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Companion Lecture Slides for Courses Taught from
Dynamic Systems Biology Modeling and Simulation (DSBMS)
JJ DiStefano III -Academic Press/Elsevier 2015

A full set of PowerPoint slides are available from the author for teaching from his textbook.  He uses them to teach a 10 week quarter upper division course at UCLA, which meets twice a week, so there are 20 lectures. They can easily be augmented or stretched for a 15 week semester course.

Importantly, the slides are editable, so they can be readily adapted to a lecturer’s personal style and course content needs.  The lectures are based on excerpts from 12 of the first 13 chapters of DSBMS. They are designed to highlight the key course material, as a study guide and structure for students following the full text content.

The complete PowerPoint slide package (~25 MB) can be obtained by instructors (or prospective instructors) by emailing the author directly, at: joed@cs.ucla.edu

Errata & Addendum for the first printing of Dynamic Systems Biology Modeling and Simulation

Author: Joseph DiStefano III, Academic Press (December 2013)

The following corrections and additions are for inclusion in the first print version of the textbook. The electronic textbook includes these corrections and additions within the text. The list appears large, but most of the entries are additions of useful Tables of Contents (TOC) for the six Appendices, in two places. Most corrections are minor.


IMPORTANT

The December 2013 print version is no longer available for sale.  These errata and addenda are corrected and included in the currently available and updated version of the textbook – in both printed and electronic versions – Updated Version JANUARY 2015.

Page

Location

Correction

v

Under Dr. Yate’s comments – second line

The line should read, “In that chapter you generously acknowledge some of us who tried to accomplish this earlier…”

xii

Chapter 14 title

Biocontrol System Modeling, Simulation & Analysis

xii

Chapter 15 title

Data-Driven Modeling & Alternative Hypothesis Testing

xiii

Chapter 16 title

Experiment Design & Optimization

xiii

Chapter 17 title

Model Reduction & Network Inference in Dynamic Systems Biology

xiii

Added TOC to Appendix A entries in main TOC

Appendix A – A SHORT COURSE IN LAPLACE TRANSFORM REPRESENTATIONS & ODE SOLUTIONS

Transform methods .................... 725
Laplace Transform Representations and Solutions .................... 726
Two-Step Solutions .................... 726
Key Properties of the Laplace Transform (LT) & its Inverse (ILT) .................... 727
Short Table of Laplace Transform Pairs .................... 730
Laplace Transform Solution of Ordinary Differential Equations (ODEs) .................... 732
Partial Fraction Expansions .................... 735
References .................... 738

xiii

Added TOC to Appendix B entries in main TOC

Appendix B –LINEAR ALGEBRA FOR BIOSYSTEM MODELING

Matrices   739
Vector Spaces (V.S.) .................... 742
Linear Equation Solutions .................... 742
Minimum Norm & Least Squares Pseudoinverse Solutions of Linear Equations .................... 743
Measures and Orthogonality .................... 743
Matrix Analysis .................... 744
Matrix Norms .................... 746
Matrix Calculus .................... 746
Computation of f(A), an Analytic Function of a Matrix .................... 748
Matrix Differential Equations .................... 753
Singular Value Decomposition (SVD) & Principal Component Analysis (PCA) .................... 754
Singular Value Decomposition (SVD) .................... 754
Principal Component Analysis (PCA) .................... 755
PCA from SVD .................... 756
Data Reduction & Geometric Interpretation .................... 756
References .................... 757

 

xiii

Added TOC to Appendix C entries in main TOC

Appendix C – INPUT-OUTPUT & STATE VARIABLE BIOSYSTEM MODELING: GOING DEEPER

Inputs & Outputs .................... 759
Dynamic Systems, Models and Causality .................... 759
Input-Output (Black-Box) Models .................... 759
Time-Invariance (TI) .................... 760
Continuous Linear System Input-Output Models .................... 761
Transfer Function (TF) Matrix for Linear TI Input-Output Models .................... 762
Structured State Variable Models .................... 763
State of a System S or Model M .................... 763
State Variable Models from Input-Output (I-O) Models .................... 763
Dynamic State Variable ODE Models for Continuous Systems .................... 764
Complete Dynamic System Models: Constrained Structures .................... 765
Linear TI State Variable Models .................... 766
Discrete-Time Dynamic System Models .................... 767
Discrete-Time Input-Output Models .................... 768
The Sampled or z-Transfer Function .................... 768
Discrete-Time State Variable Models .................... 769
Sampled Input-Output Transfer Function Matrix .................... 770
Composite Input-Output and State Variable Models .................... 770
Composite Input-Output Models .................... 770
Composite State Variable Models .................... 771
State Transition Matrix for Linear Dynamic Systems .................... 772
Input-Output Model Solutions .................... 772
State Variable Model Solutions .................... 773
The Adjoint Dynamic System .................... 775
Equivalent Dynamic Systems: Different Realizations of State Variable Models – Nonuniqueness Exposed .................... 776
Key Properties of Equivalent System Models .................... 777
Illustrative Example: A 3-Compartment Dynamic System Model & Several Discretized Versions of It .................... 778
Discretization and Sampled-Data Representations of the 3-Compartment Model .................... 779
Discretized ARMA Model with Impulse-Train Input .................... 782
Transforming Input-Output Data Models into State Variable Models: Generalized Model Building .................... 783
Time-Invariant Realizations .................... 784
SISO Models .................... 784
References .................... 786

xiii

Added TOC to Appendix D entries in main TOC

Appendix D – CONTROLLABILITY, OBSERVABILITY & REACHABILITY

Basic Concepts and Definitions .................... 787
Controllability .................... 787
Observability .................... 788
Observability and Controllability of Linear State Variable Models .................... 790
Linear Time-Varying Models .................... 790
Controllability Criterion .................... 792
Observability Criterion .................... 792
Linear Time-Invariant Models .................... 792
Practical Controllability and Observability Conditions .................... 793
Output Controllability .................... 795
Time-Invariant (TI) Models .................... 795
TI State Variable Models .................... 795
Output Function Controllability .................... 796
Reachability .................... 797
Constructibility .................... 799
Controllability and Observability with Constraints .................... 803
Positive Controllability .................... 803
Relative Controllability (Reachability) .................... 803
Conditional Controllability .................... 804
Structural Controllability and Observability .................... 804
Observability and Identifiability Relationships .................... 805
Controllability and Observability of Stochastic Models .................... 806
References .................... 807

 

xiii

Added TOC to Appendix E entries in main TOC

Appendix E – DECOMPOSITION, EQUIVALENCE, MINIMAL & CANONICAL STATE VARIABLE MODELS

Realizations (Modeling Paradigms) .................... 809
The Canonical Decomposition Theorem .................... 810
How to Decompose a Model .................... 813
Controllability and Observability Tests Using Equivalent Models .................... 813
SISO Models .................... 817
MIMO Models .................... 818
Minimal State Variable (ODE) Models from Input-Output TFs (Data) .................... 820
Canonical State Variable (ODE) Models from Input-Output Models (Data) .................... 821
Observable and Controllable Canonical Forms from Arbitrary State Variable Models Using Equivalence Properties .................... 828
References .................... 832

 

xiii

Added TOC to Appendix F entries in main TOC

Appendix F – MORE ON SIMULATION ALGORITHMS & MODEL INFORMATION CRITERIA

Additional Predictor-Corrector Algorithms .................... 833
Modified Euler 2nd-Order Predictor and Corrector Formulas .................... 833
An Iterative-Implicit Predictor-Corrector Algorithm .................... 834
Non-Iterative, Predictor-Modifier-Corrector (P-M-C) Algorithms .................... 834
A Predictor-Modifier Corrector Algorithm Exemplified .................... 835
The Backward-Euler Algorithm for Stiff ODEs .................... 836
Derivation of the Akaike Information Criterion (AIC) .................... 836
The AIC for Nonlinear Regression .................... 839
The Stochastic Fisher Information Matrix (FIM): Definitions & Derivations .................... 841
FIM for Multioutput Models .................... 842

 

xvii

Fourth line of item numbered 2.

