Reply to the Comment by S. Harvey on “Entropy,Energy, and Bending of DNA in Viral Capsids”

The comment by Stephen Harvey in this issue of the Biophysical Journal concludes with two statements regarding my recent letter about DNA packaging into viral capsids. Harvey agrees with my interpretation of the origin of the large confinement entropy predicted by the molecular-dynamics simulations of his group, and its sensitive dependence on the molecular parameters of their wormlike chain model of double-stranded DNA. On the other hand, he doubts my assertion that the confinement entropy is already included in the interstrand repulsion free energy derived from osmotic stress measurements, which constitutes the major contribution to the packaging free energy used in recent continuum theories of this process. Harvey suggests instead that the confinement entropy should be added to this free energy as a separate term (using, for instance, the method described in my letter). I will argue that this addition is redundant, and, in a brief discussion of continuum theories, will also discuss his comments as relates to the work of other researchers.     

Comment on the Letter by A. Ben-Shaul: “Entropy,Energy, and Bending of DNA in Viral Capsids”

The conformational entropic penalty associated with packaging double-stranded DNA into viral capsids remains an issue of contention. So far, models based on a continuum approximation for DNA have either left the question unexamined, or they have assumed that the entropic penalty is negligible, following an early analysis by Riemer and Bloomfield. In contrast, molecular-dynamics (MD) simulations using bead-and-spring models consistently show a large penalty. A recent letter from Ben-Shaul attempts to reconcile the differences. While the letter makes some valid points, the issue of how to include conformational entropy in the continuum models remains unresolved. In this Comment, I show that the free energy decomposition from continuum models could be brought into line with the decomposition from the MD simulations with two adjustments. First, the entropy from Flory-Huggins theory should be replaced by the estimate of the entropic penalty given in Ben-Shaul’s letter, which corresponds closely to that from the MD simulations. Second, the DNA-DNA repulsions are well described by the empirical relationship given by the Cal Tech group, but the strength of these should be reduced by about half, using parameters based on the Rau-Parsegian experiments, rather than treating them as “fitting parameters (tuned) to fit the data from (single molecule pulling) experiments.”     

Comment on the Letter by A. Ben-Shaul: “Entropy,Energy, and Bending of DNA in Viral Capsids”

The conformational entropic penalty associated with packaging double-stranded DNA into viral capsids remains an issue of contention. So far, models based on a continuum approximation for DNA have either left the question unexamined, or they have assumed that the entropic penalty is negligible, following an early analysis by Riemer and Bloomfield. In contrast, molecular-dynamics (MD) simulations using bead-and-spring models consistently show a large penalty. A recent letter from Ben-Shaul attempts to reconcile the differences. While the letter makes some valid points, the issue of how to include conformational entropy in the continuum models remains unresolved. In this Comment, I show that the free energy decomposition from continuum models could be brought into line with the decomposition from the MD simulations with two adjustments. First, the entropy from Flory-Huggins theory should be replaced by the estimate of the entropic penalty given in Ben-Shaul’s letter, which corresponds closely to that from the MD simulations. Second, the DNA-DNA repulsions are well described by the empirical relationship given by the Cal Tech group, but the strength of these should be reduced by about half, using parameters based on the Rau-Parsegian experiments, rather than treating them as “fitting parameters (tuned) to fit the data from (single molecule pulling) experiments.”     

