prediction of Coordination
Number and Relative Solvent
Accessibility in Proteins
Computational Aspects
Yacov Lifshits
13.04.2005
Introduction
There is no known algorithm for predicting solvent
accessibility or coordination number.
Many different approaches were tried, and most of them
utilized the concept of neural networks.
We shall discuss what these networks are, how do they
work, and how we use them for our cause.
Neurons
The human brain consists has about 100 billion (1011)
neurons and 100 trillion (1014) connections (synapses)
between them.
Many highly specialized types of neurons exist, and these
differ widely in appearance. Characteristically, neurons are
highly asymmetric in shape.
Neurons – cont.
Here is what a typical neuron looks like:
Neural Networks
Like the brain, an neural network is a massively parallel
collection of small and simple processing units where the
interconnections form a large part of the network's
intelligence.
Neural Networks – cont.
Artificial neural networks, however, are quite different from
the brain in terms of structure.
For example, a neural network is much smaller than the
brain. Also, the units used in a neural network are typically
far simpler than neurons.
Nevertheless, certain functions that seem exclusive to the
brain, such as learning, have been replicated on a simpler
scale with neural networks.
Neural Networks Features
• Large number of very simple units
• Connections through weighted links
• There is no “program”. The “program” is the architecture
of the network.
• There is no central control. If a portion of the network is
damaged, the network is still functional. Hopefully.
• A human observer can’t understand what is going on
inside the network. It is a sort of a “black box”.
Neural Networks - intuition
Neural networks are our way to model a brain.
The good thing about them is that you do not program
them, but instead teach them, like children.
For example, if you show a kid a couple of trees, he will
know to identify other trees. Few humans can actually
explain how to identify a tree as such, and even fewer (if
any) can write a program to do that.
So when you don’t know how the algorithm to do
something, neural networks are your second-best solution.
Neural Networks uses
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Speech recognition
Speech synthesis
Image recognition
Pattern recognition
Stock market prediction
Robot control and navigation
Artificial Neurons
The neuron is a basically a simple calculator.
It calculates a weighted sum of the inputs (plus a bias
input), and applies an activation function to the result.
Artificial Neurons – example
The above example proves that neural networks are
universal – you can implement any function with them.
Training
How do we train a neural network?
The task is similar to teaching a student.
How do we do that?
• First, we show him some examples.
• After that, we ask him to solve some problems.
• Finally, we correct him, and start the whole process again.
Hopefully, he’ll get it right after a couple of rounds…
Training – Simple case
Training the network means adjusting its
weights so that it gives correct output.
It’s rather easy to train a network that has no hidden layers
(called a perceptron).
This is done by the “gradient descent” algorithm.
Training – Gradient descent
The idea behind this algorithm is to adjust the weights to
minimize some measure of the error.
The classical measure is sum of squared errors:
( h(x) is the real output, and y is the true (“needed”) value)
This is an optimization search in a weight space.
Training – Gradient descent
First, we compute the gradient function:
And then we update the weight as follows:
(α is the learning rate)
Training – Back Propagation
In most real-life problems we need to add
a “hidden level”.
This turns out to be a problem – the
training data does not specify what the
hidden layer’s output should be.
It turns out that we can back-propagate the error
from the output layer to the hidden ones.
It works like a “generalized” gradient descent
algorithm.
Training – Back Propagation
Problems of back propagation:
• The algorithm is slow, if it does converge.
• It may get stuck in a local minimum.
• It is sensitive to initial conditions.
• It may start oscillating.
Training – OBD
A different kind of training algorithm is “Optimal Brain
Damage”, which tries to remove “unneeded” neurons.
One of its uses is to prune the network after training.
The algorithm begins with a fully connected network and
removes connections from it.
After the network is trained, the algorithm identifies an
optimal selection of connections that can be dropped.
The network is retrained, and if the performance has not
decreased, the process is repeated.
Training – cont.
Two main training modes are:
• Batch: update weights as a sum over all the training set.
• Incremental: update weights after each pattern presented.
Incremental mode requires less space complexity, and is less
likely to get stuck in a local minimum.
