Parameter Estimation and Uncertainty Quantification for Systems Biology Models

Eshan D. Mitra; William S. Hlavacek

arxiv: 1906.11365 · v1 · pith:JQ6UITFEnew · submitted 2019-06-26 · 🧬 q-bio.QM

Parameter Estimation and Uncertainty Quantification for Systems Biology Models

Eshan D. Mitra , William S. Hlavacek This is my paper

Pith reviewed 2026-05-25 14:32 UTC · model grok-4.3

classification 🧬 q-bio.QM

keywords parameter estimationuncertainty quantificationsystems biologymathematical modelingimmunoreceptor signalingprofile likelihoodBayesian inferencebootstrapping

0 comments

The pith

Mathematical models of immunoreceptor signaling need parameter estimation and uncertainty quantification to support reliable predictions.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper reviews methods and tools for fitting parameters in mathematical models of immune signaling and for measuring uncertainty in those fits. Models cannot deliver trustworthy quantitative forecasts about cellular responses without these steps. It examines gradient-based and gradient-free techniques for finding best-fit parameter values along with profile likelihood, bootstrapping, and Bayesian methods for uncertainty. The survey focuses on their use in systems-level studies of immune phenomena. A reader would care because unparameterized models limit insight into how cells process signals.

Core claim

Mathematical models can provide quantitative insight into immunoreceptor signaling, but require parameterization and uncertainty quantification before making reliable predictions. The paper reviews currently available methods and software tools to address these problems, including gradient-based and gradient-free methods for point estimation of parameter values and methods of profile likelihood, bootstrapping, and Bayesian inference for uncertainty quantification, while considering recent and potential future applications to systems-level modeling of immune-related phenomena.

What carries the argument

The reviewed suite of point-estimation methods (gradient-based and gradient-free) and uncertainty-quantification approaches (profile likelihood, bootstrapping, Bayesian inference) that convert raw models into tools capable of producing assessed predictions from data.

If this is right

Once parameters are estimated, models can generate concrete predictions about immune cell responses to stimuli.
Uncertainty methods identify which model predictions remain robust across plausible parameter ranges.
Software tools that implement these techniques lower the barrier to using models in immune research.
The same workflow supports iterative refinement of models as new data become available.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The reviewed methods could transfer to modeling in other cellular systems where data are similarly noisy.
Combining the uncertainty approaches with high-throughput data might expose which parameters most limit predictive power.
Automated pipelines that run estimation and uncertainty steps together could accelerate model-based hypothesis testing.

Load-bearing premise

The methods surveyed are applicable and sufficient for systems-level modeling of immune-related phenomena.

What would settle it

An application of the reviewed methods to a standard immunoreceptor model that yields inconsistent parameter values or unreliable uncertainty bounds when tested against independent experimental data.

Figures

Figures reproduced from arXiv: 1906.11365 by Eshan D. Mitra, William S. Hlavacek.

read the original abstract

Mathematical models can provide quantitative insight into immunoreceptor signaling, but require parameterization and uncertainty quantification before making reliable predictions. We review currently available methods and software tools to address these problems. We consider gradient-based and gradient-free methods for point estimation of parameter values, and methods of profile likelihood, bootstrapping, and Bayesian inference for uncertainty quantification. We consider recent and potential future applications of these methods to systems-level modeling of immune-related phenomena.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

A straightforward review of existing parameter estimation and UQ methods for systems biology models with no new techniques or results.

read the letter

This paper is a review that pulls together standard approaches to fitting parameters in mathematical models of immunoreceptor signaling and then quantifying the uncertainty in those fits. It covers gradient-based and gradient-free optimization for point estimates, followed by profile likelihood, bootstrapping, and Bayesian methods for uncertainty, along with mentions of software and some applications to immune-related modeling. The abstract states the scope clearly and the work stays within it. What it does well is organize these tools in one place with references, which can serve as a practical entry point for someone who needs to parameterize a model but is not already deep in the literature. The descriptions match what is commonly used in the field. Nothing here is new. The authors do not derive any method, run any comparison, or present a fresh result; they describe what already exists. That is fine for a review, but it means the paper adds no technical advance or reorganization of the material. The soft spots are limited. Coverage appears to stick to established techniques without obvious gaps in the listed categories, though a full read would be needed to check if recent developments in scalable Bayesian methods or high-dimensional identifiability are treated adequately. There are no equations or data to verify, so no issues of circularity or unsupported claims arise. The central point—that models require parameterization and uncertainty work before predictions are reliable—is correct and uncontroversial. This paper is mainly useful to systems biologists or modelers working on immune signaling who want a compact pointer to tools rather than a research contribution. A reader already familiar with the methods will not learn much new. It is the sort of piece that belongs in a methods-focused journal or as a methods reference, and it is coherent enough on its own terms to warrant sending out for peer review rather than desk rejection.

Referee Report

0 major / 2 minor

Summary. The paper reviews methods for parameter estimation (gradient-based and gradient-free optimization) and uncertainty quantification (profile likelihood, bootstrapping, and Bayesian inference) in systems biology models, with a focus on applications to immunoreceptor signaling and immune-related phenomena. It also surveys associated software tools and discusses recent and potential future uses of these approaches.

Significance. As a descriptive survey of established techniques, the manuscript could serve as a practical reference for systems biologists working on immune models, consolidating information on parameterization and UQ that is otherwise scattered across the literature. Its value depends on the breadth and accuracy of coverage rather than any new theoretical result.

minor comments (2)

[Abstract] Abstract: the scope statement could be sharpened to clarify whether the review is restricted to immunoreceptor models or extends more broadly to general systems biology.
Ensure that all cited software packages include version numbers or access dates to improve reproducibility of the recommendations.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their constructive review and recommendation of minor revision. Their summary correctly identifies the scope of the manuscript as a survey of parameter estimation and uncertainty quantification methods for systems biology models, with emphasis on immune-related applications. No specific major comments were provided in the report.

Circularity Check

0 steps flagged

Review paper with no derivations or predictions; no circularity

full rationale

The manuscript is explicitly a literature review of existing methods (gradient-based/free point estimation; profile likelihood, bootstrapping, Bayesian UQ) and software tools for systems biology parameterization. No new equations, theorems, predictions, or deductive chains are advanced that could reduce to inputs by construction. No self-citation load-bearing steps exist because the paper advances no central premise requiring external justification beyond description of published techniques. The content is self-contained as a survey and carries no circularity burden under the enumerated patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

This is a review paper that summarizes previously published methods; it introduces no free parameters, axioms, or invented entities of its own.

pith-pipeline@v0.9.0 · 5588 in / 902 out tokens · 20711 ms · 2026-05-25T14:32:00.637930+00:00 · methodology

discussion (0)

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

Overcoming Selection Bias in Statistical Studies With Amortized Bayesian Inference
stat.ML 2026-04 unverdicted novelty 6.0

Embedding selection mechanisms into generative simulators enables amortized Bayesian inference to produce debiased, well-calibrated posteriors without tractable likelihoods.

