Review Reports

Round 1

Reviewer 1 Report

This paper provides a solution to the important question of how to tackle context-dependent behavior in synthetic biology. The methodology is novel and appropriate. The manuscript is clearly written, and, although only simulated data has been used, the approach can be applied to real systems. I recommend publication.

My comments are mostly minor.

1. I find it confusing to start with Eq. 1, which has many unexplained parameters. Some of these parameters are only defined multiple pages later. I would put these equations at the end of section 2.1 when everything has been explained.

2. Eq. 7: has a typo \Phi_{p0}?

3. I would reference Eq. 8 before Eq. 10.

4. Before Eq. 11, the notation for the \epsilon is confusing. I think $p$ should be $r$.

5. "indicuble" on page 7.

6. I am not an expert on OED and would have preferred some more explanation of Eq. 30. I have not seen the Fisher information obeying a differential equation before and would have appreciated a sentence on where the likelihood appears in Eq. 30. The w_n are not defined (I presume they are sampling densities?).

7. In Eq. 36 should the Fisher information obey an integral following Eq. 32. If not, please explain why. Justification of the differential equation for the sampling frequencies would also be helpful. Is this equation necessary to ensure the c_Tot limit?

8. I would give the numerical value of the optimality score in the caption of Fig. 3 to ease comparison with Table 2.

9. It would be interesting to know how important is the choice of sampling schedule. For example, how much is the optimality score in Fig. 3 degraded by uniform sampling?

10. As I understand things, the observed covariance indicates how tight the likelihood function is around the best-fit parameter values but does not evaluate whether these values are near the true parameters. Some comments here (page 16) would be helpful, and I realize that Fig 4B partly alleviates these concerns.

11. I was confused by the "30 parameter estimates" on page 16. Are 30 parameters referred to or 30 sets of parameters?

Author Response

We thank the reviewers for their helpful comments and critique. We have outlined our response and the resulting changes below. References to line numbers are provided. Changes are highlighted in red in the revised submission.

Reviewer 1

“I find it confusing to start with Eq. 1, which has many unexplained parameters. Some of these parameters are only defined multiple pages later. I would put these equations at the end of section 2.1 when everything has been explained.”

We debated this issue when preparing the manuscript. Ultimately, we felt it was worth presenting the model (Eq. 1) up-front to provide a scaffold for the subsequent discussion of the specific physiological factors (which we expect will be less familiar to most readers, compared with a kinetic model of gene expression). To address this issue we have re-formated Table 1 to include parameter labels that provide brief descriptions, thus introducing some context for the unfamiliar parameters before the subsequent full explanation of the physiological details.

“I am not an expert on OED and would have preferred some more explanation of Eq. 30. I have not seen the Fisher information obeying a differential equation before and would have appreciated a sentence on where the likelihood appears in Eq. 30. The w_n are not defined (I presume they are sampling densities?).”

Further details on the differential/integral representation of the Fisher information can be found in references 33 and 73 (the later has been added for additional clarity). The integral representation is possible due to the assumed independence of samples, which makes the Fisher information additive over time. The quadratic form within the Fisher information integral is the result of the Gaussian log-likelihood and the assumption of normally distributed errors. These details may be distracting to the narrative. We’ve highlighted ref. 73 for the interested reader. Likewise, we added a reminder of the definition of sampling density (lines 390-391, page 11).

“In Eq. 36 should the Fisher information obey an integral following Eq. 32. If not, please explain why. Justification of the differential equation for the sampling frequencies would also be helpful. Is this equation necessary to ensure the c_Tot limit?”

We had left the integral characterization of the Fisher information implicit in Eq. 36. The reviewer is correct that this was ambiguous. We’ve revised Eq. 36 to include a differential equation constraint on the Fisher information. The differential equation for the sampling frequencies contained a typo, which has been corrected. It is equivalent to the integral formulation in Eq. 20.

“It would be interesting to know how important is the choice of sampling schedule. For example, how much is the optimality score in Fig. 3 degraded by uniform sampling?”

We did not perform comparative optimizations over subsets of the three controls (induction input, sampling schedules and growth rate) while holding the others fixed at the null values. This would have directly addressed the reviewer’s questions, but we see this as beyond the scope of the current submission. Our null experiments indicate the significant effect of reducing the fixed sampling rate on the optimality and estimate variability in the null scenario. We have added a note to this effect (lines 499-501, page 16). The need for optimized sampling schedules has been addressed previously (e.g. ref. 36).