Entropy,Energy, and Bending of DNA in Viral Capsids

Inspired by novel single-molecule and bulk solution measurements, the physics underlying the forces and pressures involved in DNA packaging into bacteriophage capsids became the focus of numerous recent theoretical models. These fall into two general categories: Continuum-elastic theories (CT), and simulation studies—mostly of the molecular dynamics (MD) genre. Both types of models account for the dependence of the force, and hence the packaging free energy (ΔF), on the loaded DNA length, but differ markedly in interpreting their origin. While DNA confinement entropy is a dominant contribution to ΔF in the MD simulations, in the CT theories this role is fulfilled by interstrand repulsion, and there is no explicit entropy term. The goal of this letter is to resolve this apparent contradiction, elucidate the origin of the entropic term in the MD simulations, and point out its tacit presence in the CT treatments.The genomic double-stranded (ds) DNA inside bacteriophage heads is highly stressed, leading to internal pressures of up to ∼50 atmospheres, reflecting the tight packing and extreme bending of this highly charged and rigid molecule (1). The interaxial distance (d) between neighboring (nonbonded) dsDNA segments in the fully packaged virus is typically ≈2.5 nm (2,3), just slightly larger than the hardcore diameter of dsDNA (b = 2.0 nm) and well into the repulsive regime (d ≤ 2.8 nm) of DNA-DNA interaction in ionic solutions (4–6). Moreover, free dsDNA in (physiological) solution is a fluctuating, semiflexible, wormlike chain (WLC), with persistence length ξ ≈ 50 nm, larger than the radius of most viral capsids. Thus, on a molecular scale, packaging the long (e.g., the 330-ξ long λ-phage genome) viral DNA into its tiny capsid requires enormous mechanical work.The force needed to package the DNA is provided by an ATP-driven motor protein situated at the capsid portal. Recent single molecule measurements reveal that this force, f(L_int), increases sharply with the loaded genome length, L_int, rising to ∼30–100 pN, depending on the virus in question (7,8). These studies inspired the formulation of many theoretical models of DNA packaging in viral capsids, which fall roughly into two categories:     

Helical packaging of semiflexible polymers in bacteriophages

We investigate multilayered helical packaging of double-stranded DNA, or of a general polymer chain with persistence length l_b, into an ideal, inert cylindrical container, reaching densities slightly below close packaging. We calculate the free energy as a function of the packaged length, based on the energies for bending, twisting, the suffered entropy loss, and the electrostatic energy in a Debye–Hückel model. In the absence of charges on the packaged polymer, a critical packaging force can be determined, similar to the mechanism involved in DNA unzipping models. When charges are taken into consideration, in the final packaging state the charges which are chemically distant become geometrically close, and therefore a steep rise is seen in the free energy. We argue that due to the extremely ordered and almost closely packaged final state the actual packaging geometry does not influence the behaviour of the free energy, pointing towards a certain universality of this state of the polymer. Our findings are compared to a recent simulations study, showing that the model is sensitive to the screening length.     

Purification and functional characterization of p16, the ATPase of the bacteriophage Φ29 packaging machinery

Bacteriophage Φ29 codes for a protein (p16) that is required for viral DNA packaging both in vivo and in vitro. Co-expression of p16 with the chaperonins GroEL and GroES has allowed its purification in a soluble form. Purified p16 shows a weak ATPase activity that is stimulated by either DNA or RNA, irrespective of the presence of any other viral component. The stimulation of ATPase activity of p16, although induced under packaging conditions, is not dependent of the actual DNA packaging and in this respect the Φ29 enzyme is similar to other viral terminases. Protein p16 competes with DNA and RNA in the interaction with the viral prohead, which occurs through the N-terminal region of the connector protein (p10). In fact, p16 interacts in a nucleotide-dependent fashion with the viral Φ29-encoded RNA (pRNA) involved in DNA packaging, and this binding can be competed with DNA. Our results are consistent with a model for DNA translocation in which p16, bound and organized around the connector, acts as a power stroke to pump the DNA into the prohead, using the hydrolysis of ATP as an energy source.     

DNA organization and thermodynamics during viral packing

An elastic DNA molecular mechanics model is used to compare DNA structures and packing thermodynamics in two bacteriophage systems, T7 and phi29. A discrete packing protocol allows for multiple molecular dynamics simulations of the entire packing event. In T7, the DNA is coaxially spooled around the cylindrical core protein, whereas the phi29 system, which lacks a core protein, organizes the DNA concentrically, but not coaxially. Two-dimensional projections of the packed structures from T7 simulations are consistent with cryo-electron micrographs of T7 phage DNA. The functional form of the force required to package the phi29 DNA is similar to forces determined experimentally, although the total free energy change is only 40% of the experimental value. Since electrostatics are not included in the simulations, this suggests that electrostatic repulsions are responsible for approximately 60% of the free energy required for packaging. The entropic penalty from DNA confinement has not been computed in previous studies, but it is often assumed to make a negligible contribution to the total work done in packing the DNA. Conformational entropy can be measured in our approach, and it accounts for 70-80% of the total work done in packing the elastic model DNA in both phages. For phi29, this corresponds to an entropic penalty of approximately 35% of the total work observed experimentally.     

