- Open Access
A strategy to characterize chlorophyll protein interaction in LIL3
© The Author(s) 2019
- Received: 9 August 2018
- Accepted: 26 December 2018
- Published: 5 January 2019
The function of proteins is at large determined by cofactors selectively bound to protein structure. Without chlorophyll specifically bound to protein, light harvesting and photosynthesis would not be possible. The binding of chlorophyll to light harvesting proteins has been extensively studied in reconstitution assays using proteins expressed in vitro; however, the mechanism of the reconstitution reaction remained unclear. We have shown that membrane integral light-harvesting-like protein, LIL3, binds chlorophyll a with a Kd of 146 nM in vitro by thermophoresis. Here, reconstitution of chlorophyll binding to LIL3 has been characterized by four different methods.
Structural changes in the reconstitution process have been investigated by light-scattering and differential Trp-fluorescence. For characterization of the chlorophyll binding site at LIL3, the analysis of LIL3 mutants has been conducted using native PAGE and thermophoresis. We find that the oxidized state of dithiothreitol is the essential component for reconstitution of chlorophyll binding to LIL3 in n-Dodecyl β-d-maltoside micelles at RT. Chlorophyll increased the polydispersity of the micellar states while dithiothreitol maintained LIL3 in a partially unfolded state at RT. Dimerization of LIL3 was abolished if amino acids N174, R176, and E171 were mutated to Ala; while, chlorophyll binding to LIL3 was abolished in mutant N174A, but retained in E171A, and R176A albeit at an about six- and five-fold decreased dissociation constant. Results show that N174 of LIL3 is essential for binding chlorophyll a.
Chlorophyll binding to LIL3 can be shown by thermophoresis, and native gel electrophoresis, while analysis of reconstitution conditions by dynamic light scattering and differential scanning fluorometry are of critical importance for method optimization.
- Chl a
The family of light-harvesting-like proteins (LIL) are regarded as evolutionary descendant of cyanobacterial high-light inducible protein (HLIP) . HLIPs were postulated to have undergone endosymbiotic gene transfer and modification, resulting in the nuclear encoded one-helix proteins (OHP) and two-helix stress-enhanced protein (SEP) . Genetic analysis specifies LIL3 as a SEP and as a precursor of the four helix non-photochemical quenching protein (PSBS) and of the four helix light-harvesting complex protein (LHC). It has been shown that LIL3 accumulation precedes chlorophyll (Chl) synthesis and assembly in protein complexes is essential for synthesis of Chl and tocopherol; although, the function of LIL3 has not been resolved [2, 3].
Reconstitution is a method extensively employed in the study of pigment binding to protein over the last 30 years. In 1987, delipidated LHC2 was isolated from thylakoid membranes and was reconstituted with pigments and xanthophyll’s . Three years later, reconstitution of recombinant LHC2 was shown to be dependent on chlorophyll a (Chl a) and carotenoid binding . Several groups reported thereafter about selective pigment binding sites using recombinant LHC proteins [5–8]. Chl a binding in the absence of carotenoids was shown for recombinant LIL3 [9, 10], and also for the recombinant reaction center protein CP43 . For Chl binding to members of the LHCs, there is broad consensus that binding is mediated by concerted action of a number of amino acids termed the LHC motif [12, 13]. In one report, the LHC motif in LIL3 was postulated to structurally anchor Geranylgeraniol-reductase (GGR) to the membrane, and to be responsible for the oligomerization of GGR .
The conserved LHC motif is an overall hydrophobic amino acid sequence composed of 22 amino acids with two charged amino acids: glutamic acid (E), arginine (R) and three glycine (G) residues within the sequence ELINGRLAMLGFLGFLVPELIT  and a consensus motif E–X–X–H/N–X–R or R–X–N/H–X–X–E found at Chl binding sites [12, 13, 15, 16]. In LHC, residues E and H/N were described to be responsible for coordination of the central Mg2+ ion of Chl. The anionic carbonyl group in E and the guanidinium group in R residues are discussed to play an important role for salt ion paring in E139–R142, E65–R185 and E180–R70 . We applied dynamic light scattering and nano-DSF for component analysis during in vitro reconstitution and find that oxidized DTT is the essential component in reconstitution of Chl a binding to LIL3.2 (LIL3). We show that oxidized DTT maintains LIL3 in a partially unfolded state in the presence of n-Dodecyl β-d-maltoside (DDM) micelles at RT. Using microscale thermophoresis (MST) and native PAGE, amino acid N174 is shown to be essential for Chl a binding to LIL3, while amino acids E171 and R176 show residual activity for reconstitution of Chl a binding to the LIL3 mutants.