“As I understand things, the observed covariance indicates how tight the likelihood function is around the best-fit parameter values but does not evaluate whether these values are near the true parameters. Some comments here (page 16) would be helpful, and I realize that Fig 4B partly alleviates these concerns.”

Our measure of fit variability in Fig 4A is not computed using the likelihood, however our original wording made this ambiguous. We have added a clarifying statement to indicate that the fit variability is computed from the repeated fitting from simulated data (lines 491-493, page 16). As the reviewer has observed, Fig 4B also partially addresses this issue.

“I was confused by the "30 parameter estimates" on page 16. Are 30 parameters referred to or 30 sets of parameters?”

We have reworded for clarity, it was 30 sets of parameter estimates, however, the set actually excludes the outliers and is therefore less than 30, see lines 508-509 (page 16-17). This was further addressed in response to reviewer 2 below.

I would reference Eq. 8 before Eq. 10.

Unfortunately, we were unable to locate the equation references indicated in this comment. We have left the equation ordering unchanged.

Minor Edits:

“Eq. 7: has a typo \Phi_{p0}?” [Fixed]

Before Eq. 11, the notation for the \epsilon is confusing. I think $p$ should be $r$. [Fixed a typo]

"indicuble" on page 7. [Fixed]

I would give the numerical value of the optimality score in the caption of Fig. 3 to ease comparison with Table 2. [Added]

Reviewer 2 Report

The authors propose an approach for the context-dependent characterisation of biological parts in Synthetic Biology. The effort spent on developing a suitable model structure and integrating optimal experimental design methodologies common to other engineering disciplines can be appreciated and the results demonstrate a) the relevance of a context-aware mathematical formalisation of the behaviour of synthetic components, b) the usefulness of OED to enable improved model identification and prediction of systems dynamics.

However, I believe a number of points should be clarified to ensure full-transparency and utility of the approach.

Comments:

(i)             While the hypothesis of an ‘idealized scenario’ is explicitly reported in the main text (and partially mitigated towards the end of it) with reference to the application of OED to a model parametrised by the true values, other assumptions- which could challenge the practical implementation of the approach, are overlooked. Namely:

a.     The explored experimental schemes consider full observability of the system, e.g. both mRNA and proteins can be measured simultaneously. However, this flexibility seems unrealistic, at least with experimental setups enabling tight control on the dynamic of the perturbation stimulus. How would the accuracy of parameter estimates being affected if only mRNA/protein could be measured?

b.     It would be nice to clarify how the number of samples and subexperiments for the considered scenario was defined. On the former, it would be interesting to see how the informative content of intuitively conceived experiments compares to optimised ones, when the overall sample size increases (12 fluorescence images, for example, are normally acquired in 1 hour of experiment).

c.     The model formalises the dynamics of the copy number of mRNAs and proteins. However, as these chemical species are normally measured in arbitrary units, the parameter estimates characterising the behaviour of biological parts will actually depend on the instrument adopted for the observation. This aspect should be highlighted and strategies to overcome the consequent limited exportability of quantitative characteristics should be proposed;

d.     The selected input represents the number of molecules of the TF. As the authors mentioned, this would rarely apply experimentally and, even if it was, it would rely on the possibility of an extremely accurate operativity of the actuators used for the input administration. An expansion on if and how this could be achieved and what the consequences on the parameter estimates would be would improve the manuscript. In this context, how were the boundaries on the input defines?

(ii)            The authors should clarify the statement inherent to the removal of outliers within the parameter estimates obtained over the 30 iterations. What is the origin of the non-convergence or convergence to erroneous estimates? If the outliers were removed, how could the authors use the 30 parameter vectors to simulate the model response to a new dynamic experiment [line 313]?  

(iii)          [Lines 336-339]: The authors might consider rephrasing the sentence to prevent misleading interpretations. Indeed, intrinsic parameters are associated with the biological part but the mapping between the genetic sequence, the parameter value and hence the component behaviour is not immediate. As a minimum, estimating the intrinsic parameters could pave the way to such a connection.

(iv)           Note that reference 83 is misleading, as the online OED approach therein does not use model-predictive control.  