Roderick K. Clayton: a life,and some personal recollections

Roderick K. Clayton passed away on October 23, 2011, at the age of 89, shortly after the plan for this dedicatory issue of Photosynthesis Research had been hatched. I had just written a lengthy letter to him to re-establish contact after a hiatus of 2 or 3 years, and to suggest that I visit him to talk about his life. It isn’t clear whether he saw the letter or not, but it was found at his home in Santa Rosa, California. Fortunately, Rod has written two memoirs for Photosynthesis Research that not only cover much of his research on reaction centers (Photosynth Res 73:63–71, 2002) but also provide a humorous and honest look at his personal life (Photosynth Res 19:207–224, 1988). I cannot hope to improve on these and will try, instead, to fill in some of the gaps that Rod’s own writing has left, and offer some of my own personal recollections over the more recent years.     

After 2 years of a pandemic,students are struggling to find strong reference letters

Writing and receiving reference letters in the time of COVID. Subject Categories: Careers

“People influence people. Nothing influences people more than a recommendation from a trusted friend. A trusted referral influences people more than the best broadcast message.” —Mark Zuckerberg.

I regularly teach undergraduate courses in genetics and genomics. Sure enough, at the end of each semester, after the final marks have been submitted, my inbox is bombarded with reference letter requests. “Dear Dr. Smith, I was a student in your Advanced Genetics course this past term and would be forever grateful if you would write me a reference for medical school…” I understand how hard it can be to find references, but I have a general rule that I will only write letters of support for individuals that I have interacted with face‐to‐face on at least a few occasions. This could include, for example, research volunteers in my laboratory, honors thesis students that I have supervised, and students who have gone out of their way to attend office hours and/or been regularly engaged in class discussions. I am selective about who I will write references for, not because I am unkind or lazy, but because I know from experience that a strong letter should include concrete examples of my professional interactions with the individual and should speak to their character and their academic abilities. In today''s highly competitive educational system, a letter that merely states that a student did well on the midterm and final exams will not suffice to get into medical or graduate school.However, over the past 2 years many, if not most, students have been attending university remotely with little opportunity to foster meaningful relationships with their instructors, peers, and mentors, especially for those in programs with large enrollments. Indeed, during the peak of Covid‐19, I stopped taking on undergraduate volunteers and greatly reduced the number of honors students in my laboratory. Similarly, my undergraduate lectures have been predominantly delivered online via Zoom, meaning I did not see or speak with most of the students in my courses. It did not help that nearly all of them kept their cameras and microphones turned off and rarely attended online office hours. Consequently, students are desperately struggling to identify individuals who can write them strong letters of reference. In fact, this past spring, I have had more requests for reference letters than ever before, and the same is true for many of my colleagues. Some of the emails I have received have been heartfelt and underscore how taxing the pandemic has been on young adults. With permission, I have included an excerpt from a message I received in early May:Hi Dr. Smith. You may not remember me, but I was in Genome Evolution this year. I enjoyed the class despite being absent for most of your live Zoom lectures because of the poor internet connection where I live. Believe it or not, my mark from your course was the highest of all my classes this term! Last summer, I moved back home to rural Northern Ontario to be closer to my family. My mom is a frontline worker and so I''ve been helping care for my elderly grandmother who has dementia as well as working part‐time as a tutor at the local high school to help pay tuition. All of this means that I''ve not paid as much attention to my studies as I should have. I''m hoping to go to graduate school this coming fall, but I have yet to find a professor who will write a reference for me. Would you please, please consider writing me a letter?I am sympathetic to the challenges students faced and continue to face during Covid‐19 and, therefore, I have gone out of my way to provide as many as I can with letters of support. But, it is no easy feat writing a good reference for someone you only know via an empty Zoom box and a few online assignments. My strategy has been to focus on their scholarly achievements in my courses, providing clear, tangible examples from examinations and essays, and to highlight the notable aspects of their CVs. I also make a point to stress how hard online learning can be for students (and instructors), reiterating some of the themes touched upon above. This may sound unethical to some readers but, in certain circumstances, I have allowed students to draft their own reference letters, which I can then vet, edit, and rewrite as I see fit.But it is not just undergraduates. After months and months of lockdowns and social distancing, many graduate students, postdocs, and professors are also struggling to find suitable references. In April, I submitted my application for promotion to Full Professor, which included the names of 20 potential reviewers. Normally, I would have selected at least some of these names from individuals I met at recent conferences and invited to university seminars, except I have not been to a conference in over 30 months. Moreover, all my recent invited talks have been on Zoom and did not include any one‐on‐one meetings with faculty or students. Thus, I had to include the names of scientists that I met over 3 years ago, hoping that my research made a lasting impression on them. I have heard similar anecdotes from many of my peers both at home and at other universities. Given all of this, I would encourage academics to be more forthcoming than they may have traditionally been when students or colleagues approach them for letters of support. Moreover, I think we could all be a little more forgiving and understanding when assessing our students and peers, be it for admissions into graduate school, promotion, or grant evaluations.Although it seems like life on university campuses is returning to a certain degree of normality, many scholars are still learning and working remotely, and who knows what the future may hold with regard to lockdowns. With this uncertainty, we need to do all we can to engage with and have constructive and enduring relationships with our university communities. For undergraduate and graduate students, this could mean regularly attending online office hours, even if it is only to introduce yourself, as well as actively participating in class discussions, whether they are in‐person, over Zoom, or on digital message boards. Also, do not disregard the potential and possibilities of remote volunteer research positions, especially those related to bioinformatics. Nearly, every laboratory in my department has some aspect of their research that can be carried out from a laptop computer with an Internet connection. Although not necessarily as enticing as working at the bench or in the field, computer‐based projects can be rewarding and an excellent path to a reference letter.If you are actively soliciting references, try and make it as easy as possible on your potential letter writers. Clearly and succinctly outline why you want this person to be a reference, what the letter writing/application process entails, and the deadline. Think months ahead, giving your references ample time to complete the letter, and do not be shy about sending gentle reminders. It is great to attach a CV, but also briefly highlight your most significant achievements in bullet points in your email (e.g., Dean''s Honours List 2021–22). This will save time for your references as they will not have to sift through many pages of a CV. No matter the eventual result of the application or award, be sure to follow up with your letter writers. There is nothing worse than spending time crafting a quality support letter and never learning the ultimate outcome of that effort. And, do not be embarrassed if you are unsuccessful and need to reach out again for another round of references—as Winston Churchill said, “Success is stumbling from failure to failure with no loss of enthusiasm.”     