Add footnote on word “logo.” Footnote should read:

Biomodeling/Theory+Data Images (The Logo: parent and children) are reproduced above and in the chapters and back cover of this book with permission by the author Joseph DiStefano III.  It is a Trademark ™ and service mark of the author, Copyright © 2012.

2 & 3

Humpty Dumpty  

Cartoon design by Allegra DiStefano.  Quote attributed to Schnell et al. 2007. 

Also, the 1 in Humpty-Dumpty quote on bottom of page 3  should not be italicized.

30

Fig. 1.9

Add to end of Figure legend:

Biomodeling/Theory+Data Image (The Logo) is reproduced here and in other chapters and back cover of this book with permission by the author Joseph DiStefano III.  It is a Trademark (TM) and service mark of the author, Copyright © 2012.

41

Quotes

Both quotes should be centered.

61

Example 2.21

Typo: In Example 2.21, last equation should have dv/da replaced by dv/dt

82

E2.3

Exercise 2.3 should begin with "Transform the equation in Exercise E2.1…."

119

Numbered bullets

Numbered bullets should be black, not red.

141

E3.8

In the 6th line, the last equation should read:

k1*=2k1  (lower case k)

149

Just above Example 4.2

Inline equation for VBLOOD should be inverted: .

158

Table 4.1

The title of Table 4.1 should be in boldface.

178

Last paragraph

“If this assumption... “  should not be indented.

239

Bullet 2.

“ks” inside the matrix brackets also should be caps, i.e. cap K11, K21 and K22 

245

Remark following

Eq. (5.41)

The “u” in u(t)should be boldface, reading as u(t).

265

Volume & Temperature Effects

Add another space between “V is” and

273

3rd paragraph

The “Km” in last sentence of the third paragraph should be italic Km

274

Eq. 6.40

Equation number (6.40) should be black, not red.

279

Eq. 6.46

Equation number (6.46) should be black, not red.

279

Eq. 6.46

At the end of the top equation, the minus sign should have a space after it, to separate it from the s.

291

1st paragraph

Fifth line from the top, the cursive “s” should be a non-cursive, italicized “s

300

Under Eq. 6.90

The following phrase should be bolded as well as italicized to read: 

the modern QSSA is simply: tC << tS.”

323

Eqs. 7.25 & 7.26

 (7.25) should have  and Eq. 7.26 third row should be:

0  1  1 -1  0   0.

333

Just above Eq. 7.30

The space between x1 and x2 should be smaller (they multiply).

355

Line 13

 “larger (volumetric) plasma...” should read “smaller (volumetric) plasma...”.

355

Line 16

Inline equation:  Fp = FB / (1 – Hct) should read:  Fp = FB(1 – Hct)

(i.e. no slash, multiplication, not division)

363

2nd remark

The last words of the last line should read “ from Blood or Plasma is cAFCardiac.”

The “X” “times” symbol is extraneous in this product of cA and FCardiac .

369

Fig. 8.8

The figure legend should read as follows (i.e. with more matching caps):

“Whole body PBTK model structure.  Left: PBTK model with rate constants (kij day-1) shown on arrows. Right: Same model structure, but with whole-body Mn distribution (% of total) and Mn compartment interchange rates as mass fluxes (μg Mn/day) shown on arrows. The olfactory submodel nodes: OLFACTORY EPITHELIUM 1 (EP1), OLFACTORY EPITHELIUM 2 (EP2) and OLFACTORY BULB (BULB) (boxed in); brain compartments: OLFACTORY submodel components + STRIATUM, CEREBELLUM and brain-resto/olfactory tract and tubercle (B-RESTO/OTT) (boxed in). Whole body components (nodes) include (lumped) CENTRAL + LUNG1 + BLOOD, LUNG2, (lumped) Rest-of-body (RESTO), and (lumped) PANCREAS/TESTES/KIDNEY (P-T-K), and LIVER, (gray).  EP2 and LUNG2 were needed to accommodate best 2-exponential fits to epithelium and lung data in preliminary analyses.  Exogenous inputs are u1 into EPI and u2 into CENTRAL + LUNG1 + BLOOD.