 

Minor comments:

-       Line numbers are missing starting from section 2

-       [Line 101]: ‘each parameter is expect’->  ‘each parameter is expected’

-       [Line 138]: ‘dissociation constants […] has been observed ’ -> ‘dissociation constant […] has been observed’

-       [Line 141]: ‘for an indicuble prmoter’ -> ‘for an inducible promoter’

-       [Line 171]: remove ‘)’ at the end of the sentence

-       [Line 181]: Missing point at the end of the sentence.

-       [Line 270]: ‘an optimal experimental for our model’ -> ‘an optimal experiment for our model’

-       [Line 396]: ‘generalizable of component’ -> ‘generalizability of component’

-       [Line 402]: ‘approachs’ -> ‘approaches’

-       The manuscript uses ‘behavior’ and ‘behaviour’. Please adopt consistent notation.

Author Response

We thank the reviewers for their helpful comments and critique. We have outlined our response and the resulting changes below. References to line numbers are provided. Changes are highlighted in red in the revised submission.

Reviewer 2

“The explored experimental schemes consider full observability of the system, e.g. both mRNA and proteins can be measured simultaneously. However, this flexibility seems unrealistic, at least with experimental setups enabling tight control on the dynamic of the perturbation stimulus. How would the accuracy of parameter estimates being affected if only mRNA/protein could be measured?”

We agree with the reviewer that full observability of the system is a demanding assumption, given current experimental technologies. For this model, observing only one species results in a structurally unidentifiable parameter set, and so the reusable, dynamic characterization of a genetic part cannot be achieved. We have added an additional paragraph to the discussion, addressing these issues (lines 573-578, page 18). There we note that emerging dynamic experimental techniques are making dynamic control easier to achieve and we cite past works/reviews that support the potential for implementation of these more demanding experiments in the future (ref. 30, 85).

“ It would be nice to clarify how the number of samples and subexperiments for the considered scenario was defined.”

Our null experiments were selected based on our experience with past gene expression models. We assumed the null experiment would be designed with no specific information about the dynamic or steady state response of the given gene construct. However, we assumed an astute experimenter may know something of the time scale, growth rates and saturating behaviour involved in gene expression. This led us to our selection of the growth rates, log distributed inputs, and chosen sampling rate/experimental length. Further we selected the maximum number of samples per species in the experiment, 12, as reasonably small but also sufficiently rich for the 6 input steps (at least two measurements per step are possible). Of course, other choices would also be reasonable. We added a note, highlighting our motivation for the null experimental choices (lines 449-451, page 13). In the end, some of these choices are somewhat arbitrary. Our goal was to select null experiments that are sufficiently rich, which we believe is true of our choices.

“ On the former, it would be interesting to see how the informative content of intuitively conceived experiments compares to optimised ones, when the overall sample size increases (12 fluorescence images, for example, are normally acquired in 1 hour of experiment).”

We agree with the reviewer that future works should investigate the trade-offs and robustness of optimal designs for physiologically aware models like the one used here. Trade-offs between experimental effort and optimality and whether there are robustly informative designs that are near-optimal for many systems would be interesting avenues for further investigation.

“The model formalises the dynamics of the copy number of mRNAs and proteins. However, as these chemical species are normally measured in arbitrary units, the parameter estimates characterising the behaviour of biological parts will actually depend on the instrument adopted for the observation. This aspect should be highlighted and strategies to overcome the consequent limited exportability of quantitative characteristics should be proposed”

We very much agree with the reviewer that optimal experiments would significantly benefit from formulation with absolute units and proper calibration methods allowing for inter-lab comparability. We have added additional citations and specific reference to related efforts (especially by Jacob Beal and the iGEM InterLab study) in a new paragraph in the discussion (line 582-586, page 18).

“ The selected input represents the number of molecules of the TF. As the authors mentioned, this would rarely apply experimentally and, even if it was, it would rely on the possibility of an extremely accurate operativity of the actuators used for the input administration. An expansion on if and how this could be achieved and what the consequences on the parameter estimates would be would improve the manuscript. In this context, how were the boundaries on the input defines?”

