Graph Formations of PartialOrder MultipleSequence Alignments Using Nano and MicroScale Reconfigurabl

1
Graph Formations of Partial-Order
Multiple-Sequence Alignments Using Nano- and
Micro-Scale Reconfigurable Meshes

• Mary M. Eshaghian-Wilner, Ling Lau, Shiva Navab,
  and David Shen
• Department of Electrical EngineeringUniversity
  of California, Los Angeles
• maryew_at_ee.ucla.edu, jonlau_at_ucla.edu,
  shiva_n_at_ee.ucla.edu, dshen727_at_ucla.edu

The authors are listed alphabetically by last
name.
2
Overview

• Background
• Bioinformatics sequence processing
• Multiple Sequence Alignment
• Partial-order graph formation algorithm
• Spin-wave reconfigurable mesh
• Electrical VLSI reconfigurable mesh

3
Motivation and Background

• Problems in computation biology involves sequence
  alignment.
• Sequences in Biological Data
• DNA contains 4 base pairs A, T, C, G.
• An average human gene contains as many as 30,000
  base pairs.
• In protein, there are different types of amino
  acid sequences.

4
Sequence Alignment

• Graph Formation Problem Description
• Form graphical representation using sorted
  sequences
• Example of how to obtain sorted sequences
• Alignment algorithms
• CLUSTLW, T-COFFEE, MAFFT, POA Partial Order
  Alignment

5
Partial Order Alignment

• POA aligns unsorted sequences using dynamic
  programming (Chris Lee 2002).
• We denote the graph formation of the sorted
  sequences as
• Partial Order Multiple Sequence Alignment Graph
  (PO-MSAG)

Chris Lee. MSA using Partial Order Graph, 2002
6
Sequence Alignment Example
There are four sequences with four similar
subsequences and three different ones.
The similar subsequences within the four
sequences are now extracted while the different
ones are kept separate.
Now expand this problem to a larger scale.
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Partial Order Graph Formation On an Architecture

• Goal
• To form the PO-MSAG on an architecture after the
  given input sequence data has been aligned.
• Architecture Reconfigurable Mesh
• Micro-scale Standard Electrical VLSI
  Reconfigurable Mesh
• Nano-scale Spin-wave Reconfigurable Mesh
  (Eshaghian et al., 2006)

8
Standard VLSI Reconfigurable Mesh
Figures obtained from Slides prepared by Heiko
Schröder, 1998
9
Spin-wave Reconfigurable Mesh
10
Spin-wave Signal Propagation

• Each node can transmit/receive at a unique
  frequency
• Takes O(1) for signal propagation through entire
  bus
• Define this constant time as t0 L / V (L
  Length of bus, V velocity of signal)
• Example of bus

Nodes
Transmitter/Receiver
Freq. A
Freq. B
Freq. C
Freq. D
Bus
Switch
11
Directing the Spin-wave Signal Propagation

• Sent wave signals travel in two opposite
  directions
• Closed switch forces both waves in the same
  direction

Transmitter/Receiver
Switch
Bus
12
Directing the Spin-wave Signal Propagation

• Switch closed while sending to force direction
• Switch opened so that all signals can travel
  through bus

Transmitter/Receiver
Switch
Bus
13
PO-MSAG Formation

• Overall idea
• To record the connectivity between the nodes
• To eliminate all repeated nodes using parallel
  processing
• To form graph based on the connections
• Problems considered
• Dataset with constant number of variables
• Dataset with as many as O(N) variables

14
PO-MSAG for Constant Variation Using Spin-wave
Overview

• Initial Mapping
• Neighbor Recording
• Node Elimination
• Memory Update

15
PO-MSAG for Constant Variation Using Spin-wave
Example

• Example sequence DNA (restricted to 5 variables
  A, T, C, G, )
• Number of sequences N Length of each sequence
  L
• Architecture Spin-wave Reconfigurable Mesh
• Size of Mesh NL

16
PO-MSAG for Constant Variation Using Spin-wave
Initial Mapping

• Each node on the Reconfigurable Mesh has 7 memory
  slots the number of different variables 2.
• O(1) time to place each nodes own data to its
  second memory slot.