Reference graph

Works this paper leans on

79 extracted references · 79 canonical work pages · cited by 1 Pith paper · 4 internal anchors

[1]

R. J. Brownlie, R. Zamoyska, T cell receptor signalling networks: branched, diversiﬁed and bounded., Nature reviews. Immunology 1 3 (2013) 257–269

work page 2013
[2]

J. M. Dal Porto, S. B. Gauld, K. T. Merrell, D. Mills, A. E. Pugh- Bernard, J. Cambier, B cell antigen receptor signaling 101., Molecula r immunology 41 (2004) 599–613

work page 2004
[3]

Rivera, A

J. Rivera, A. M. Gilﬁllan, Molecular regulation of mast cell activation ., The Journal of allergy and clinical immunology 117 (2006) 1214–1225

work page 2006
[4]

Y. T. Lin, N. E. Buchler, Accelerated Bayesian inference of gene ex- pression models from snapshots of single-cell transcripts, arXiv ( 2018) 1812.02911

work page internal anchor Pith review Pith/arXiv arXiv 2018
[5]

Hoops, R

S. Hoops, R. Gauges, C. Lee, J. Pahle, N. Simus, M. Singhal, L. Xu , P. Mendes, U. Kummer, COPASI - A COmplex PAthway SImulator, Bioinformatics 22 (2006) 3067–3074

work page 2006
[6]

A. Raue, B. Steiert, M. Schelker, C. Kreutz, T. Maiwald, H. Hass , J. Vanlier, C. T¨ onsing, L. Adlung, R. Engesser, W. Mader, T. Heine - mann, J. Hasenauer, M. Schilling, T. H¨ ofer, E. Klipp, F. Theis, U. Klingm¨ uller, B. Sch¨ oberl, J. Timmer, Data2Dynamics: A model- ing environment tailored to parameter estimation in dynamical syste ms, Bioinformatic...

work page 2015
[7]

Fr¨ ohlich, C

F. Fr¨ ohlich, C. Loos, J. Hasenauer, Scalable Inference of Ord inary Dif- ferential Equation Models of Biochemical Processes, in: G. Sanguin etti, V. A. Huynh-Thu (Eds.), Gene Regulatory Networks: Methods and Protocols, Springer, New York, 2019, pp. 385–422

work page 2019
[8]

E. D. Mitra, R. Suderman, J. Colvin, A. Ionkov, A. Hu, H. M. Saur o, R. G. Posner, W. S. Hlavacek, PyBioNetFit and the Biological Proper ty Speciﬁcation Language, arXiv (2019) 1903.07750

work page internal anchor Pith review Pith/arXiv arXiv 2019
[9]

B. M. Gyori, J. A. Bachman, K. Subramanian, J. L. Muhlich, L. Gale scu, P. K. Sorger, From word models to executable models of signaling net - works using automated assembly, Molecular Systems Biology 13 (201 7) 954

work page
[10]

P. V. Todorov, B. M. Gyori, J. A. Bachman, K. Peter, INDRA-I PM : interactive pathway modeling using natural language with automat ed assembly, Bioinformatics (2019) doi:10.1093/bioinformatics/btz28 9

work page doi:10.1093/bioinformatics/btz28 2019
[11]

J. R. Faeder, M. L. Blinov, W. S. Hlavacek, Rule-based modeling o f biochemical systems with BioNetGen, Methods in Molecular Biology 500 (2009) 113–167

work page 2009
[12]

L. A. Chylek, L. A. Harris, C.-S. Tung, J. R. Faeder, C. F. Lope z, W. S. Hlavacek, Rule-based modeling: a computational approach fo r studying biomolecular site dynamics in cell signaling systems, Wiley Interdisciplinary Reviews: Systems Biology and Medicine 6 (2013) 13– 36

work page 2013
[13]

Hucka, A

M. Hucka, A. Finney, H. M. Sauro, H. Bolouri, J. C. Doyle, H. Kita no, A. P. Arkin, B. J. Bornstein, D. Bray, A. Cornish-Bowden, A. A. Cu el- lar, S. Dronov, E. D. Gilles, M. Ginkel, V. Gor, I. I. Goryanin, W. J. Hedley, T. C. Hodgman, J.-H. Hofmeyr, P. J. Hunter, N. S. Juty, J . L. Kasberger, A. Kremling, U. Kummer, N. Le Nov` ere, L. M. Loew, D. Lu- cio...

work page 2003
[14]

Hucka, F

M. Hucka, F. T. Bergmann, S. Hoops, S. M. Keating, S. Sahle, J . C. Schaﬀ, L. P. Smith, D. J. Wilkinson, The Systems Biology Markup Language (SBML): Language Speciﬁcation for Level 3 Version 1 Co re., Journal of integrative bioinformatics 12 (2015) 266

work page 2015
[15]

Zhang, M

F. Zhang, M. Meier-Schellersheim, SBML Level 3 package: Multis tate, Multicomponent and Multicompartment Species, Version 1, Release 1 , Journal of Integrative Bioinformatics 15 (2018) 20170077

work page 2018
[16]

L. A. Harris, J. S. Hogg, J.-J. Tapia, J. A. P. Sekar, S. Gupta, I. Korsun- sky, A. Arora, D. Barua, R. P. Sheehan, J. R. Faeder, BioNetGen 2.2: Advances in rule-based modeling, Bioinformatics 32 (2016) 3366–33 68

work page 2016
[17]

Le Nov` ere, B

N. Le Nov` ere, B. Bornstein, A. Broicher, M. Courtot, M. Don izelli, H. Dharuri, L. Li, H. Sauro, M. Schilstra, B. Shapiro, J. L. Snoep, M. Hucka, BioModels Database: a free, centralized database of cu rated, published, quantitative kinetic models of biochemical and cellular sys- tems., Nucleic Acids Research 34 (2006) D689–D691

work page 2006
[18]

D. T. Gillespie, Stochastic Simulation of Chemical Kinetics, Annual Review of Physical Chemistry 58 (2006) 35–55

work page 2006
[19]

Suderman, E

R. Suderman, E. D. Mitra, Y. T. Lin, K. E. Erickson, S. Feng, W. S. Hlavacek, Generalizing Gillespie’s direct method to enable network-free simulations, Bulletin of Mathematical Biology (2018) doi:10.1007/s11538–018–0418–2

work page doi:10.1007/s11538 2018
[20]