The precision of the TF control required is a weakness of the proposed experiments. It is our expectation that techniques such as optogenetic and microfluidic control, possibly combined with real-time, closed-loop feedback, may lead to increased experimental precision. In the case considered here, the requirement is to map the experimental input (e.g. light, chemical inducer), to the expected average copy number of TF per cell. This could potentially be achieved through precise calibration experiments, achievable with current techniques (with considerable effort, admittedly). Future work could also address both variability in the input and robustness to input errors and variance. It may also be easier to target weaker TF’s for study first, as these would require less precision in the copy number control as the promoter will have a larger dynamic range (thus smaller relative error). We have added a comment in the discussion outlining these points (line 567-573, page 18). We have also clarified that the TF range of 0 to 1000 was chosen to span the dynamic input of the promoter well in excess, and therefore does not rely on information that wouldn’t be available to an actual experimenter. We clarified this in line 297-298 (page 9). In practice the user would be expected to use the largest achievable input range.

“ The authors should clarify the statement inherent to the removal of outliers within the parameter estimates obtained over the 30 iterations. What is the origin of the non-convergence or convergence to erroneous estimates? If the outliers were removed, how could the authors use the 30 parameter vectors to simulate the model response to a new dynamic experiment [line 313]?”

Outliers in the parameter estimation either converged to parameter estimates with relative errors at least several orders of magnitude (in some cases terminated by reaching the maximum number of iterations). The non-converging fits we investigated were likely converging towards erroneous estimates. We believe these outliers are likely due to problems with numerical fitting of non-linear models, where the fitting algorithm was getting lost in non-sensitive regions of parameter space or a combination of initial conditions and random errors directed the algorithm to erroneous local optima. The small number of outliers suggests that these types of failure are comparatively rare. This implies that the outlined experiments are rich enough to provide good convergence properties from many parameter starting points. It is possible that a stochastic or multi-start fitting procedure could eliminate these outliers entirely. We added some additional remarks to SI to provide some extra context, see page S12. To simulate the model response we only used the non-outlier fits. We have corrected the text to reflect this, see line 508-509 (page 16-17).

“The authors might consider rephrasing the sentence to prevent misleading interpretations. Indeed, intrinsic parameters are associated with the biological part but the mapping between the genetic sequence, the parameter value and hence the component behaviour is not immediate. As a minimum, estimating the intrinsic parameters could pave the way to such a connection.” … “Note that reference 83 is misleading, as the online OED approach therein does not use model-predictive control. “

We scaled back the claim about intrinsic parameter correspondence to sequence properties, and have highlighted the need for future work, see line 531-535 (page 17). We removed reference to model-predictive control for ref. 83 (now ref. 84).

Minor Edits:

Line numbers are missing starting from section 2 [Fixed]

[Line 101]: ‘each parameter is expect’->  ‘each parameter is expected’ [Fixed]

[Line 138]: ‘dissociation constants […] has been observed ’ -> ‘dissociation constant […] has been observed’ [Fixed]

[Line 141]: ‘for an indicuble prmoter’ -> ‘for an inducible promoter’ [Fixed]

[Line 171]: remove ‘)’ at the end of the sentence [Fixed]

[Line 181]: Missing point at the end of the sentence. [Fixed]

[Line 270]: ‘an optimal experimental for our model’ -> ‘an optimal experiment for our model’ [Fixed]

[Line 396]: ‘generalizable of component’ -> ‘generalizability of component’ [Fixed]

[Line 402]: ‘approachs’ -> ‘approaches’ [Fixed]

The manuscript uses ‘behavior’ and ‘behaviour’. Please adopt consistent notation. [Fixed]

Reviewer 3 Report

The manuscript presents a model that distinguishes the intrinsic characteristics  of the physiological context. In addition, the authors propose the use of model-based  experiment design to improve the estimation of parameters of the proposed model from experimental data.

The work is well written and clearly explained. It shows the potential benefits of accounting for the physiological context in the design of synthetic circuits and illustrates the benefits of optimal experimental design to improve model identifiability. It would be really nice that the authors find the way to test their model and experimental design approach in vivo.

There are, however, some aspects that should be taken into account before publication.

Title:
Most of the manuscript is devoted to model derivation and it seems that the originality of the work lies in the model. The formulation and solution of the OED problem as an optimal control problem is not really new (see detailed comments below). Thus  I would suggest modifying the title to put the focus on the modelling.

Introduction:
The authors state " This simultaneous optimization of sampling and experimental perturbations is an improvement over previous OED methods used in systems biology". Indeed the following work address the simultaneous design of inputs and sampling times, using an optimal control framework:

Balsa-Canto, E., Alonso, A.A., Banga, J.R. Computational procedures for optimal experimental design in biological systems.
IET Systems Biology; 2(4), pp. 163-172 ; 2008

Kutalik et al , 2004 had previously addressed the importance of selecting optimal sampling times (reference 72 in the manuscript).