DDM and DTT are key components to establish reconstitution of LIL3
Mulitmodal polydisperse mean peak intensity profiles
DDM DTT LIL3
DDM DTT Chl a
DDM DTT Chl a LIL3
10.33 ± 0.14
359.56 ± 18.03
1.10 ± 0.02
10.21 ± 0.10
441.13 ± 96.89
1.11 ± 0.03
11.34 ± 0.22
332.17 ± 40.82
1.22 ± 0.04
11.42 ± 0.50
399.23 ± 87.55
10.46 ± 0.18
455.47 ± 118.62
1.11 ± 0.01
366.53 ± 128.27
10.53 ± 0.32
1.13 ± 0.02
13.85 ± 3.76
443.20 ± 318.05
559.30 ± 142.94
12.64 ± 0.94
1.15 ± 0.58
10.58 ± 0.08
358.27 ± 10.63
1.18 ± 0.03
262.23 ± 40.05
10.68 ± 0.14
1.18 ± 0.08
12.24 ± 1.20
567.3 ± 359.54
0.99 ± 0.03
283.6 ± 47.97
4293.3 ± 622.73
12.38 ± 2.00
LIL3 shows a stepwise thermal unfolding in the presence of oxidized DTT
The stability of LIL3 in DDM micelles increases in the presence of Chl a
LIL3 mutant N174A does not interact with Chl a
It has been shown that reconstitution of LIL3 can be well documented using nanoscale thermophoresis and native PAGE. In a reconstitution buffer containing DDM and oxidized DTT, the LIL3 protein remains soluble and in a partially unfolded state upon heat denaturation whereby its interaction with Chl a can be studied at RT.
Helical regions containing Trp in LIL3 interact with transmembrane domains
Complete denaturation of LHC2 had been described already , as an essential requirement for reconstitution, and the protocol has been maintained in all LHC proteins reconstituted thereafter [4, 5, 18]. However, the principle of unfolding/refolding of the transmembrane domains in LHC upon heat denaturation and especially the question how this could influence the mechanism of reconstitution is not understood well . The dynamic scanning of protein endogenous Trp-fluorescence changes during continuous heating of a protein sample has been developed in recent years as a superior label-free method to study the dynamics of protein folding (Application note, Prometheus, protein stability, Nanotemper Technologies GmbH). The unfolding reaction of the protein is hereby determined as change in the Trp-fluorescence at 350 nm and 330 nm and the first derivative of the ratio between both wavelengths is analyzed against the temperature variable. Hereby, determination of the ratio of the fluorescence yield has the advantage to cancel out background noise.
The folding state of helical domains correlates with reconstitution of Chl a
Amino acid N174 is binding Chl in LIL3
The LIL3 mutant analysis showed that selected amino acids of the LHC motif responsible for Chl binding in LHC [5–8], also in part apply to Chl binding in LIL3. In the LIL3 N174A substitution mutant, Chl a binding was abolished, showing that N174 localized in the LHC motif consensus sequence is essential for Chl a binding to LIL3 (Fig. 5). The LIL3 E171A and R176A substitution mutants retained the ability to interact with Chl a, but with a six- and five-fold lower affinity (Fig. 4). Despite the determination of Kd for Chl binding in both mutants, thermophoretic mobility could not be saturated with LIL3 protein to reach a plateau. This suggests that also for the N174A substitution mutant a binding constant could have been determined if the recombinant mutants could be expressed and purified at higher concentration. Nevertheless, the LIL3 binding constant for Chl a is in general significantly weaker than for other photosystem Chl a-binding proteins indicating a different functional role of Chl binding to LIL3 [9, 10].
Chl molecules in LHC that are comparable to the evolutionary conserved binding site in LIL3 are bound to amino acids from two LHC motives located distant in primary sequence [17, 28]. For LIL3, dimerization has previously been suggested to establish the binding site despite the absence of a second LHC motif and Chl a binding to LIL3.2 had been suggested to precede dimerization in WT LIL3 in vitro . The significant reduction in Chl a binding strength for recombinant LIL3 E171A, and R176A mutants could therefore be explained by the finding that both mutant proteins were no longer able to dimerize (Additional file 7: Fig. S6). Interestingly, substitution mutant N174A lacked both dimerization and Chl binding. This implied that besides amino acids R176 and E171 also N174 is required to establish the dimerization site. We therefore propose an extension of our previously suggested model  to underline the importance of all three amino acids of the LHC binding motif for dimerization and to establish Chl binding to N174 in LIL3 (Fig. 7).