M. W. Sneddon, J. R. Faeder, T. Emonet, Eﬃcient modeling, simu la- tion and coarse-graining of biological complexity with NFsim, Nature Methods 8 (2011) 177–183

work page 2011
[21]

J. J. Mor´ e, The Levenberg-Marquardt Algorithm: Implement ation and Theory, in: Numerical Analysis, Springer Berlin Heidelberg, 1978, pp . 105–116

work page 1978
[22]

R. Byrd, P. Lu, J. Nocedal, C. Zhu, A Limited Memory Algorithm fo r Bound Constrained Optimization, SIAM Journal on Scientiﬁc Comput - ing 16 (1995) 1190–1208

work page 1995
[23]

Sengupta, K

B. Sengupta, K. J. Friston, W. D. Penny, Eﬃcient gradient com putation for dynamical models, NeuroImage 98 (2014) 521–527. 17

work page 2014
[24]

A. Raue, M. Schilling, J. Bachmann, A. Matteson, M. Schelke, D. Kaschek, S. Hug, C. Kreutz, B. D. Harms, F. J. Theis, U. Klingm¨ uller, J. Timmer, Lessons learned from quantitative dynam i- cal modeling in systems biology, PLOS ONE 8 (2013) e74335

work page 2013
[25]

H. Hass, C. Loos, E. R. Alvarez, J. Timmer, J. Hasenauer, C. K reutz, Benchmark problems for dynamic modeling of intracellular processes , Bioinformatics (2019) doi:10.1093/bioinformatics/btz020

work page doi:10.1093/bioinformatics/btz020 2019
[26]

V. Raia, M. Schilling, M. B¨ ohm, B. Hahn, A. Kowarsch, A. Raue, C. Sticht, S. Bohl, M. Saile, P. M¨ oller, N. Gretz, J. Timmer, F. Theis, W. D. Lehmann, P. Lichter, U. Klingm¨ uller, Dynamic mathematical modeling of IL13-induced signaling in Hodgkin and primary mediasti- nal B-cell lymphoma allows prediction of therapeutic targets, Canc er Research 71 (2...

work page 2011
[27]

Crauste, J

F. Crauste, J. Maﬁlle, L. Boucinha, S. Djebali, O. Gandrillon, J. M arvel, C. Arpin, Identiﬁcation of Nascent Memory CD8 T Cells and Modeling of Their Ontogeny, Cell Systems 4 (2017) 306–317.e4

work page 2017
[28]

A. C. Hindmarsh, P. N. Brown, K. E. Grant, S. L. Lee, R. Serba n, D. E. Shumaker, C. S. Woodward, SUNDIALS: Suite of Nonlinear and Diﬀer - ential/Algebraic Equation Solvers, ACM Transactions on Mathematic al Software 31 (2005) 363–396

work page 2005
[29]

Fr¨ ohlich, T

F. Fr¨ ohlich, T. Kessler, D. Weindl, A. Shadrin, L. Schmiester, H . Hache, A. Muradyan, M. Sch¨ utte, J.-H. Lim, M. Heinig, F. J. Theis, H. Lehrach, C. Wierling, B. Lange, J. Hasenauer, Eﬃcient Parameter Estimation En- ables the Prediction of Drug Response Using a Mechanistic Pan-Canc er Pathway Model, Cell Systems 7 (2018) 567–579.e6

work page 2018
[30]

A. G. Baydin, B. A. Pearlmutter, A. A. Radul, J. M. Siskind, Auto - matic diﬀerentiation in machine learning: a survey, Journal of March ine Learning Research 18 (2018) 1–43

work page 2018
[31]

The Stan Math Library: Reverse-Mode Automatic Differentiation in C++

B. Carpenter, M. D. Hoﬀman, M. Brubaker, D. Lee, P. Li, M. Be tan- court, The Stan Math Library: Reverse-Mode Automatic Diﬀerent iation in C++, arXiv (2015) 1509.07164. 18

work page internal anchor Pith review Pith/arXiv arXiv 2015
[32]

Carpenter, A

B. Carpenter, A. Gelman, M. D. Hoﬀman, D. Lee, B. Goodrich, M . Be- tancourt, M. Brubaker, J. Guo, P. Li, A. Riddell, Stan: A Probabilist ic Programming Language, Journal of Statistical Software 76 (201 7)

work page
[33]

Rackauckas, Y

C. Rackauckas, Y. Ma, V. Dixit, X. Guo, M. Innes, J. Revels, J. Nyberg, V. Ivaturi, A Comparison of Automatic Diﬀerentiation and Continuou s Sensitivity Analysis for Derivatives of Diﬀerential Equation Solutions , arXiv (2018) 1812.01892

work page arXiv 2018
[34]

A. H. Gandomi, X.-S. Yang, S. Talatahari, A. H. Alavi, Metaheuris tic algorithms in modeling and optimization, in: A. H. Gandomi, X.-S. Yang, S. Talatahari, A. H. Alavi (Eds.), Metaheuristic Applications in Structures and Infrastructures, Elsevier, Amsterdam, 2013, pp. 1–24

work page 2013
[35]

Storn, K

R. Storn, K. Price, Diﬀerential evolution - A simple and eﬃcient he uris- tic for global optimization over continuous spaces, Journal of Glob al Optimization 11 (1997) 341–359

work page 1997
[36]

Glover, M

F. Glover, M. Laguna, R. Mart ´ ı, Fundamentals of scatter sea rch and path relinking, Control and Cybernetics 29 (2000) 652–684

work page 2000
[37]

Eberhart, J

R. Eberhart, J. Kennedy, A new optimizer using particle swarm t heory, in: MHS’95. Proceedings of the Sixth International Symposium on Mic ro Machine and Human Science, IEEE, 1995, pp. 39–43

work page 1995
[38]

Kirkpatrick, C

S. Kirkpatrick, C. D. Gellat, M. P. Vecchi, Optimization by Simulate d Annealing, Science 220 (1983) 671–680

work page 1983
[39]

D. R. Penas, J. R. Banga, P. Gonz´ alez, R. Doallo, Enhanced pa rallel diﬀerential evolution algorithm for problems in computational syste ms biology, Applied Soft Computing 33 (2015) 86–99

work page 2015
[40]

A. O. S. Moraes, J. F. Mitre, P. L. C. Lage, A. R. Secchi, A robu st parallel algorithm of the particle swarm optimization method for large dimensional engineering problems, Applied Mathematical Modelling 39 (2015) 4223–4241

work page 2015
[41]