Measurements are from 8 of the 11 compartments, as shown.”

371

Eq. 8.19

The lambda symbols should be closer to the parentheses.

380

9 lines from bottom

AUCP should be AUCp

387

Last paragraph

In the second to last line, “complete dissolution” should read “incomplete dissolution.”

388

Relative bioavailability (RB) paragraph

There should be a comma after “same route” to read as follows:

Relative bioavailability (RB)of two different preparations (1 and 2) of the same drug, introduced via the same route, is defined as:

388

Bioequivalence paragraph

In the third line, BE should be italicized.

391

Fig. 8.17 legend

PR1 and PR2 should read “PR1” and “PR2” (matching the figure) respectively.

391

Eq. (8.46)

The Qs in (8.46) should both be lowercase.

396

Example 8.11

There should be spaces between each of the three equation lines.

428

Last sentence

The sentence beginning on the last line and continuing onto the next page, first two lines, should be fully deleted, i.e. delete the entire sentence starting with, “A mode, however, has a “shape” (eigenvector) as well as a “frequency” (eigenvalue) component, so it is represented more completely as a two-dimensional function … each with its own ... and eigenvector vj.”

429

1st paragraph

Shorten to: “ A most important feature of linear modes is that they are a minimal set of invariants of the dynamical system and, for any set of ICs or input(s), the modes accurately capture essential system dynamics.  Importantly, λj can be complex as well as real.”

431

E9.2 a)

[xeye]T should be corrected to read [xe ye]T  (space out).

432

E9.9

Another space should be added after ODEs:

437

2nd paragraph

In the last line, Kuo et al. should be corrected to Meshkat et al.

437

Fig. 10.1

In the figure legend, “y” should be in green, like in the figure.

442

3rd paragraph

4th line from the bottom, Kuo should be replaced with Meshkat.

444

Transfer Functions & SI

There should be no comma before (10.7) in last line.

451

First equation list

All equations should be aligned.

454

Eq. 10.60

Another space should be added before tє[t0, T]

456

Eq. 10.68

The third equation line from the bottom should be centered.

457

Eq. 10.70-10.75

There should be more line space separating each of these equations.

460

Line between Eq. 10.90 and 10.91

Add another space between kjj, and  j=2, ....

462

Above Fig 10.7

Delete the 2 or 3 extra spaces after the first “<” symbol, in all rows.

463

Top of the page

Ditto. i.e. delete the 2 or 3 extra spaces after the first “<” symbol, in all rows.

465

Eq. 10.100

Add more spaces after the comma, before t ≥ 0.

470

Fig 10.10 caption

Change “constrained” to “unconstrained”

471

Fig 10.11 caption

Change “unconstrained” to “constrained”

478

5th line from the bottom

Delete “a,b” in first reference and replace “Kuo” with “Meshkat” in second reference.

486

Kuo, C., Meshkat, N., ... reference

Reverse order of first two authors.

494

Example 11.3

Add more line space between the two equation lines.

497

1st sentence

x(t,p) should read x(t, p)

506

Example 11.7

RMS should be italicized in both places.

512

Fig. 11.7 caption

Figure legend should be deleted.

514

Fig. 11.9 caption

Figure legend should be deleted.

515

Fig. 11.10 caption

Figure legend should be deleted.

515

Fig. 11.11 caption

Figure legend should be deleted.

531

Eqs. 12.13 & 12.14

Add a space between pj and fj.

534

Eq. 12.26

Delete space between W and E in the middle of the equation.

534

Eq. 12.29

Add a space between z1(t2) and z2(t2)

535

Just above Eq. 12.32

Add a space between pP and a b c.

544

Just below Eq. 12.46

Subscript j should be italicized.

547

Example 12.5

p1 p2 p3 column headers should be moved slightly down.

549

First Remark

The parentheses in the Hessian matrix approximation equation should be larger, the same size as the contents.

549

Just below Eq. 12.52

Paragraph should be left justified.

549

Example 12.6

CORR should be italicized.

550

Eq. 12.53

This equation should all be colored dark green.

552

Blue header COV(p)

(p) should be italicized.

557

Von Neumann Quote

Should be centered.

592

E13.5

“50 units” should be replaced with “100%”

594

Kuo, C., Meshkat, N., ... reference

Reverse order of first two authors.

604

Table 14.1

4th equation should be indented like the next 4.

617

2nd line

Insert square brackets in front of - a and after the root sign, before the /

626

Last paragraph

Second and third lines, delete “presence of”.

627

Line 11

Delete comma after “consolidation”

669

Kuo, C., Meshkat, N., ... reference

Reverse order of first two authors

679

Table 16.1

Hij and SI (within column headers) should be italicized. Also, insert line separators between numbered equations.

682

Identifiability Analysis for Each Hij

Hij should be italicized.

683

Table 16.2

Table should read as attached file, including colors (and numbered 16.2, not 0.1).

687

Cutset Analysis Solution paragraph

Each red superscript B should be italicized.

687

Footnote

Replace “Kuo” with “Meshkat.”

689

2nd paragraph

Italicized “dependent parameters” and “independent parameters” should be just boldface, no italicized.

690

Blue section header

kji should be italicized.

694

Blue section header

F should be italicized.

697

Footnote 11

“Web site” should be one word.

700

Last paragraph

Kuo should be replaced with Meshkat.

704

Kuo, C., Meshkat, N., reference

Reverse order of first two authors

710

Eq. 17.5

Subscripts should all be aligned.

714

Just above Example 17.3

“web site” should be one word.

720

Blue section header

Add “(MPSA)” to end of the header.

725

Under title

Add TOC.

Transform methods .................... 725
Laplace Transform Representations and Solutions .................... 726
Two-Step Solutions .................... 726
Key Properties of the Laplace Transform (LT) & its Inverse (ILT) .................... 727
Short Table of Laplace Transform Pairs .................... 730
Laplace Transform Solution of Ordinary Differential Equations (ODEs) .................... 732
Partial Fraction Expansions .................... 735
References .................... 738

 

730

Example A.12

e-2t in the first step of the solution should be e-t.

732

Example A.15

Last line of example (at top), comma should be close to the 0, not next to t ≤ 1

736

Eq. A.25

Shorten space between first two parts of the equation.  Its a product.

740

Under title

Add TOC.

Matrices .................... 739
Vector Spaces (V.S.) .................... 742
Linear Equation Solutions .................... 742
Minimum Norm & Least Squares Pseudoinverse Solutions of Linear Equations .................... 743
Measures and Orthogonality .................... 743
Matrix Analysis .................... 744
Matrix Norms .................... 746
Matrix Calculus .................... 746
Computation of f(A), an Analytic Function of a Matrix .................... 748
Matrix Differential Equations .................... 753
Singular Value Decomposition (SVD) & Principal Component Analysis (PCA) .................... 754
Singular Value Decomposition (SVD) .................... 754
Principal Component Analysis (PCA) .................... 755
PCA from SVD .................... 756
Data Reduction &Geometric Interpretation .................... 756
References .................... 757

 

759

Under title

Add TOC.

Appendix C – INPUT-OUTPUT & STATE VARIABLE BIOSYSTEM MODELING: GOING DEEPER

Inputs & Outputs .................... 759
Dynamic Systems, Models and Causality .................... 759
Input-Output (Black-Box) Models .................... 759
Time-Invariance (TI) .................... 760
Continuous Linear System Input-Output Models .................... 761
Transfer Function (TF) Matrix for Linear TI Input-Output Models .................... 762
Structured State Variable Models .................... 763
State of a System S or Model M .................... 763
State Variable Models from Input-Output (I-O) Models .................... 763
Dynamic State Variable ODE Models for Continuous Systems .................... 764
Complete Dynamic System Models: Constrained Structures .................... 765
Linear TI State Variable Models .................... 766
Discrete-Time Dynamic System Models .................... 767
Discrete-Time Input-Output Models .................... 768
The Sampled or z-Transfer Function .................... 768
Discrete-Time State Variable Models .................... 769
Sampled Input-Output Transfer Function Matrix .................... 770
Composite Input-Output and State Variable Models .................... 770
Composite Input-Output Models .................... 770
Composite State Variable Models .................... 771
State Transition Matrix for Linear Dynamic Systems .................... 772
Input-Output Model Solutions .................... 772
State Variable Model Solutions .................... 773
The Adjoint Dynamic System .................... 775
Equivalent Dynamic Systems: Different Realizations of State Variable Models – Nonuniqueness Exposed .................... 776
Key Properties of Equivalent System Models .................... 777

Illustrative Example:  A 3-Compartment Dynamic System Model & Several Discretized Versions of It

.................... 778
Discretization and Sampled-Data Representations of the 3-Compartment Model .................... 779
Discretized ARMA Model with Impulse-Train Input .................... 782
Transforming Input-Output Data Models into State Variable Models: Generalized Model Building .................... 783
Time-Invariant Realizations .................... 784
SISO Models .................... 784
References .................... 786

 

779

Eq. C.78

Under the matrices, change “= cΓ11” to “=11” (upper to lower case gamma)

784

SISO Models – first sentence

Change “y = cTu” to “y = cTx

787

Under title

Add TOC.

Basic Concepts and Definitions .................... 787
Controllability .................... 787
Observability .................... 788
Observability and Controllability of Linear State Variable Models .................... 790
Linear Time-Varying Models .................... 790
Controllability Criterion .................... 792
Observability Criterion .................... 792
Linear Time-Invariant Models .................... 792
Practical Controllability and Observability Conditions .................... 793
Output Controllability .................... 795
Time-Invariant (TI) Models .................... 795
TI State Variable Models .................... 795
Output Function Controllability .................... 796
Reachability .................... 797
Constructibility .................... 799
Controllability and Observability with Constraints .................... 803
Positive Controllability .................... 803
Relative Controllability (Reachability) .................... 803
Conditional Controllability .................... 804
Structural Controllability and Observability .................... 804
Observability and Identifiability Relationships .................... 805
Controllability and Observability of Stochastic Models .................... 806
References .................... 807

 

787

1st line under Controllability

Change “iff” to “(iff)”

804

2nd paragraph

First letter of the last line of the second paragraph – change “N” to “N”.

809

Under title

Add TOC.

Realizations (Modeling Paradigms) .................... 809
The Canonical Decomposition Theorem .................... 810
How to Decompose a Model .................... 813
Controllability and Observability Tests Using Equivalent Models .................... 813
SISO Models .................... 817
MIMO Models .................... 818
Minimal State Variable (ODE) Models from Input-Output TFs (Data) .................... 820
Canonical State Variable (ODE) Models from Input-Output Models (Data) .................... 821
Observable and Controllable Canonical Forms from Arbitrary State Variable Models Using Equivalence Properties .................... 828
References .................... 832

 

811

In Other Words

Bold italic “In Other Words:”

833

Under title

Add TOC.

Additional Predictor-Corrector Algorithms .................... 833
Modified Euler 2nd-Order Predictor and Corrector Formulas .................... 833
An Iterative-Implicit Predictor-Corrector Algorithm .................... 834
Non-Iterative, Predictor-Modifier-Corrector (P-M-C) Algorithms .................... 834
A Predictor-Modifier Corrector Algorithm Exemplified .................... 835
The Backward-Euler Algorithm for Stiff ODEs .................... 836
Derivation of the Akaike Information Criterion (AIC) .................... 836
The AIC for Nonlinear Regression .................... 839
The Stochastic Fisher Information Matrix (FIM): Definitions & Derivations .................... 841
FIM for Multioutput Models .................... 842