Materials and methods.
Section 2.1.4.
The authors comment that Kr was found to be practically unidentifiable. Have the authors confirmed that the parameter is structurally
identifiable?  If the problem is of practical nature, why not including it into the OED scheme?
What are the expected consequences of fixing this parameter to a given value?


Section 2.2.
- The sentences "Past experimental design effort in systems biology ...."  lines 209-212 should be revised in view of the above-mentioned works.


- The authors state that the noise is heteroscedastic; still the definition of the Fisher information matrix would correspond to the homoscedastic case. This should be corrected.

- Right after line 220, the authors state " This OED procedure was developed with chemical and bioprocess models in mind; it has seen
limited use in a systems or synthetic biology context".
I guess the authors refer to the optimal control and multiple shooting frameworks.
However, it should be noted that Bandara et al.  ( reference 28 in the manuscript) used that approach for both experimental design and
parameter estimation. The authors used the software tool VPLAN (http://ginger.iwr.uni-heidelberg.de/vplan/index.php/Main_Page), 
based on the multiple shooting methods by H. G. Bock and J. P. Schlöder. The authors should emphasise the differences (novelties, advantages)
of their approach to that previously implemented in VPLAN.

Results
In Figure 2G both models seem to be not that sensitive to input modifications.
This result seems to contrast with the dynamics observed in Figures 3D, E and F. Of course, the control profile in Figure 2 G is "smoother",
but still is there any other reason for those differences in response?


Minor comments

Introduction: course-grained should be replaced by
coarse-grained

Section 3.2 line 270:  "optimal experimental" should be "optimal experimental scheme" or "optimal experiment"

Author Response

We thank the reviewers for their helpful comments and critique. We have outlined our response and the resulting changes below. References to line numbers are provided. Changes are highlighted in red in the revised submission.

Reviewer 3

“Most of the manuscript is devoted to model derivation and it seems that the originality of the work lies in the model. The formulation and solution of the OED problem as an optimal control problem is not really new (see detailed comments below). Thus  I would suggest modifying the title to put the focus on the modelling.”

We agree with the reviewer that the submission’s novelty is in the derivation of the model and the application of the OED to a new setting, rather than the OED formulation itself. However, because the OED work represents a significant component of the analysis, we want the title to reflect the use of these tools.  We have removed the subtitle (an optimal control approach) to reduce emphasis on the OED aspect.

“The authors state ‘This simultaneous optimization of sampling and experimental perturbations is an improvement over previous OED methods used in systems biology’. Indeed the following work address the simultaneous design of inputs and sampling times, using an optimal control framework: Balsa-Canto, et al. Computational procedures … IET Systems Biology; 2008”

We have added some clarifying remarks to the introduction to emphasize the differences from past work on optimal sample selection, lines 74-77 (page 2). We now cite this paper in the introduction. We thank the reviewer for pointing out this oversight.

“The authors comment that Kr was found to be practically unidentifiable. Have the authors confirmed that the parameter is structurally identifiable? If the problem is of practical nature, why not including it into the OED scheme? What are the expected consequences of fixing this parameter to a given value?”

We have not performed a full analysis of K_r’s structural identifiability. In preliminary simulations over wide parameter ranges (outside the feasible set listed in Table 1) we found it to be practically identifiable. This identifiability suffers greatly when parameters are restricted to the reasonable ranges in Table 1. We expect that setting K_r to zero or a small constant will have a negligible effect if the promoter leak is very weak. Stronger leaks may pose a problem because fixing the leak incorrectly may bias other parameter estimates (and the leak will have a much greater effect of component behaviour). We have provided additional comment on this in the discussion (lines 578-582, page 18).

“The sentences "Past experimental design effort in systems biology ...."  lines 209-212 should be revised in view of the above-mentioned works.”

We have included the additional reference to previous sample scheduling (Balsa-Canto et al. 2008). This section of the methods was removed as it repeated the introduction, see lines 74-77 (page 2).

“The authors state that the noise is heteroscedastic; still the definition of the Fisher information matrix would correspond to the homoscedastic case. This should be corrected.”

We have added additional clarification. We used the homoskedastic FIM, even though the model is heteroskedastic. See lines 393-395 and 498 (pages 11 and 16, respectively, in the parenthetical remarks). Our initial tests showed that the additional terms in the FIM needed for the heteroskedastic error had negligible effects on the experimental designs but increased the computational cost appreciably. We therefore neglected the extra terms in the FIM for the analysis in this work.