D. R. Penas, P. Gonz´ alez, J. A. Egea, R. Doallo, J. R. Banga, P arameter estimation in large-scale systems biology models: a parallel and self- adaptive cooperative strategy, BMC Bioinformatics 18 (2017) 52. 19

work page 2017
[42]

L. A. Chylek, V. Akimov, J. Dengjel, K. T. G. Rigbolt, B. Hu, W. S. Hlavacek, B. Blagoev, Phosphorylation site dynamics of early T-cell receptor signaling, PLOS ONE 9 (2014) e104240

work page 2014
[43]

J. A. Egea, E. Balsa-Canto, M.-S. G. Garc ´ ıa, J. R. Banga, Dynamic opti- mization of nonlinear processes with an enhanced scatter search m ethod, Industrial & Engineering Chemistry Research 48 (2009) 4388–440 1

work page 2009
[44]

A. F. Villaverde, F. Fr¨ olich, D. Weindl, J. Hasenauer, J. R. Bang a, Benchmarking optimization methods for parameter estimation in larg e kinetic models, Bioinformatics 35 (2019) 830–838

work page 2019
[45]

J. A. Nelder, R. Mead, A simplex method for function minimization, The Computer Journal 7 (1965) 308–313

work page 1965
[46]

D. Lee, M. Wiswall, A parallel implementation of the simplex function minimization routine, Computational Economics 30 (2007) 171–187

work page 2007
[47]

K. C. Chen, A. Csikasz-Nagy, B. Gyorﬀy, J. Val, B. Novak, J. J . Tyson, Kinetic analysis of a molecular model of the budding yeast cell cycle, Molecular Biology of the Cell 11 (2000) 369–391

work page 2000
[48]

K. C. Chen, L. Calzone, A. Csikasz-Nagy, F. R. Cross, B. Nova k, J. J. Tyson, Integrative analysis of cell cycle control in budding yeast, Molec- ular Biology of the Cell 15 (2004) 3841–3862

work page 2004
[49]

C. Oguz, T. Laomettachit, K. C. Chen, L. T. Watson, W. T. Bau mann, J. J. Tyson, Optimization and model reduction in the high dimensional parameter space of a budding yeast cell cycle model, BMC Systems Biology 7 (2013) 53

work page 2013
[50]

Pargett, D

M. Pargett, D. M. Umulis, Quantitative model analysis with divers e bio- logical data: Applications in developmental pattern formation, Met hods 62 (2013) 56–67

work page 2013
[51]

Pargett, A

M. Pargett, A. E. Rundell, G. T. Buzzard, D. M. Umulis, Model-ba sed analysis for qualitative data: An application in Drosophila germline stem cell regulation, PLOS Computational Biology 10 (2014) e10034 98

work page 2014
[52]

E. D. Mitra, R. Dias, R. G. Posner, W. S. Hlavacek, Using both qu al- itative and quantitative data in parameter identiﬁcation for system s biology models, Nature Communications 9 (2018) 3901. 20

work page 2018
[53]

A. E. Smith, D. W. Coit, Penalty functions, in: T. Baeck, D. Foge l, Z. Michalewicz (Eds.), Handbook of Evolutionary Computation, Oxfo rd University Press, New York, 1997

work page 1997
[54]

Harmon, L

B. Harmon, L. A. Chylek, Y. Liu, E. D. Mitra, A. Mahajan, E. A. Saada, B. R. Schudel, D. A. Holowka, B. A. Baird, B. S. Wilson, W. S. Hlavacek, A. K. Singh, Timescale separation of positive and negative signaling creates history-dependent responses to IgE receptor stimula- tion, Scientiﬁc Reports 7 (2017) 15586

work page 2017
[55]

Kreutz, A

C. Kreutz, A. Raue, D. Kaschek, J. Timmer, Proﬁle likelihood in sy s- tems biology, FEBS Journal 280 (2013) 2564–2571

work page 2013
[56]

Kreutz, A

C. Kreutz, A. Raue, J. Timmer, Likelihood based observability an al- ysis and conﬁdence intervals for predictions of dynamic models, BMC Systems Biology 6 (2012)

work page 2012
[57]

H. Hass, C. Kreutz, J. Timmer, D. Kaschek, Fast integration- based pre- diction bands for ordinary diﬀerential equation models, Bioinformat ics 32 (2016) 1204–1210

work page 2016
[58]

Kaschek, W

D. Kaschek, W. Mader, M. Fehling-Kaschek, M. Rosenblatt, J. Timmer, Dynamic Modeling, Parameter Estimation, and Uncertainty Analysis in R, Journal of Statistical Software 88 (2019)

work page 2019
[59]

G. H. Givens, J. A. Hoeting, Bootstrapping, in: Computational Statis- tics, John Wiley & Sons, 2nd edition, 2013, pp. 287–321

work page 2013
[60]

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numer- ical Recipes 3rd Edition: The Art of Scientiﬁc Computing, Cambridge University Press, Cambridge, 2007

work page 2007
[61]

S. Chib, E. Greenberg, Understanding the Metropolis-Hasting s Algo- rithm, The American Statistician 49 (1995) 327–335

work page 1995
[62]

D. J. Earl, M. W. Deem, Parallel tempering: Theory, applications , and new perspectives, Physical Chemistry Chemical Physics 7 (2005) 3 910

work page 2005
[63]

A Conceptual Introduction to Hamiltonian Monte Carlo

M. Betancourt, A Conceptual Introduction to Hamiltonian Mon te Carlo, arXiv (2017) 1701.02434. 21

work page internal anchor Pith review Pith/arXiv arXiv 2017
[64]

Gelman, D

A. Gelman, D. B. Rubin, Inference from Iterative Simulation Usin g Multiple Sequences, Statistical Science 7 (1992) 457–511

work page 1992
[65]

Vehtari, A

A. Vehtari, A. Gelman, D. Simpson, B. Carpenter, P.-C. B¨ urkner, Rank- normalization, folding, and localization: An improved R for assessing convergence of MCMC, arXiv (2019) 1903.08008

work page arXiv 2019
[66]

R. M. Neal, MCMC using Hamiltonian dynamics, arXiv (2012) 1206.1901

work page arXiv 2012
[67]

M. D. Hoﬀman, A. Gelman, The No-U-Turn Sampler: Adaptively Se t- ting Path Lengths in Hamiltonian Monte Carlo, Journal of Machine Learning Research 15 (2014) 1593–1623

work page 2014
[68]

Bales, A

B. Bales, A. Pourzanjani, A. Vehtari, L. Petzold, Selecting the Metric in Hamiltonian Monte Carlo, arXiv (2019) 1905.11916

work page arXiv 2019
[69]