Role of DNA-DNA interactions on the structure and thermodynamics of bacteriophages Lambda and P4

Electrostatic interactions play an important role in both packaging of DNA inside bacteriophages and its release into bacterial cells. While at physiological conditions DNA strands repel each other, the presence of polyvalent cations such as spermine and spermidine in solutions leads to the formation of DNA condensates. In this study, we discuss packaging of DNA into bacteriophages P4 and Lambda under repulsive and attractive conditions using a coarse-grained model of DNA and capsids. Packaging under repulsive conditions leads to the appearance of the coaxial spooling conformations; DNA occupies all available space inside the capsid. Under the attractive potential both packed systems reveal toroidal conformations, leaving the central part of the capsids empty. We also present a detailed thermodynamic analysis of packaging and show that the forces required to pack the genomes in the presence of polyamines are significantly lower than those observed under repulsive conditions. The analysis reveals that in both the repulsive and attractive regimes the entropic penalty of DNA confinement has a significant non-negligible contribution into the total energy of packaging. Additionally we report the results of simulations of DNA condensation inside partially packed Lambda. We found that at low densities DNA behaves as free unconfined polymer and condenses into the toroidal structures; at higher densities rearrangement of the genome into toroids becomes hindered, and condensation results in the formation of non-equilibrium structures. In all cases packaging in a specific conformation occurs as a result of interplay between bending stresses experienced by the confined polymer and interactions between the strands.     

Strongly correlated electrostatics of viral genome packaging

The problem of viral packaging (condensation) and ejection from viral capsid in the presence of multivalent counterions is considered. Experiments show divalent counterions strongly influence the amount of DNA ejected from bacteriophage. In this paper, the strong electrostatic interactions between DNA molecules in the presence of multivalent counterions is investigated. It is shown that experiment results agree reasonably well with the phenomenon of DNA reentrant condensation. This phenomenon is known to cause DNA condensation in the presence of tri- or tetra-valent counterions. For divalent counterions, the viral capsid confinement strongly suppresses DNA configurational entropy, therefore the correlation between divalent counterions is strongly enhanced causing similar effect. Computational studies also agree well with theoretical calculations.     