“Right after line 220, the authors state ‘This OED procedure was developed with chemical and bioprocess models in mind; it has seen limited use in a systems or synthetic biology context’. I guess the authors refer to the optimal control and multiple shooting frameworks.”

We specifically had in mind direct optimal control approaches using multiple-shooting or collocation and including computation of first and second-order derivative information. These techniques are a counterpoint to gradient-free optimization methods (including global stochastic methods) which have been used more widely in systems/synthetic biology (i.e. Balsa-Canto et al. 2008 or Ruess et al. 2013 and 2015). The global methods can be easier to set up (they require fewer derivatives etc.) but can be more computationally costly, with the potential benefit of finding a global optima. The local methods (as used here), can be be more time consuming to program and only guarantee local optima. However they can be much more computationally efficient, and local optima may often be sufficient for greatly improving experimental designs. We found most examples given by Bock (and colleagues), in which the actual algorithm was developed/presented were related to chemical and bioprocess models. Likewise work by Van Telen et al. (2014) and Hoang et al. (2013) give bioprocess examples.

“However, it should be noted that Bandara et al.  ( reference 28 in the manuscript) used that approach for both experimental design and parameter estimation. The authors used the software tool VPLAN based on the multiple shooting methods by H. G. Bock and J. P. Schlöder.”

As the reviewer has noted, Bandara et al., is an example (we believe the only one), of these techniques being applied in practice to a systems biology problem. (Ruess et al. (2015) applies OED but not using gradient based methods and not with simultaneous sample optimization.) However, Bandara’s work is not focused on developing the algorithm and devotes little time to its explanation. We have altered our exposition of the technique to address the reviewer’s concerns, see lines 63 and 350-352 (pages 2 and 10, respectively). We believe it is accurate to say that these OED techniques (specifically the algorithms) are introduced and demonstrated on bioprocess and chemical models (most likely because dynamic control has not been as easily available in systems/synthetic biology until recently). But we have avoided saying the algorithms were developed specifically for bio/chemical processes. We have specifically noted Bandara as a systems biology example.

“The authors should emphasise the differences (novelties, advantages)

of their approach to that previously implemented in VPLAN.”

We have not made significant contributions to the fundamentals of the multiple-shooting OED algorithm. We have combined ideas from several past works, but most of these additions are minor. Instead, in this work we have formulated a way to use OED for component characterization in synthetic biology such that intrinsic and context effects can be separated.

Accomplishing that required more complex experiments than those previously considered,  necessitating optimization of induction, growth rate and sample scheduling simultaneously. This added design complexity required highly efficient optimization tools. Our initial tests with stochastic/global optimization (e.g. genetic algorithms) proved too slow and thus adapting multiple shooting or collocation was necessary. We have adapted the multiple-shooting approach to design multiple sub-experiments and controls for a novel application of the algorithm. This required some re-formulation for efficient implementation. Our experiments are fairly non-standard (even within the OED literature) and it would have been difficult to implement them in VPLAN or other optimal control packages. (We have not been able to find sufficient documentation for VPLAN to make a full comparison.) We chose to use CasADi as is being actively developed and documented, provides great flexibility in implementing the OED algorithm needed for multiple sub-experiments, and uses state-of-the-art algorithmic differentiation. Van Telen et al. have used CasADi for OED (applied to bioprocesses) in a previous work.

“In Figure 2G both models seem to be not that sensitive to input modifications.

This result seems to contrast with the dynamics observed in Figures 3D, E and F. Of course, the control profile in Figure 2 G is ‘smoother’, but still is there any other reason for those differences in response?”

Controls in Fig 2G occur over smaller time intervals, leaving less time for the system to respond, and are mostly in the more linear range of the promoter (i.e. of smaller magnitude).

Minor Edits

Introduction: course-grained should be replaced by coarse-grained [Fixed]

Section 3.2 line 270:  "optimal experimental" should be "optimal experimental scheme" or "optimal experiment" [Fixed]

Round 2

Reviewer 3 Report

The authors have addressed my major concerns. The only remaining issue would be the use of homoscedastic FIM for heteroscedastic cases. The fact that the heteroscedastic case requires more computational effort and does not significantly improve results deserves further investigation in a future work.