J. K. Medley, A. P. Goldberg, J. R. Karr, Guidelines for reprodu cibly building and simulating systems biology models, IEEE Transactions on Biomedical Engineering 63 (2016) 2015–2020

work page 2016
[70]

Waltemath, O

D. Waltemath, O. Wolkenhauer, How modeling standards, softw are, and initiatives support reproducibility in systems biology and systems medicine, IEEE Transactions on Biomedical Engineering 63 (2016) 1999–2006

work page 2016
[71]

F. T. Bergmann, S. Hoops, B. Klahn, U. Kummer, P. Mendes, J. Pahle, S. Sahle, COPASI and its applications in biotechnology, Journal of Biotechnology 261 (2017) 215–220

work page 2017
[72]

Fr¨ ohlich, B

F. Fr¨ ohlich, B. Kaltenbacher, F. J. Theis, J. Hasenauer, Sca lable Pa- rameter Estimation for Genome-Scale Biochemical Reaction Networ ks, PLoS Computational Biology 13 (2017) e1005331

work page 2017
[73]

C. F. Lopez, J. L. Muhlich, J. A. Bachman, P. K. Sorger, Progr amming biological models in Python using PySB, Molecular Systems Biology 9 (2013) 646

work page 2013
[74]

J. A. Egea, D. Henriques, T. Cokelaer, A. F. Villaverde, A. MacN amara, D.-P. Danciu, J. R. Banga, J. Saez-Rodriguez, MEIGO: An open-so urce software suite based on metaheuristics for global optimization in sy stems biology and bioinformatics, BMC Bioinformatics 15 (2014) 136. 22

work page 2014
[75]

Eydgahi, W

H. Eydgahi, W. W. Chen, J. L. Muhlich, D. Vitkup, J. N. Tsitsiklis, P. K. Sorger, Properties of cell death models calibrated and compa red using Bayesian approaches, Molecular Systems Biology 9 (2013)

work page 2013
[76]

Stapor, D

P. Stapor, D. Weindl, B. Ballnus, S. Hug, C. Loos, A. Fiedler, S. K rause, S. Hroß, F. Fr¨ ohlich, J. Hasenauer, PESTO: Parameter EStimatio n TOolbox, Bioinformatics 34 (2018) 705–707

work page 2018
[77]

Kerketta, ´A

R. Kerketta, ´A. M. Hal´ asz, M. P. Steinkamp, B. S. Wilson, J. S. Ed- wards, Eﬀect of Spatial Inhomogeneities on the Membrane Surfac e on Receptor Dimerization and Signal Initiation, Frontiers in Cell and De- velopmental Biology 4 (2016)

work page 2016
[78]

S. S. Andrews, N. J. Addy, R. Brent, A. P. Arkin, Detailed simula tions of cell biology with Smoldyn 2.1, PLoS Computational Biology 6 (2010) e1000705

work page 2010
[79]

R. A. Kerr, T. M. Bartol, B. Kaminsky, M. Dittrich, J.-C. J. Chan g, S. B. Baden, T. J. Sejnowski, J. R. Stiles, Fast Monte Carlo Simulatio n Methods for Biological Reaction-Diﬀusion Systems in Solution and on Surfaces, SIAM Journal on Scientiﬁc Computing 30 (2008) 3126–3 149. 23

work page 2008

[1] [1]

R. J. Brownlie, R. Zamoyska, T cell receptor signalling networks: branched, diversiﬁed and bounded., Nature reviews. Immunology 1 3 (2013) 257–269

work page 2013

[2] [2]

J. M. Dal Porto, S. B. Gauld, K. T. Merrell, D. Mills, A. E. Pugh- Bernard, J. Cambier, B cell antigen receptor signaling 101., Molecula r immunology 41 (2004) 599–613

work page 2004

[3] [3]

Rivera, A

J. Rivera, A. M. Gilﬁllan, Molecular regulation of mast cell activation ., The Journal of allergy and clinical immunology 117 (2006) 1214–1225

work page 2006

[4] [4]

Y. T. Lin, N. E. Buchler, Accelerated Bayesian inference of gene ex- pression models from snapshots of single-cell transcripts, arXiv ( 2018) 1812.02911

work page internal anchor Pith review Pith/arXiv arXiv 2018

[5] [5]

Hoops, R

S. Hoops, R. Gauges, C. Lee, J. Pahle, N. Simus, M. Singhal, L. Xu , P. Mendes, U. Kummer, COPASI - A COmplex PAthway SImulator, Bioinformatics 22 (2006) 3067–3074

work page 2006

[6] [6]

A. Raue, B. Steiert, M. Schelker, C. Kreutz, T. Maiwald, H. Hass , J. Vanlier, C. T¨ onsing, L. Adlung, R. Engesser, W. Mader, T. Heine - mann, J. Hasenauer, M. Schilling, T. H¨ ofer, E. Klipp, F. Theis, U. Klingm¨ uller, B. Sch¨ oberl, J. Timmer, Data2Dynamics: A model- ing environment tailored to parameter estimation in dynamical syste ms, Bioinformatic...

work page 2015

[7] [7]

Fr¨ ohlich, C

F. Fr¨ ohlich, C. Loos, J. Hasenauer, Scalable Inference of Ord inary Dif- ferential Equation Models of Biochemical Processes, in: G. Sanguin etti, V. A. Huynh-Thu (Eds.), Gene Regulatory Networks: Methods and Protocols, Springer, New York, 2019, pp. 385–422

work page 2019

[8] [8]

E. D. Mitra, R. Suderman, J. Colvin, A. Ionkov, A. Hu, H. M. Saur o, R. G. Posner, W. S. Hlavacek, PyBioNetFit and the Biological Proper ty Speciﬁcation Language, arXiv (2019) 1903.07750

work page internal anchor Pith review Pith/arXiv arXiv 2019

[9] [9]

B. M. Gyori, J. A. Bachman, K. Subramanian, J. L. Muhlich, L. Gale scu, P. K. Sorger, From word models to executable models of signaling net - works using automated assembly, Molecular Systems Biology 13 (201 7) 954

work page

[10] [10]

P. V. Todorov, B. M. Gyori, J. A. Bachman, K. Peter, INDRA-I PM : interactive pathway modeling using natural language with automat ed assembly, Bioinformatics (2019) doi:10.1093/bioinformatics/btz28 9

work page doi:10.1093/bioinformatics/btz28 2019

[11] [11]

J. R. Faeder, M. L. Blinov, W. S. Hlavacek, Rule-based modeling o f biochemical systems with BioNetGen, Methods in Molecular Biology 500 (2009) 113–167

work page 2009

[12] [12]