A

A


C
G
C
G




2
2
2
2
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PO-MSAG for Constant Variation Using Spin-wave
Neighbor Recording

• Each node records its own left and right
  neighbors.
• Store these variables into the nodes first and
  third memory slots, respectively.
• O(1) time complexity

A

A


A
A

A
X
C
G
C
G



C
G

X




A

1
1
3
3
C
G
1
1
3
3
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PO-MSAG for Constant Variation Using Spin-wave
Node Elimination 1

• Goal
• To select one node of each type to represent the
  repeated nodes of that type in every column
• Challenge
• Within a column, the rows in which each type of
  node lies is unknown, thus choosing one node
  becomes difficult.
• Solution
• To select the first (uppermost) node of each type
  that appears in a column

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PO-MSAG for Constant Variation Using Spin-wave
Node Elimination 2

• Close switch above forcing all sent signals
  downward
• All nodes send signal downward and open switch
  above
• Disable nodes that receive a signal
• One node of certain type remains to represent
  disabled nodes of that type
• All other A, T, C, G, and nodes perform this
  simultaneously by using their own frequency
  channels

Freq A
Freq
Only one A remains
Example of the third column
A
A

A
A

Only one remains




A

A

A
A

A

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PO-MSAG for Constant Variation Using Spin-wave
Memory Update 1

• All disabled, repeated nodes still hold
  connectivity information via their right
  neighbors
• Want to avoid losing connectivity information
• Have disabled nodes send their right neighbors to
  their respective representative node
• Representative node store the received
  information

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PO-MSAG for Constant Variation Using Spin-wave
Memory Update 2

• Close switch below forcing signals upward.
• Disabled node checks right neighbor for A if so,
  send A signal upward while opening switch below
• If representative node of each type receives an A
  signal, place an A in the next available right
  neighbor memory if it is not already there
• This still runs in O(1) time.

Example using the second column
Freq
Freq T
Freq G

Receives an A signal
There is already an A in node s right neighbor
memory slot 3 (from the neighbor recording step)
so no addition A will be added.
G
T

A

A
A
3
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PO-MSAG for Constant Variation Using Spin-wave
Memory Update 3

• All nodes perform previous procedure sequentially
  for all other right neighbors (checking memory
  slot 3 for T, C, G, and sequentially).
• Memory update for one right neighbor done in
  constant time, so doing it for four more is still
  constant time O(1) 4 O(1) O(1).
• PO-MSAG formation with constant variation using
  Spin-wave Reconfigurable Mesh is complete (graph
  retrieval/drawing is beyond our scope, but can be
  done with third-party graphing program).

Example of the second and third columns

A
A
A
T


G

C

T
G
T
A
A
A

T

A
C
A
T


A
T

G



T
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PO-MSAG for Constant Variation Using Spin-wave
Overall Performance
24
PO-MSAG for Constant Variation Using Electrical
VLSI

• Overall highly similar procedure
• Differences
• Node elimination must be done sequentially since
  VLSI does not have frequency channels
• Memory update stage must also be done
  sequentially
• Same overall performance of O(1) since constant
  variation done sequentially is still constant

25
PO-MSAG for Constant Variation Using Electrical
VLSI Overall Performance
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PO-MSAG for O(N) Variation Overview

• Assumptions
• Extend Mesh size to 2N2L
• Node has O(1) access to row index
• Highlighted empty columns called graph columns
• Algorithm
• Same initial mapping, neighbor recording, and
  node elimination
• Difference in Graph Formation
• Count disabled nodes
• Place active nodes in graph column
• Place right neighbors in graph column
• Disable repeated right neighbors

2L
A
B
C
C
D
F
G
B
C
D
G
F
C
G
E
G
K
K
K
B
E
K
G
C
1 2 3 4
1
C
B
A
C
K
G
B
B
A
1 2 3
1 2
1
D
F
T
B
D
D
F
G
T
1 2
E
H
S
B
C
D
E
H
S
1
2N
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Spin-wave Signal Superposition

• Close all switches
• All nodes transmit a signal with amplitude 1 in
  own frequency and open all switches
• Signals in the same frequency superpose as they
  meet
• When the first signal reaches the end, all
  signals will have superposed
• Superposition used to count number of disabled
  nodes
• Example of superposition in one frequency

Transmitter/Receiver
Switch
Bus

• Time complexity O(1)

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PO-MSAG for O(N) Variation Using Spin-wave
Counting Disabled Nodes