Thermodynamics of drug-DNA interactions: entropy-driven intercalation and enthalpy-driven outside binding in the ellipticine series

Viscosimetric and kinetic results allow one to characterize three modes of DNA binding in the ellipticine series: (1) Ellipticine and its 9 methoxy derivative, which present maximal DNA lengthening properties and bind DNA through a single step mechanism, can be considered as pure intercalators. (2) Ellipticinium derivatives and short-chain substituted oxazolopyridocarbazoles, which present intermediate DNA lengthening properties, bind DNA through a two-step mechanism, one being intercalation. (3) Long-chain substituted oxazolopyridocarbazole derivatives, which display the smallest DNA lengthening properties, bind DNA through a single-step mechanism, probably resulting from an outside binding mode. The viscosimetric and kinetic results are compared with the thermodynamic results obtained from the temperature dependence of the binding constants. It appears that drugs binding on the outside of the DNA double helix tend to have large enthalpy and small entropy contributions, whereas pure intercalating drugs have contributions from both enthalpy and entropy, with entropy dominating by about 2:1. Drugs showing two binding modes exhibit a continuum between the aforementioned extremes, with no breaks in behavior. From this comparison, a correlation between thermodynamic data and DNA binding modes is proposed. Possible molecular implications of both enthalpy and entropy to DNA binding free energy are discussed.     

Thermodynamics of Conformational Transitions in a Disordered Protein Backbone Model

Conformational entropy is expected to contribute significantly to the thermodynamics of structural transitions in intrinsically disordered proteins or regions in response to protein/ligand binding, posttranslational modifications, and environmental changes. We calculated the backbone (dihedral) conformational entropy of oligoglycine $\left({\text{Gly}}_N\right)$, a protein backbone mimic and model intrinsically disordered region, as a function of chain length ($N=3$, 4, 5, 10, and 15) from simulations using three different approaches. The backbone conformational entropy scales linearly with chain length with a slope consistent with the entropy of folding of well-structured proteins. The entropic contributions of second-order dihedral correlations are predominantly through intraresidue ?-ψ pairs, suggesting that oligoglycine may be thermodynamically modeled as a system of independent glycine residues. We find the backbone conformational entropy to be largely independent of global structural parameters, like the end-to-end distance and radius of gyration. We introduce a framework referred to herein as “ensemble confinement” to estimate the loss (gain) of conformational free energy and its entropic component when individual residues are constrained to (released from) particular regions of the ?-ψ map. Quantitatively, we show that our protein backbone model resists ordering/folding with a significant, unfavorable ensemble confinement free energy because of the loss of a substantial portion of the absolute backbone entropy. Proteins can couple this free-energy reservoir to distal binding events as a regulatory mechanism to promote or suppress binding.     

基于生物适应进化原理论证生物进化的动力

文章从现有主流生物进化理论存在的问题入手, 以生物适应进化原理为认识基础, 讨论生物进化的动力, 以求对生物进化机制有一个新的认识。在薛定谔“生命赖负熵生存”观点的指导下, 提出了“负熵流”包括能量流、物质流和信息流, 以及负熵流是生命生存和发育的动力的观点。作者在原有生物适应进化原理基础上, 修改完善并提出了“DNA、RNA和蛋白质在环境作用下的生物适应进化调控系统”理论, 并根据系统发育是个体发育的“积分”的观点, 推论得出生物与环境的负熵差引起的负熵流也是生命进化的动力, 对生物进化机制作出了新的理解。基于这样的生物进化机制的认识, 提出了“进化是一个子系统在其上一等级系统中, 将自身全部或部分信息遗传给下一代子系统, 并在其适应上一等级系统过程中, 产生一些新质, 终止一些旧质, 从而在其上一等级系统中得以延续的变化过程”的概念, 并探讨了一些与进化有关的其他争议问题。     

Water-membrane partition thermodynamics of an amphiphilic lipopeptide: an enthalpy-driven hydrophobic effect

To shed light on the driving force for the hydrophobic effect that partitions amphiphilic lipoproteins between water and membrane, we carried out an atomically detailed thermodynamic analysis of a triply lipid modified H-ras heptapeptide anchor (ANCH) in water and in a DMPC (1,2-dimyristoyl-sn-glycero-3-phosphocholine) bilayer. Combining molecular mechanical and continuum solvent approaches with an improved technique for solute entropy calculation, we obtained an overall transfer free energy of ~−13 kcal mol⁻¹. This value is in qualitative agreement with free energy changes derived from a potential of mean force calculation and indirect experimental observations. Changes in free energies of solvation and ANCH conformational reorganization are unfavorable, whereas ANCH-DMPC interactions—especially van der Waals—favor insertion. These results are consistent with an enthalpy-driven hydrophobic effect, in accord with earlier calorimetric data on the membrane partition of other amphiphiles. Furthermore, structural and entropic analysis of molecular dynamics-generated ensembles suggests that conformational selection may play a hitherto unappreciated role in membrane insertion of lipid-modified peptides and proteins.     

