Method and apparatus for multivariable analysis of biological measurements

• US 7,225,172 B2
• Filed: 11/26/2002
• Issued: 05/29/2007
• Est. Priority Date: 07/01/1999
• Status: Expired due to Fees

• Current Assignee: Yeda Research and Development Co. Ltd. (Weizmann Institute of Science)
• Original Assignee: Yeda Research and Development Co. Ltd. (Weizmann Institute of Science)
• Inventors: Kam, Zvi
• Primary Examiner(s): Hirl; Joseph P.
• Application Number:
  US10/304,551
• Publication Number:
  US 20030158829A1
• Time in Patent Office: 1,645 Days
• Field of Search: 706/15, 706/16, 706/924, 364/578, 707/100
• US Class Current: 706/15
• CPC Class Codes: G06N 3/02 Neural networks
• CPC Class Codes: G16B 25/00 ICT specially adapted for hybridisation; ICT specially adapted for gene or protein expression
• CPC Class Codes: G16B 40/00 ICT specially adapted for biostatistics; ICT specially adapted for bioinformatics-related machine learning or data mining, e.g. knowledge discovery or pattern finding
• CPC Class Codes: G16B 40/20 Supervised data analysis
• CPC Class Codes: G16B 45/00 ICT specially adapted for bioinformatics-related data visualisation, e.g. displaying of maps or networks
• CPC Class Codes: G16B 5/00 ICT specially adapted for modelling or simulations in systems biology, e.g. gene-regulatory networks, protein interaction networks or metabolic networks
• CPC Class Codes: G16B 5/30 Dynamic-time models
• CPC Class Codes: G16H 50/20 for computer-aided diagnosis, e.g. based on medical expert systems
• CPC Class Codes: Y02A 90/10 Information and communication technologies [ICT] supporting adaptation to climate change, e.g. for weather forecasting or climate simulation
• CPC Class Codes: Y10S 706/924 Medical

Abstract

In a method and apparatus for analyzing multivariable data sets, a general computerized platform is provided for evaluating the relationship between large number of measurements of sets of variables characterizing components of complex states of a system under induced stimulation or controlled conditions. The linked responses of variables and their temporal relations tell about the network of interactions and their hierarchy. Processing of data sets by a simple neural network gives a matrix of weight parameters, that allow to identify fingerprints of complex states characterized by patterns of measured variable and estimate the interactions between the components characterized by the measured variables. The results are provided numerically and by color-coded presentation indicating dominating relations between variables and strongly responding variables. When applied to dynamic responses of a system, the analysis can construct a schematic hierarchical architecture of the network of interaction between the components of the studied system. Applications in biology include analysis of measurements characterizing responses of molecular components in cells under changes induced by stimuli (e.g. drugs, growth factors, hormones, mutations or forced expression of a proteins), and identification of complex cellular states (e.g. proliferation, differentiation, transformation, starvation, necrosis, apoptosis, and the time dependencies of the above effects).

Claims

1. Apparatus for analyzing a biological system defined by multivariable data sets including a plurality of perturbations (inputs) and measured response (outputs) variables, said apparatus comprising:

a neural network capable of receiving signals contained in said data sets and processing said inputs according to an artificial intelligence program to yield the outputs; and

means for obtaining a trained matrix of weight parameters for said neural network and said data sets through a sequence of iterations, starting at random guess for the weights, and correcting the trained weight matrix according to a learning rule until the errors between the processed inputs and the outputs diminishes;

means for obtaining an average matrix of weight parameters of many trained weight matrices including sequentially and repeatedly averaging said many trained weight matrices, each initialized by a different set of a plurality of random weight parameters, and until the averaged matrix of weight parameters converge;

means of evaluation of the relationship between said variables from said weight parameters; and

means for collecting data sets which include a plurality of induced and measured variables which characterize stimuli applied to cells and responses of said cells to said stimuli, wherein said weight parameters of the neural network provide identification of finger prints of complex cellular states,

wherein said data sets comprise experimentally determined data which characterize variations in measurable components of a biological process.

2. Apparatus according to claim 1 wherein said external stimuluss selected from the group consisting of a drug, growth factor, hormone, a mutated proteins and forced expression or suppression of cellular component, and said complex cellular state is starvation, appoptosis, cell differentiation, mitogenicity of proliferating cells or cell cycle arrest.

3. Apparatus according to claim 1 for construction of hierarchical architecture of interaction network between said components of said biological process by analysis of cell responses to external stimuli, comprising:

means for collecting time dependent data sets which includes a plurality of changing variables which characterize responses of said cells to said stimuli, wherein said weight parameters allow the construction of hierarchical architecture of said interaction network.

4. Apparatus according to claim 3 wherein said network is a signaling pathway in cells.

5. Apparatus according to claim 1 wherein said neural network matrix of weight parameters is represented by a color coded image, in which dominating positive and negative weight parameters are easily identified.

6. Apparatus according to claim 1 wherein said matrix of weight parameters W_ji operates on input variables I(k)_j, though a monotonic transfer function to generate output variables O(k)_i, according to:

$\begin{array}{cc}{O<br><br>\left(k\right)}_j=f<br><br>\left\{\underset{i=1,N}{\sum <br><br>}<br><br>W_{\mathrm{ji}}*{I<br><br>\left(k\right)}_j+B_j\right\}<br><br>\left(k=1,L;<br><br>j=1,M\right).& \left(\mathrm{Eq}.<br><br>1\right)\end{array}$

7. Process for analyzing a biological system defined by multivariable data sets including a plurality of perturbations and measured response variables, said process comprising:

providing a neural network;

applying signals representative of variables contained in said data sets to said neural network and through a sequence of iterations, starting at a random guess for trained weight parameters, and correcting the trained weight parameters according to a learning rule until the error between the signal and the responses diminishes, and repeatedly averaging a plurality of trained weight parameters each initialized by a different random guess for the trained weight parameters, until an average of the plurality of trained weight parameters converge; and

generating from the average trained weight parameters an evaluation, indicating relationship between said variables,

wherein said matrix of weight parameters W_ji operates on input variables I(k)_j, through a monotonic transfer function to generate output variables O(k)_j, according to;

$\begin{array}{cc}{O<br><br>\left(k\right)}_i=f<br><br>\left\{\underset{i=1,N}{\sum <br><br>}<br><br>W_{\mathrm{ji}}*{I<br><br>\left(k\right)}_j+B_j\right\}<br><br>\left(k=1,L;<br><br>j=1,M\right)& \left(\mathrm{Eq}.<br><br>1\right)\end{array}$

to provide identification of finger prints of complex cellular states.

8. Method comprising the steps of

obtaining a data set comprising a plurality of input/output multivariable vectors representative of a biological process involving many interacting multifunctional components in at least one pathway,

establishing a neural network comprised of single layer network operators, applying the data set to the neural network, and

training the neural network by a training algorithm to implement a transformation by a matrix of weights, including sequentially initializing a plurality of weight matrices, wherein each of the weight matrices is initialized with a different random guess and iteratively correcting each of the weight matrices until the processed inputs and outputs are within a small error for each of the weight matrices, yielding a plurality of trained weight matrices, of the plurality of trained weight matrices to form the matrix of weights, till convergence to the process of averaging together the plurality of trained weight matrices, determining from said matrix of weights the hierarchical structure between said components,

wherein the hierarchical structure is portrayed by drawing the vectors between the variables as determined by the magnitude of the matrix of weights, and

wherein weights smaller than a preselected threshold are ignored in the portrayal providing for distinct neural network identification of finger prints of complex cellular states.

9. The method of claim 8 wherein the data set of input/output multivariable vectors constitutes time dependent data.

10. The method of claim 9 wherein the data set includes an input set including a measured set of variables at consecutive times, and an output set comprised of the same data as the input set, but shifted forward in time to a later time, so that the neural network learns to take in data at one time and give out data at the later time.

11. Method comprising the steps of

obtaining a data set comprising a plurality of input multivariable vectors representative of a biological system involving many interacting multifunctional components in at least one pathway, that define a complex biological state,

determining a corresponding output vector for each input vector that defines classes for the input vectors,

establishing a neural network comprised of single layer network operators, applying the data set to the neural network,

training the neural network by a training algorithm to implement a transformation by a matrix of weights, including sequentially initializing a plurality of weight matrices, wherein each of the weight matrices is initialized with a random guess and iteratively modified according to a learning rule until the transformation of inputs by the weight matrix gives the outputs,

averaging the trained solutions for the plurality of weight matrices to obtain a converged averaged weight matrix, whereby the modified neural network can sort newly presented input vectors into the classes that were defined by the output set of vectors in the training to provide classification of finger prints of complex cellular states.

12. Apparatus for processing input vectors representative of a biological process involving many interacting multifunctional components in at least one pathway comprising,

a neural network composed of single layer network operators trained by a training algorithm to implement a transformation by a matrix of weights, the training including sequentially initializing a plurality of weight matrices, wherein each of the weight matrices is initialized with a random guess and iteratively modified according to a learning rule until the weight matrix produces a solution that transforms the inputs to the outputs within a small error, and then averaging the trained solutions of the weight matrices, each obtained from a different plurality of initial weights to obtain a converged averaged weight matrix, and

a device for recognizing a predetermined input vector based on the output vectors received by the mechanism,

wherein the input vectors are sorted according to predetermined criteria for the output vectors to provide classification of finger prints of complex cellular states.