• Close all switches
• All disabled nodes transmit amplitude 1 signal in
  own frequency and then open switches
• Active nodes receive for t0 amount of time (time
  taken for first signal to reach end of bus)
• Example of the first column

Transmitter/Receiver
Switch
Top
Bottom
Bus
G
A
A
A
A
Receives 3
Receives 0
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PO-MSAG for O(N) Variation Using Spin-wave
Indexing Active Nodes
Example using only the first two columns

• Open all switches
• All active nodes communicate over common
  frequency fActive
• First active node closes switch behind and
  broadcasts its number of repeated nodes 2 down
  the channel
• When successive active nodes receive that signal,
  they superpose a 2 signal.
• Magnitude received by active node is its index in
  the graph column to the right
• Example of first column
• Time Complexity O(1)

Receives 0
Receives 0
Repeated Nodes 3
Repeated Nodes 4
Receives 5
Repeated Nodes 0
Freq. Active Amp. 3 2 5
Freq. Active Amp. 5 (0 2) 7
Transmitter/Receiver
Switch
Top
Bottom
G
A
A
A
A
Receives 5Sends 2
Receives 0
Sends 5
(Not on Freq. Active Channel)
(Not on Freq. Active Channel)
(Not on Freq. Active Channel)
Bus
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PO-MSAG for O(N) Variation Using Spin-wave
Placing Active Nodes

• Using magnitudes previously received as indices,
  each active node copies itself to its right graph
  column
• Now these active node copies are noted as label 1
  and are Bold
• Active nodes now retrieve their own right
  neighbors and copy them directly below
• These right neighbor copies are noted as label 2
  and are Italicized

Example using only the first two columns
A
B
B
C
G
B
Remember that there are actually 2N rows, not
only just the seven shown.
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PO-MSAG for O(N) Variation Using Spin-wave
Indexing Disabled Nodes

• Each active node of each type sends its graph
  column index 2 downward in its own frequency
• Each disabled node of that type receives the
  signal and superposes 1 signal
• Signal received by disabled node is its graph
  column index
• Time Complexity O(1)

Freq. A Amp. 0 2 2
Freq. A Amp. 2 1 3
Freq. A Amp. 3 1 4
Freq. A Amp. 4 1 5
Transmitter/Receiver
Switch
Top
Bottom
G
A
A
A
A
Receives 2
Receives 3
Receives 4
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PO-MSAG for O(N) Variation Using Spin-wave
Placing Disabled Nodes Right Neighbors

• Magnitude previously received by each disabled
  node is its graph column index
• Each disabled node retrieves its right neighbor
  and copies him to its graph column based on its
  graph column index
• These right neighbor copies are noted as label 2
  and are Italicized
• Eliminate repeated right neighbors under a single
  active node type. This can be done in O(1) using
  our Node Elimination procedure.

Example using only the first two columns
K
Received 2
B
A
Received 2
Received 3
B
D
Received 3
Received 4
B
C
Received 4
Received 5
Note that this B is not eliminated because it
belongs to the active node G, not A.
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PO-MSAG for O(N) Variation Using Spin-wave
Summary

• Graph formed in highlighted graph columns.
• Bold nodes in graph column represents nodes in
  actual graph.
• Italicized nodes in graph column are the right
  side connections of nodes in actual graph

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PO-MSAG for O(N) Variation Using Spin-wave Graph
Representation
After the actual retrieval and drawing of the
graph
35
PO-MSAG for O(N) Variation Using Spin-wave
Overall Performance
36
PO-MSAG for O(N) Variation Using Electrical VLSI
Overview

• Algorithm similar that for constant variation
• Major differences from spin-wave
• Nodes no longer have their own frequency-based
  communication channels
• Node elimination and memory update done
  sequentially via the same method used on in the
  case with constant variation
• Time complexity degrades to O(N)

37
PO-MSAG for O(N) Variation Using Electrical VLSI
Overall Performance
38
Summary
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Conclusion

• Techniques for Partial-Order Multiple-Sequence
  Alignment Graph formation using spin-wave and
  VLSI reconfigurable meshes
• Future Work
• Extend the algorithms to large-scale graph
  databases
• Extend problem to incorporate biological
  pathways, sequence splicing, or any other areas
  that demand efficient computing tools for
  sequence alignment.

40
References

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• Thank you for attending this presentation!!!