Each cycle through the training set is called an epoch.
Training – General problems
Overfitting: If we give a lot of
unnecessary parameters to the
network, or train it for too long,
it may “get lost”.
An extreme case of overfitting is
a network that has 100% success rate
on the training set, but behaves randomly on other values.
Poor data set: To train a network well, we must include all
possible cases (but not too much).
The network learns the easiest feature first!
Back to the problem
Until now, we discussed neural networks where all
connections go “forward” only (called feed-forward
networks).
They are not suitable for problem we are trying to solve,
however.
The major weakness of FF networks is the use of a local
input window of fixed size, which cannot
provide any access to long-range information.
Back to the problem – cont.
Networks for contact prediction, for instance, have windows
of size 1–15 amino acids.
Larger windows usually do not work, in part because the
increase in the number of parameters leads to overfitting.
There are ways to prevent it, but it is no the main problem.
The main problem is that long-range signals are very weak
compared to the additional “noise” introduced by a larger
window. Thus, larger windows tend to dilute sparse
information present in the input that is relevant for the
prediction.
Recurrent Neural Networks
One of the methods used to try to overcome these
limitations consists of using bidirectional recurrent
neural networks (BRNNs).
An RNN is a neural network that allows “backward”
connections. This means, that it can re-process the output.
Our brain, as you can surely guess, is a recurrent network.
Sadly, the issues of RNN training and architecture are too
complicated for this lecture. An intuitive explanation will be
presented, however.
The Network used
The BRNN
The input, vector It, encodes the external input at
time t. In the most simple case, it encodes one amino acid,
using orthogonal encoding.
The output prediction has the functional form
Ot = η(Ft , Bt , It)
and depends on the forward (upstream) context Ft, the
backward (downstream context) Bt, and the input It at
time t.
The Past and the Future
Ft and Bt store information about the “past” and the
“future” of the sequence. They make the whole difference,
because now we can utilize global information.
The funtions satisfy the recurrent bidirectional equations:
Ft = φ(Ft-1, It)
Bt = β(Bt+1, It)
where φ() and β() are learnable nonlinear state transition
functions, implemented by two NNs (left
and right subnetworks in the picture).
The Past and the Future
Intuitively, we can think of Ft and Bt
as “wheels” that can be rolled along
the protein.
To predict the class at position t, we roll the wheels in
opposite directions from the N- and C-terminus up to position
t and then combine what is read on the wheels with It to
calculate the proper output using η.
The difference it makes
Hence the probabilistic output Ot depends on the input It and
on the contextual information from the entire protein,
summarized by the pair (Ft , Bt)!
In contrast, in a conventional NN approach, the probability
distribution depends only on a relatively short subsequence
of amino acids.
Training the BRNNs
The BRNNs are trained by back-propagation on the relative
entropy error between the output and target distributions.
The authors use a hybrid between online and batch training,
with 300 batch blocks (2–3 proteins each) per training set.
Thus, weights are updated 300 times per epoch after each
block.
When the error does not decrease for 50 consecutive
epochs, the learning rate is divided by 2, and training is
restarted. Training stops after 8 or more reductions, which
usually happens after 1,500–2,500 epochs.
The experiment
The authors used a network of 16 Sun Microsystems
UltraSparc workstations for training and testing, roughly
equivalent to 2 years of a single CPU.
Seven different BRNNs
were trained, and the
final result was the
average of their outputs.
The results
The predictors achieve performances within the
71–74% range for contact numbers, depending on radius,
and greater than 77% for accessibility in the most interesting
range.
These improve the previous results by 3-7%.
The results – cont.
The improvements are believed to be due to both an
increase in the size of the training sets and in the
architectures developed.
The most important thing about the architectures is their
ability to capture long-range interactions that are beyond the
reach of conventional feed-forward neural networks, with
their relatively small and fixed input window sizes.
References
• Prediction of Coordination Number and Relative Solvent
Accessibility in Proteins, Baldi et al.
• Exploiting the past and the future in protein secondary
structure prediction, Baldi et al.
• Artificial Intelligence - a modern approach, Russel, Norvig.