LIL3 may have a structural, but different functional evolution compared to LHCP
The LHC motif is conserved from the early one-helix cyanobacterial HLIPs via the two-helical SEPs to the three-helical LHCs . It has been discussed that the one-helical cyanobacterial HliD forms a dimer and in its dimeric form binds six chlorophylls and two β-carotenes . We have proposed that hetero-dimerization of the two-helical LIL3 protein precedes binding of two molecules of Chl a and that Chl a binding is independent of the presence of carotenoids [9, 10]. Our current data strongly support the previous findings that in LIL3, dimerization establishes a foundation for effective Chl binding as shown here by residue N174 which is predicted to be positioned on opposite faces of the transmembrane domains in LIL3; while, in LHCP dimerization of two LHC motives facilitate Chl binding (Fig. 7).
LHC has been proposed to descend from an internal gene duplication of the SEPs . According to present understanding, the pool of two-helix SEPs diverged into a diverse protein group consisting of early light induced proteins (ELIPs), PSBS and LHC in plantae . The indications of an inherent need for dimerization of LIL3 and HliD to facilitate Chl binding, could explain the advantage of genetically diverged proteins ELIPs, PSBS and LHCs. In LHC2, the proposed internal gene duplication of transmembrane helices 1 and 3 resulted in the duplication of the LHC motif and formation of a structural basis for increased chlorophyll binding capacity (14/monomer). If positioned in evolutionary context, interaction of the amino-acids in the internal LHC motif can be regarded as a hetero-dimerization. Together with the hetero-trimerization of LHC isomers in the LHC-trimer the Chl binding capacity of LHC increases to 42 molecules, with 24 Chl a and 18 Chl b per complex . However, if scaled down to the Chl binding LHC motif as characterized in LIL3, also in LHC only one Chl molecule is directly bound per motif . For LIL3, the predicted dimerization of the two transmembrane a-helices via the Chl binding amino acids of the LHC motif indicates a structural conservation of the motif but different evolution of the proteins function.
A combination of several different methods have been applied to characterize Chl interaction with LIL3. The combination of results from MST and native PAGE both support that amino acid N174 is binding Chl a in LIL3. The combination of results from DLS and nanoDSF clarified the change in the interaction of LIL3 and Chl a with DTT and DDM and of Chl a with DDM micelles and the transition during the reconstitution steps have been followed. The strategy significantly increased our functional understanding of the Chl protein interaction and how to characterize in vitro reconstitution further.
Aim and design of study
This study was directed to improve our understanding of the principles and mechanisms of reconstitution, a frequently used method in plant biology for analysis of protein-pigment interaction. We have previously contributed to modify the reconstitution protocol [9, 10] and established MST, DLS and ELS in our laboratory to elucidate the basis of the molecular interactions. NanoDSF experiments were performed by AMJ at NanoTemper Technologies GmbH (Munich, Germany).
Protein expression and purification
Site directed LIL3.2 (AT5G47110) mutants (LIL3.2 E171A, N174A and R176A) were purchased from life technologies in a pMA-T vector, were further amplified by forward and revers primers gtcatatgatgtctatatccatggcgt and cctaggtcacttctttgaagaaac respectively and transferred to the pET151d vector (Invitrogen) by Topo cloning. Mutants were expressed with a N-terminal His-tag in E. coli BL21 [F–ompT hsdS(rB– mB–) gal dcm λ(DE3)] and harvested as described in . LIL3 mutants were purified as in . The purified proteins were separated by SDS PAGE [12% (w/v)], stained with Coomassie Brilliant Blue (CBB) and blotted with a His (1:3000, Sigma Aldrich) primary antibody as described in .
Reconstitution assays were performed based on protocols as described [4, 5, 9]. For both LIL3.1 and LIL3.2 isoforms from Arabidopsis thaliana, very similar results were obtained . Based on the higher purification yield only experimental work with LIL3.2 is shown here. In brief; LIL3 inclusion bodies (30 μM) were solubilized in a reaction buffer containing 100 mM Tris pH 11, 5 mM 6-aminocaproic acid, 1 mM benzamidine and 12.5% sucrose and n-Dodecyl β-d-maltoside (DDM) at a final concentration of 6 mM DDM respectively. 100 mM DTT and 6 μM Chl a (solubilized in diethyl ether/Ethanol 1:1) were added prior to heating samples to 100 °C for 1 min followed by a 2-h incubation at RT in the dark.