Radicals in Berkeley?

In a previous autobiographical sketch for DNA Repair (Linn, S. (2012) Life in the serendipitous lane: excitement and gratification in studying DNA repair. DNA Repair 11, 595–605), I wrote about my involvement in research on mechanisms of DNA repair. In this Reflections, I look back at how I became interested in free radical chemistry and biology and outline some of our bizarre (at the time) observations. Of course, these studies could never have succeeded without the exceptional aid of my mentors: my teachers; the undergraduate and graduate students, postdoctoral fellows, and senior lab visitors in my laboratory; and my faculty and staff colleagues here at Berkeley. I am so indebted to each and every one of these individuals for their efforts to overcome my ignorance and set me on the straight and narrow path to success in research. I regret that I cannot mention and thank each of these mentors individually.     

1 July 1858: what Wallace knew; what Lyell thought he knew; what both he and Hooker took on trust; and what Charles Darwin never told them

At the Linnean Society on 1 July 1858, Charles Lyell and Joseph Hooker, using only an extract from Charles Darwin's unpublished essay of 1844, and a copy of a recent letter to Asa Gray in Boston, argued successfully that Darwin understood how species originate long before a letter from Alfred Russel Wallace outlining his own version of the theory of evolution arrived at Darwin's home. That letter from Ternate in the Malay Archipelago, however, was not the first letter Darwin received from Wallace. This article will contend that two of the three letters Wallace sent Darwin between 10 October 1856 and 9 March 1858 arrived much earlier than Darwin recorded, thereby allowing him time to assess Wallace's ideas and claim an independent understanding of how the operation of divergence and extinction in the natural world leads strongly marked varieties to be identified as new species. By the time of the Linnean meeting Darwin's new ideas had filtered into his letters and ‘big’ species book, despite the absence of any independent evidence from the natural world to justify his constant insistence to have been guided only by inductive reasoning. © 2013 The Linnean Society of London, Biological Journal of the Linnean Society, 2013, 109 , 725–736.     

Free energy calculations shed light on the nuclear pore complex’s selective barrier nature

The nuclear pore complex (NPC) is the exclusive gateway for traffic control across the nuclear envelope. Although smaller cargoes (less than 5–9 nm in size) can freely diffuse through the NPC, the passage of larger cargoes is restricted to those accompanied by nuclear transport receptors (NTRs). This selective barrier nature of the NPC is putatively associated with the intrinsically disordered, phenylalanine-glycine repeat-domains containing nucleoporins, termed FG-Nups. The precise mechanism underlying how FG-Nups carry out such an exquisite task at high throughputs has, however, remained elusive and the subject of various hypotheses. From the thermodynamics perspective, free energy analysis can be a way to determine cargo’s transportability because the traffic through the NPC must be in the direction of reducing the free energy. In this study, we developed a computational model to evaluate the free energy composed of the conformational entropy of FG-Nups and the energetic gain associated with binding interactions between FG-Nups and NTRs and investigated whether these physical features can be the basis of NPC’s selectivity. Our results showed that the reduction in conformational entropy by inserting a cargo into the NPC increased the free energy by an amount substantially greater than the thermal energy (≫k_BT), whereas the free energy change was negligible (<k_BT) for small cargoes (less than ~6 nm in size), indicating the size-dependent selectivity emerges from the entropic effect. Our models suggested that the entropy-induced selectivity of the NPC depends sensitively upon the physical parameters such as the flexibility and the length of FG-Nups. On the other hand, the energetic gain via binding interactions effectively counteracted the entropic reduction, increasing the size limit of transportable cargoes up to the nuclear pore size. We further investigated the geometric effect of the binding spot spatial distribution and found that the clustered binding spot distribution decreased the free energy more efficiently as compared to the scattered distribution.