L. A. Chylek, L. A. Harris, C.-S. Tung, J. R. Faeder, C. F. Lope z, W. S. Hlavacek, Rule-based modeling: a computational approach fo r studying biomolecular site dynamics in cell signaling systems, Wiley Interdisciplinary Reviews: Systems Biology and Medicine 6 (2013) 13– 36

work page 2013

[13] [13]

Hucka, A

M. Hucka, A. Finney, H. M. Sauro, H. Bolouri, J. C. Doyle, H. Kita no, A. P. Arkin, B. J. Bornstein, D. Bray, A. Cornish-Bowden, A. A. Cu el- lar, S. Dronov, E. D. Gilles, M. Ginkel, V. Gor, I. I. Goryanin, W. J. Hedley, T. C. Hodgman, J.-H. Hofmeyr, P. J. Hunter, N. S. Juty, J . L. Kasberger, A. Kremling, U. Kummer, N. Le Nov` ere, L. M. Loew, D. Lu- cio...

work page 2003

[14] [14]

Hucka, F

M. Hucka, F. T. Bergmann, S. Hoops, S. M. Keating, S. Sahle, J . C. Schaﬀ, L. P. Smith, D. J. Wilkinson, The Systems Biology Markup Language (SBML): Language Speciﬁcation for Level 3 Version 1 Co re., Journal of integrative bioinformatics 12 (2015) 266

work page 2015

[15] [15]

Zhang, M

F. Zhang, M. Meier-Schellersheim, SBML Level 3 package: Multis tate, Multicomponent and Multicompartment Species, Version 1, Release 1 , Journal of Integrative Bioinformatics 15 (2018) 20170077

work page 2018

[16] [16]

L. A. Harris, J. S. Hogg, J.-J. Tapia, J. A. P. Sekar, S. Gupta, I. Korsun- sky, A. Arora, D. Barua, R. P. Sheehan, J. R. Faeder, BioNetGen 2.2: Advances in rule-based modeling, Bioinformatics 32 (2016) 3366–33 68

work page 2016

[17] [17]

Le Nov` ere, B

N. Le Nov` ere, B. Bornstein, A. Broicher, M. Courtot, M. Don izelli, H. Dharuri, L. Li, H. Sauro, M. Schilstra, B. Shapiro, J. L. Snoep, M. Hucka, BioModels Database: a free, centralized database of cu rated, published, quantitative kinetic models of biochemical and cellular sys- tems., Nucleic Acids Research 34 (2006) D689–D691

work page 2006

[18] [18]

D. T. Gillespie, Stochastic Simulation of Chemical Kinetics, Annual Review of Physical Chemistry 58 (2006) 35–55

work page 2006

[19] [19]

Suderman, E

R. Suderman, E. D. Mitra, Y. T. Lin, K. E. Erickson, S. Feng, W. S. Hlavacek, Generalizing Gillespie’s direct method to enable network-free simulations, Bulletin of Mathematical Biology (2018) doi:10.1007/s11538–018–0418–2

work page doi:10.1007/s11538 2018

[20] [20]

M. W. Sneddon, J. R. Faeder, T. Emonet, Eﬃcient modeling, simu la- tion and coarse-graining of biological complexity with NFsim, Nature Methods 8 (2011) 177–183

work page 2011

[21] [21]

J. J. Mor´ e, The Levenberg-Marquardt Algorithm: Implement ation and Theory, in: Numerical Analysis, Springer Berlin Heidelberg, 1978, pp . 105–116

work page 1978

[22] [22]

R. Byrd, P. Lu, J. Nocedal, C. Zhu, A Limited Memory Algorithm fo r Bound Constrained Optimization, SIAM Journal on Scientiﬁc Comput - ing 16 (1995) 1190–1208

work page 1995

[23] [23]

Sengupta, K

B. Sengupta, K. J. Friston, W. D. Penny, Eﬃcient gradient com putation for dynamical models, NeuroImage 98 (2014) 521–527. 17

work page 2014

[24] [24]

A. Raue, M. Schilling, J. Bachmann, A. Matteson, M. Schelke, D. Kaschek, S. Hug, C. Kreutz, B. D. Harms, F. J. Theis, U. Klingm¨ uller, J. Timmer, Lessons learned from quantitative dynam i- cal modeling in systems biology, PLOS ONE 8 (2013) e74335

work page 2013

[25] [25]

H. Hass, C. Loos, E. R. Alvarez, J. Timmer, J. Hasenauer, C. K reutz, Benchmark problems for dynamic modeling of intracellular processes , Bioinformatics (2019) doi:10.1093/bioinformatics/btz020

work page doi:10.1093/bioinformatics/btz020 2019

[26] [26]

V. Raia, M. Schilling, M. B¨ ohm, B. Hahn, A. Kowarsch, A. Raue, C. Sticht, S. Bohl, M. Saile, P. M¨ oller, N. Gretz, J. Timmer, F. Theis, W. D. Lehmann, P. Lichter, U. Klingm¨ uller, Dynamic mathematical modeling of IL13-induced signaling in Hodgkin and primary mediasti- nal B-cell lymphoma allows prediction of therapeutic targets, Canc er Research 71 (2...

work page 2011

[27] [27]

Crauste, J

F. Crauste, J. Maﬁlle, L. Boucinha, S. Djebali, O. Gandrillon, J. M arvel, C. Arpin, Identiﬁcation of Nascent Memory CD8 T Cells and Modeling of Their Ontogeny, Cell Systems 4 (2017) 306–317.e4

work page 2017

[28] [28]

A. C. Hindmarsh, P. N. Brown, K. E. Grant, S. L. Lee, R. Serba n, D. E. Shumaker, C. S. Woodward, SUNDIALS: Suite of Nonlinear and Diﬀer - ential/Algebraic Equation Solvers, ACM Transactions on Mathematic al Software 31 (2005) 363–396

work page 2005

[29] [29]

Fr¨ ohlich, T

F. Fr¨ ohlich, T. Kessler, D. Weindl, A. Shadrin, L. Schmiester, H . Hache, A. Muradyan, M. Sch¨ utte, J.-H. Lim, M. Heinig, F. J. Theis, H. Lehrach, C. Wierling, B. Lange, J. Hasenauer, Eﬃcient Parameter Estimation En- ables the Prediction of Drug Response Using a Mechanistic Pan-Canc er Pathway Model, Cell Systems 7 (2018) 567–579.e6

work page 2018

[30] [30]

A. G. Baydin, B. A. Pearlmutter, A. A. Radul, J. M. Siskind, Auto - matic diﬀerentiation in machine learning: a survey, Journal of March ine Learning Research 18 (2018) 1–43

work page 2018

[31] [31]