Dynamic light scattering, DLS
Dynamic light scattering (DLS) was applied to determine if LIL3 was integrated to the DDM micelle structure during reconstitution using a Zetasizer Nano ZSP (Malvern, UK). The intensity distribution profile [diameter (d. nm)] of Chl a and Chl a reconstituted with LIL3.2 was recorded upon dissolving reaction components in reconstitution buffer containing 6 mM DDM and 100 mM DTT at 25 °C. Recording was conducted when all reaction components were assembled, 1 min after boiling, and 2 h after boiling under reconstitution conditions (100 mM Tris, 5 mM 6-aminocaproic acid, 1 mM benzamidine and 12.5% sucrose, 100 mM DTT, pH 11). The average of the peak value weighted by the mean hydrodynamic diameter is given for all samples. In dynamic light scattering (DLS) analysis, the mean hydrodynamic diameter of particles (hd) can be determined from the particles characteristic Brownian motion. An intensity distribution of determined hd-values displays the dispersity of the sample. Care has to be taken to interpret concentration changes of sample as changes of the intensity values are proportional to h d 6 . Cumulative analysis is not valid for poly-disperse samples. Therefore, the distribution means in the linear range is reported, not Z-Average and PDI [31–35].
Thermal unfolding, nanoDSF
Samples for thermal unfolding were prepared by combining the same volume of LIL3.2 sample (5 μM) in DDM micelles (6 mM) in reconstitution buffer (100 mM Tris, 5 mM 6-aminocaproic acid, 1 mM benzamidine and 12.5% sucrose, pH 11) in the absence or presence of DTT. Fluorescence based thermal experiments were performed using Prometheus NT.48 (NanoTemper Technologies, Germany). All capillaries containing 10 μl LIL3.2 recombinant protein were sealed. The temperature was increased by a rate of 1 °C/min from 20 to 110 °C and the fluorescence at emission wavelengths of 330 nm and 350 nm was measured. For interpretation of spectra, application notes from the company were considered.
Electrophoretic light scattering, ELS
Electrophoretic light scattering was applied to determine the zeta potential (stability) of the DDM micelle, LIL3 dimer, Chl a and LIL3 reconstituted with Chl a following the reconstitution procedure. Experiments were performed in triplicate and the average plotted. Standard deviation was calculated for the three independent measurements.
Microscale thermophoresis, MST
The intrinsic fluorescence of Chl a, was monitored at a final concentration of 30 nM Chl a diluted in reconstitution buffer containing 6 mM DDM, while non-fluorescent LIL3.2 mutants E171A, N174A and R176A were titrated in a 1:1 dilution series (concentrations between 2.500 µM and 0.61 nM) in reconstitution buffer containing 6 mM DDM. After a 2-h incubation at RT, samples were loaded into Monolith™ NT.115 MST Premium Coated Capillaries (NanoTemper Technologies, Munich, Germany) and measured using a Monolith NT.115 at RT and analyzed by the MO. Control Software, LED/excitation 10%, MST power setting 40%. Results are recorded as normalized fluorescence (Fnorm = Fhot/Finitial) and presented as differential fluorescence [ΔFnorm = Fnorm (bound) − Fnorm (unbound)] which reads as ΔFnorm = baseline corrected Fnorm (‰) . Lil3.2 mutant dimer analysis was performed as described for wild type LIL3.2 .
LIL3.2 mutants bound to Chl a was isolated by LDS-Native (LN) PAGE on 3–12% polyacrylamide gels (Novex, Life technologies, California USA) with a cathode buffer supplemented with 74 μM LDS . Pigment and pigment binding protein were detected before protein staining by fluorescence scanning at 800 nm in a LI-COR Odyssey® CLx and stained by CBB as described .
Absorbance spectra were recorded from 200 to 400 nm (Shimadzu UV–VIS 2401PC, Duisburg, Germany). Spectra of DTT were measured at pH 6 in dH2O and at pH11 in reconstitution buffer. Spectra of LIL3.2 were recorded upon solubilization in 6 mM DDM, pH 11 in reconstitution buffer and in the presence or absence of DTT and upon reconstitution with Chl a.
AM: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Writing—original draft, Writing—review and editing; LE: Conceptualization, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Supervision, Validation, Visualization, Writing—original draft, Writing—review and editing. Both authors read and approved the final manuscript.
We are grateful for the research funding received from the Norwegian Research Council NFR 240770.
The authors declare that they have no competing interests.
Availability of data and materials
The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.
Consent for publication
Ethics approval and consent to participate
We are grateful for the research funding received from the Norwegian Research Council NFR 240770. The funding body had no role in the design of the study and collection, analysis, and interpretation of data and in writing the manuscript.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.
- Engelken J, Brinkmann H, Adamska I. Taxonomic distribution and origins of the extended LHC (light-harvesting complex) antenna protein superfamily. BMC Evol Biol. 2010;10:233.PubMedPubMed CentralGoogle Scholar
- Reisinger V, Ploscher M, Eichacker LA. Lil3 assembles as chlorophyll-binding protein complex during deetiolation. FEBS Lett. 2008;582(10):1547–51.View ArticleGoogle Scholar
- Tanaka R, Rothbart M, Oka S, Takabayashi A, Takahashi K, Shibata M, et al. LIL3, a light-harvesting-like protein, plays an essential role in chlorophyll and tocopherol biosynthesis. Proc Natl Acad Sci USA. 2010;107(38):16721–5.View ArticleGoogle Scholar
- Plumley FG, Schmidt GW. Reconstitution of chlorophyll a/b light-harvesting complexes: xanthophyll-dependent assembly and energy transfer. Proc Natl Acad Sci USA. 1987;84(1):146–50.View ArticleGoogle Scholar
- Paulsen H, Rumler U, Rudiger W. Reconstitution of pigment-containing complexes from light-harvesting chlorophyll-A/B-binding protein overexpressed in Escherichia coli. Planta. 1990;181(2):204–11.View ArticleGoogle Scholar
- Ballottari M, Mozzo M, Croce R, Morosinotto T, Bassi R. Occupancy and functional architecture of the pigment binding sites of photosystem II antenna complex Lhcb5. J Biol Chem. 2009;284(12):8103–13.View ArticleGoogle Scholar
- Caffarri S, Croce R, Cattivelli L, Bassi R. A look within LHCII: differential analysis of the Lhcb1–3 complexes building the major trimeric antenna complex of higher-plant photosynthesis. Biochemistry. 2004;43(29):9467–76.View ArticleGoogle Scholar
- Morosinotto T, Baronio R, Bassi R. Dynamics of chromophore binding to Lhc proteins in vivo and in vitro during operation of the xanthophyll cycle. J Biol Chem. 2002;277(40):36913–20.View ArticleGoogle Scholar
- Mork-Jansson AE, Eichacker LA. Characterization of chlorophyll binding to LIL3. PLoS ONE. 2018;13(2):e0192228.View ArticleGoogle Scholar
- Mork-Jansson AE, Gargano D, Kmiec K, Furnes C, Shevela D, Eichacker LA. Lil3 dimerization and chlorophyll binding in Arabidopsis thaliana. FEBS Lett. 2015;589(20 Pt B):3064–70.View ArticleGoogle Scholar
- Ji L, Xie SS, Yue L, Zhu GF, Du LF. Soluble expression of Spinach psbC gene in Escherichia coli and in vitro reconstitution of CP43 coupled with chlorophyll a only. Plant Physiol Biochem. 2014;79:19–24.View ArticleGoogle Scholar
- Jansson S. The light-harvesting chlorophyll a/b-binding proteins. Biochim Biophys Acta. 1994;1184(1):1–19.View ArticleGoogle Scholar
- Jansson S. A guide to the Lhc genes and their relatives in Arabidopsis. Trends Plant Sci. 1999;4(6):236–40.View ArticleGoogle Scholar
- Takahashi K, Takabayashi A, Tanaka A, Tanaka R. Functional analysis of light-harvesting-like protein 3 (LIL3) and its light-harvesting chlorophyll-binding motif in Arabidopsis. J Biol Chem. 2013;289:987–99.View ArticleGoogle Scholar
- Eggink LL, Hoober JK. Chlorophyll binding to peptide maquettes containing a retention motif. J Biol Chem. 2000;275(13):9087–90.View ArticleGoogle Scholar
- Green RR, Pichersky E. Hypothesis for the evolution of three-helix Chl a/b and Chl a/c light-harvesting antenna proteins from two-helix and four-helix ancestors. Photosynth Res. 1994;39(2):149–62.View ArticleGoogle Scholar
- Kuhlbrandt W, Wang DN, Fujiyoshi Y. Atomic model of plant light-harvesting complex by electron crystallography. