Thermodynamic principles of enzymatic regulation in biomolecular condensates from reaction-coupled molecular modeling

Reviewer #1 (Public review):

Summary:

A well-presented computational work on how post-translational modifications take place from a thermodynamic and mechanistic point of view.

Strengths:

A model capable of recapitulating complex phenomena to simulate, such as phosphorylation.

Weaknesses:

The methodology relies on multiple user-defined parameters that alter the setup. Below are the specific concerns:

(1) The abstract reads: 'First, reactions that weaken favorable interactions are thermodynamically suppressed within condensates. As a consequence, regulation of condensate solubility is most efficient when PTMs tune interactions to values close to the solubility threshold.' This phrasing is confusing. PTMs that weaken interactions will, in principle, shift the solubility to higher values, and therefore closer to the thermodynamic conditions that allow for condensate formation, but if those transitions are most efficient when they tune interactions to values close to the solubility threshold, they will not be suppressed? The authors have to make this statement clearer to readers, which is particularly important in the abstract of the manuscript

(2) The computational framework used by the authors is reasonable given the coarse-grained nature of the model required to study this problem. However, there are multiple user-defined variables that require further validation in order to make their choices justifiable:

a) NN and NK have the same interaction epsilon value, as well as K-K. This would effectively make kinase form condensates on their own if the right stoichiometry was imposed. This should be re-evaluated with a reduced K-K interaction to validate whether the conclusions remain invariant with this assumption.

b) N, P and K beads also have the same molecular diameter. This should be justified, for instance, with solvent available surface area calculations to determine the excluded volume for the different species, or by citing other works that support this approach.

c) The phosphorylation reaction takes place when 2 particles are found within a 1.5sigma distance; however, this value choice is not justified. The authors should prove how variations to this choice affect their conclusions.

(3) Figure 2a is informative although not entirely intuitive to follow. It can be concluded, as the authors mention, that the capacity to form condensates decreases as phosphorylation is favored. Therefore, as the text also says, there is a higher fraction of P particles as lambdaP increases; however, the fraction NP/NT appears to decrease based on the color scale. According to the figure caption, this is meant to represent the fraction of P particles over the total, but this should not exceed 1. This should be clarified and better explained in a revised version. Moreover, the information related to this, shown in Figure S4a, is very informative, and I advise the authors to include it as part of the main set of figures, as it will potentially help many readers to follow the manuscript better. Moreover, in Figure S4a, some lines appear to be disconnected; this probably comes from trajectory merging; the authors must check this.

(4) 'At the interface, N and K concentrations remain relatively high, but scaffold proteins experience fewer stabilizing interactions, lowering the energetic cost of phosphorylation. This leads to enhanced reaction activity specifically at the boundary between phases.' This statement perfectly explains why the density profiles of K and N do not match the phosphorylation probability curve. This probability is determined by the energetic impact of the reaction and the probability of encountering each other in space, but also on the short timescale diffusion: N and K proteins have greater access to more microstates at the interface and can access them faster, while having enough density to encounter each other. It would be interesting for the authors to prove or invalidate this argument. At the very least, it should be mentioned.

(5) Characterizing the real impact of condensate interfaces in real size condensates is an interesting approach, nonetheless this paragraph lacks most of the necessary details to be robust and obtain any reliable conclusion out of it in its current form:

a) There are several CALVADOS parametrizations, which one do the authors use? The force field must be cited.

b) R is not well defined in the caption.

c) In the rendered images, periodic boundary conditions appear not to be implemented; this should be clarified

d) In the Intermolecular energy profiles, it seems that FUS-LC has no condensate bulk.

e)How is the interface width calculated?

f) Why do the authors choose the energy profile and not density? Or other observables such as the radius of gyration.

g) The interface width will depend on the temperature, and how distant this temperature is from the critical temperature for phase separation. Currently, this information is lacking.

h) Variations in the temperature, quantity used to define the interface, should be addressed in order to make the interfacial importance claim robust.

(6) 'Since the size of typical cellular condensates rarely exceeds the 2 μm diameter'. This statement should be supported by multiple references.

(7) Figure S2 should be improved: The use of 'weak' or 'strong' labels is subjective and it is unclear which parameters are being used. Moreover, 'exp reference' is not described or cited. Furthermore, this plot shows what appear to be sketched curves. The calculation of the coexistence densities to construct this phase diagram is trivial for the system studied here; the authors should provide direct estimates.

Reviewer #2 (Public review):

Summary:

The manuscript "Thermodynamic principles of enzymatic regulation in biomolecular condensates from reaction-coupled molecular modeling" reports results of a very coarse-grained molecular dynamics (MD) simulation of three types of particles that undergo phase separation and chemical reactions. The study focuses on a molecule that can exist in two states (phosphorylated vs. unphosphorylated), whereas the third species is an enzyme that catalyzes the reaction in one direction of the transition. This topic of chemically active multicomponent mixtures is timely, and its connection to biomolecular condensates is well motivated in the introduction. Using their minimal setup, the authors find that driven reactions affect the composition of the dilute and dense region, and can even suppress phase separation completely. Moreover, the reaction fluxes are heterogeneous and exhibit a pronounced peak at the interface. The authors then interpret this acceleration of reactions in light of the role of condensates as reaction centers and conclude that the effect they report is relevant in cells.

Strengths:

A strength of the manuscript is the setup of a minimal system to understand the complex roles of enzymatically controlled, active reactions in condensates. This is a subtle topic since the physics of phase separation, implying non-ideal systems, affects the reactions, which can then no longer be described in a dilute approximation. The authors tried to take special care to ensure thermodynamic consistency, which is key to describing the interplay of the two effects accurately. The authors also perform relevant numerical tests, e.g., by determining the effect of reactions on the phase diagram, and measuring densities and reaction fluxes carefully. Moreover, they attempt to interpret the obtained quantities with intuitive pictures, although this is not always convincing.

Weaknesses:

The main weakness of the work is its presentation: I could not follow the detailed setup of the model since important details (such as the concrete interaction potentials and particularly the implementation of the reactions) are not described thoroughly. In particular, the implementation of the actively driven reaction is mysterious, and a proper negative control without activity is missing. Such a control is crucial since it would allow testing whether the implementation of the code ensures local detailed balance and thus thermodynamic consistency. Furthermore, such a passive null model would surely help in establishing the effects of activity, which is currently unclear. Since I don't understand the detailed setup, I cannot judge whether the major result, namely that reactions are accelerated at interfaces, is correct. It might very well be true, but I'm unable to judge this based on the current presentation. I detail my criticism in separate points below, and I hope that addressing these points helps the authors to improve their manuscript:

(1) I find the model setup unclear, which makes it difficult for me to gauge the correctness of the results. I think the details of the model need to be explained in more detail, both in the main text and the SI. There are three different aspects that I find lacking:

1a) The setup of the interactions in the model is unclear. First, only single interaction parameters \epsilon_i are specified, but the simulation likely needs to specify pairwise interactions. Table S2 is not particularly helpful since it uses a different notation (Is this switch of notation necessary?). Second, the statement that k_BT = 0.75 is confusing since k_BT should have units of energy. Third, the authors mention "a truncated and shifted LJ potential", but it is unclear whether this is the potential they use or not. Given this lack of details, I would not be able to immediately repeat the simulation, even without reactions.

1b) In the main text (page 6), it is unclear whether an active or passive system is studied. The subsequent results suggest that the system is active (and thus has sustained energy fluxes), but this needs to be explained in detail. In any case, I would like to see an explicit activity parameter, so that a passive control can be added. For instance, I would expect that a passive system remains the same when reaction rates are changed, but the energetics are kept constant. In any case, since it is not explained how activity enters the system, the subsequent results are unclear to me.

1c) It is unclear how thermodynamic consistency (i.e., local detailed balance) is ensured. For instance, how is the formation of a scaffold-enzyme complex performed (page 6)? The SI is also light on details. For instance, it is unclear whether the transitions in Equations (1-8) refer to individual particles (in this case, how are bimolecular reactions implemented?) or refer to densities or even overall particle counts. It is also suspicious that the reactions are given for the "dilute limit", whereas the main text clearly discusses condensed regions. It is also unclear how ΔU is calculated and what it means. Generally, I would expect a detailed discussion of detailed balance conditions in the SI, if not even in the main text. Here, it might help to clearly separate thermodynamic aspects (involving detailed balance) from kinetic considerations.

(2) If the authors study an active system, reporting averaged concentrations and partition coefficients might be misleading. Generally, active systems develop gradients in the dilute and dense regions (Figure 1), so any averaged measurement (such as a density) will depend on the size of the region. It is thus necessary to clearly define the measurements in the main text (so readers know how to interpret the plots), and the discussion needs to be much more careful, particularly when comparing to phase diagrams, which typically discuss thermodynamically large systems.

(3) The strongly increased fluxes at the interface are a bit suspicious, particularly since they are hardly visible in passive systems (Figure S6). The enhancement might originate from large reaction rates, leading to a short reaction-diffusion length scale (although I would then expect balanced reactions in the phases). Alternatively, they might originate from the microscopic details, such as the cut-off length of the kinase-interaction range. In any case, it would be important to establish a negative control using a passive setup and (based on this) explain the observed flux increase clearly.

(4) I am not convinced by the statement about the bias of reactions in the dense and dilute phase, e.g., on page 12. I would find it extremely helpful to start with a passive system (without energy input), where I would expect balanced chemical potentials, so that all reactions are balanced at all points in the system. Already in this case, there might be accelerated reactions at the interface (due to kinetic details), but the two reactions need to be balanced to have overall homogeneous chemical potentials. Starting from such a base state, one could then discuss how activity biases reactions in a certain direction. While the current explanation correctly mentions that a transition can be hindered by energetics, it fails to account for the different abundances. In a passive system, these two aspects are perfectly balanced, leading to a linking of reaction rate constants and partition coefficients (e.g., see https://arxiv.org/abs/2202.13646). These aspects need to be discussed much more cleanly (and they are intimately linked to the setup of the model, which is currently unclear; see point 1).

(5) I think the title is misleading. The authors do not establish new "Thermodynamic principles". I am also not sure what they mean by "reaction-coupled molecular modeling". Finally, the 
"enzymatic regulation" is hardly discussed in the main text, which instead seems to emphasize the accelerated reactions at the interface.