The Stan Math Library: Reverse-Mode Automatic Differentiation in C++

B. Carpenter, M. D. Hoﬀman, M. Brubaker, D. Lee, P. Li, M. Be tan- court, The Stan Math Library: Reverse-Mode Automatic Diﬀerent iation in C++, arXiv (2015) 1509.07164. 18

work page internal anchor Pith review Pith/arXiv arXiv 2015

[32] [32]

Carpenter, A

B. Carpenter, A. Gelman, M. D. Hoﬀman, D. Lee, B. Goodrich, M . Be- tancourt, M. Brubaker, J. Guo, P. Li, A. Riddell, Stan: A Probabilist ic Programming Language, Journal of Statistical Software 76 (201 7)

work page

[33] [33]

Rackauckas, Y

C. Rackauckas, Y. Ma, V. Dixit, X. Guo, M. Innes, J. Revels, J. Nyberg, V. Ivaturi, A Comparison of Automatic Diﬀerentiation and Continuou s Sensitivity Analysis for Derivatives of Diﬀerential Equation Solutions , arXiv (2018) 1812.01892

work page arXiv 2018

[34] [34]

A. H. Gandomi, X.-S. Yang, S. Talatahari, A. H. Alavi, Metaheuris tic algorithms in modeling and optimization, in: A. H. Gandomi, X.-S. Yang, S. Talatahari, A. H. Alavi (Eds.), Metaheuristic Applications in Structures and Infrastructures, Elsevier, Amsterdam, 2013, pp. 1–24

work page 2013

[35] [35]

Storn, K

R. Storn, K. Price, Diﬀerential evolution - A simple and eﬃcient he uris- tic for global optimization over continuous spaces, Journal of Glob al Optimization 11 (1997) 341–359

work page 1997

[36] [36]

Glover, M

F. Glover, M. Laguna, R. Mart ´ ı, Fundamentals of scatter sea rch and path relinking, Control and Cybernetics 29 (2000) 652–684

work page 2000

[37] [37]

Eberhart, J

R. Eberhart, J. Kennedy, A new optimizer using particle swarm t heory, in: MHS’95. Proceedings of the Sixth International Symposium on Mic ro Machine and Human Science, IEEE, 1995, pp. 39–43

work page 1995

[38] [38]

Kirkpatrick, C

S. Kirkpatrick, C. D. Gellat, M. P. Vecchi, Optimization by Simulate d Annealing, Science 220 (1983) 671–680

work page 1983

[39] [39]

D. R. Penas, J. R. Banga, P. Gonz´ alez, R. Doallo, Enhanced pa rallel diﬀerential evolution algorithm for problems in computational syste ms biology, Applied Soft Computing 33 (2015) 86–99

work page 2015

[40] [40]

A. O. S. Moraes, J. F. Mitre, P. L. C. Lage, A. R. Secchi, A robu st parallel algorithm of the particle swarm optimization method for large dimensional engineering problems, Applied Mathematical Modelling 39 (2015) 4223–4241

work page 2015

[41] [41]

D. R. Penas, P. Gonz´ alez, J. A. Egea, R. Doallo, J. R. Banga, P arameter estimation in large-scale systems biology models: a parallel and self- adaptive cooperative strategy, BMC Bioinformatics 18 (2017) 52. 19

work page 2017

[42] [42]

L. A. Chylek, V. Akimov, J. Dengjel, K. T. G. Rigbolt, B. Hu, W. S. Hlavacek, B. Blagoev, Phosphorylation site dynamics of early T-cell receptor signaling, PLOS ONE 9 (2014) e104240

work page 2014

[43] [43]

J. A. Egea, E. Balsa-Canto, M.-S. G. Garc ´ ıa, J. R. Banga, Dynamic opti- mization of nonlinear processes with an enhanced scatter search m ethod, Industrial & Engineering Chemistry Research 48 (2009) 4388–440 1

work page 2009

[44] [44]

A. F. Villaverde, F. Fr¨ olich, D. Weindl, J. Hasenauer, J. R. Bang a, Benchmarking optimization methods for parameter estimation in larg e kinetic models, Bioinformatics 35 (2019) 830–838

work page 2019

[45] [45]

J. A. Nelder, R. Mead, A simplex method for function minimization, The Computer Journal 7 (1965) 308–313

work page 1965

[46] [46]

D. Lee, M. Wiswall, A parallel implementation of the simplex function minimization routine, Computational Economics 30 (2007) 171–187

work page 2007

[47] [47]

K. C. Chen, A. Csikasz-Nagy, B. Gyorﬀy, J. Val, B. Novak, J. J . Tyson, Kinetic analysis of a molecular model of the budding yeast cell cycle, Molecular Biology of the Cell 11 (2000) 369–391

work page 2000

[48] [48]

K. C. Chen, L. Calzone, A. Csikasz-Nagy, F. R. Cross, B. Nova k, J. J. Tyson, Integrative analysis of cell cycle control in budding yeast, Molec- ular Biology of the Cell 15 (2004) 3841–3862

work page 2004

[49] [49]

C. Oguz, T. Laomettachit, K. C. Chen, L. T. Watson, W. T. Bau mann, J. J. Tyson, Optimization and model reduction in the high dimensional parameter space of a budding yeast cell cycle model, BMC Systems Biology 7 (2013) 53

work page 2013

[50] [50]

Pargett, D

M. Pargett, D. M. Umulis, Quantitative model analysis with divers e bio- logical data: Applications in developmental pattern formation, Met hods 62 (2013) 56–67

work page 2013

[51] [51]

Pargett, A

M. Pargett, A. E. Rundell, G. T. Buzzard, D. M. Umulis, Model-ba sed analysis for qualitative data: An application in Drosophila germline stem cell regulation, PLOS Computational Biology 10 (2014) e10034 98

work page 2014

[52] [52]

E. D. Mitra, R. Dias, R. G. Posner, W. S. Hlavacek, Using both qu al- itative and quantitative data in parameter identiﬁcation for system s biology models, Nature Communications 9 (2018) 3901. 20

work page 2018

[53] [53]

A. E. Smith, D. W. Coit, Penalty functions, in: T. Baeck, D. Foge l, Z. Michalewicz (Eds.), Handbook of Evolutionary Computation, Oxfo rd University Press, New York, 1997

work page 1997

[54] [54]

Harmon, L

B. Harmon, L. A. Chylek, Y. Liu, E. D. Mitra, A. Mahajan, E. A. Saada, B. R. Schudel, D. A. Holowka, B. A. Baird, B. S. Wilson, W. S. Hlavacek, A. K. Singh, Timescale separation of positive and negative signaling creates history-dependent responses to IgE receptor stimula- tion, Scientiﬁc Reports 7 (2017) 15586

work page 2017

[55] [55]

Kreutz, A

C. Kreutz, A. Raue, D. Kaschek, J. Timmer, Proﬁle likelihood in sy s- tems biology, FEBS Journal 280 (2013) 2564–2571

work page 2013

[56] [56]

Kreutz, A

C. Kreutz, A. Raue, J. Timmer, Likelihood based observability an al- ysis and conﬁdence intervals for predictions of dynamic models, BMC Systems Biology 6 (2012)

work page 2012

[57] [57]

H. Hass, C. Kreutz, J. Timmer, D. Kaschek, Fast integration- based pre- diction bands for ordinary diﬀerential equation models, Bioinformat ics 32 (2016) 1204–1210

work page 2016

[58] [58]

Kaschek, W

D. Kaschek, W. Mader, M. Fehling-Kaschek, M. Rosenblatt, J. Timmer, Dynamic Modeling, Parameter Estimation, and Uncertainty Analysis in R, Journal of Statistical Software 88 (2019)

work page 2019

[59] [59]

G. H. Givens, J. A. Hoeting, Bootstrapping, in: Computational Statis- tics, John Wiley & Sons, 2nd edition, 2013, pp. 287–321

work page 2013

[60] [60]

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numer- ical Recipes 3rd Edition: The Art of Scientiﬁc Computing, Cambridge University Press, Cambridge, 2007

work page 2007

[61] [61]

S. Chib, E. Greenberg, Understanding the Metropolis-Hasting s Algo- rithm, The American Statistician 49 (1995) 327–335

work page 1995

[62] [62]

D. J. Earl, M. W. Deem, Parallel tempering: Theory, applications , and new perspectives, Physical Chemistry Chemical Physics 7 (2005) 3 910

work page 2005

[63] [63]

A Conceptual Introduction to Hamiltonian Monte Carlo

M. Betancourt, A Conceptual Introduction to Hamiltonian Mon te Carlo, arXiv (2017) 1701.02434. 21

work page internal anchor Pith review Pith/arXiv arXiv 2017

[64] [64]

Gelman, D

A. Gelman, D. B. Rubin, Inference from Iterative Simulation Usin g Multiple Sequences, Statistical Science 7 (1992) 457–511

work page 1992

[65] [65]

Vehtari, A

A. Vehtari, A. Gelman, D. Simpson, B. Carpenter, P.-C. B¨ urkner, Rank- normalization, folding, and localization: An improved R for assessing convergence of MCMC, arXiv (2019) 1903.08008

work page arXiv 2019

[66] [66]

R. M. Neal, MCMC using Hamiltonian dynamics, arXiv (2012) 1206.1901

work page arXiv 2012

[67] [67]

M. D. Hoﬀman, A. Gelman, The No-U-Turn Sampler: Adaptively Se t- ting Path Lengths in Hamiltonian Monte Carlo, Journal of Machine Learning Research 15 (2014) 1593–1623

work page 2014

[68] [68]

Bales, A

B. Bales, A. Pourzanjani, A. Vehtari, L. Petzold, Selecting the Metric in Hamiltonian Monte Carlo, arXiv (2019) 1905.11916

work page arXiv 2019

[69] [69]

J. K. Medley, A. P. Goldberg, J. R. Karr, Guidelines for reprodu cibly building and simulating systems biology models, IEEE Transactions on Biomedical Engineering 63 (2016) 2015–2020

work page 2016

[70] [70]

Waltemath, O

D. Waltemath, O. Wolkenhauer, How modeling standards, softw are, and initiatives support reproducibility in systems biology and systems medicine, IEEE Transactions on Biomedical Engineering 63 (2016) 1999–2006

work page 2016

[71] [71]

F. T. Bergmann, S. Hoops, B. Klahn, U. Kummer, P. Mendes, J. Pahle, S. Sahle, COPASI and its applications in biotechnology, Journal of Biotechnology 261 (2017) 215–220

work page 2017

[72] [72]

Fr¨ ohlich, B

F. Fr¨ ohlich, B. Kaltenbacher, F. J. Theis, J. Hasenauer, Sca lable Pa- rameter Estimation for Genome-Scale Biochemical Reaction Networ ks, PLoS Computational Biology 13 (2017) e1005331

work page 2017

[73] [73]

C. F. Lopez, J. L. Muhlich, J. A. Bachman, P. K. Sorger, Progr amming biological models in Python using PySB, Molecular Systems Biology 9 (2013) 646

work page 2013

[74] [74]

J. A. Egea, D. Henriques, T. Cokelaer, A. F. Villaverde, A. MacN amara, D.-P. Danciu, J. R. Banga, J. Saez-Rodriguez, MEIGO: An open-so urce software suite based on metaheuristics for global optimization in sy stems biology and bioinformatics, BMC Bioinformatics 15 (2014) 136. 22

work page 2014

[75] [75]

Eydgahi, W

H. Eydgahi, W. W. Chen, J. L. Muhlich, D. Vitkup, J. N. Tsitsiklis, P. K. Sorger, Properties of cell death models calibrated and compa red using Bayesian approaches, Molecular Systems Biology 9 (2013)

work page 2013

[76] [76]

Stapor, D

P. Stapor, D. Weindl, B. Ballnus, S. Hug, C. Loos, A. Fiedler, S. K rause, S. Hroß, F. Fr¨ ohlich, J. Hasenauer, PESTO: Parameter EStimatio n TOolbox, Bioinformatics 34 (2018) 705–707

work page 2018

[77] [77]

Kerketta, ´A

R. Kerketta, ´A. M. Hal´ asz, M. P. Steinkamp, B. S. Wilson, J. S. Ed- wards, Eﬀect of Spatial Inhomogeneities on the Membrane Surfac e on Receptor Dimerization and Signal Initiation, Frontiers in Cell and De- velopmental Biology 4 (2016)

work page 2016

[78] [78]

S. S. Andrews, N. J. Addy, R. Brent, A. P. Arkin, Detailed simula tions of cell biology with Smoldyn 2.1, PLoS Computational Biology 6 (2010) e1000705

work page 2010

[79] [79]

R. A. Kerr, T. M. Bartol, B. Kaminsky, M. Dittrich, J.-C. J. Chan g, S. B. Baden, T. J. Sejnowski, J. R. Stiles, Fast Monte Carlo Simulatio n Methods for Biological Reaction-Diﬀusion Systems in Solution and on Surfaces, SIAM Journal on Scientiﬁc Computing 30 (2008) 3126–3 149. 23

work page 2008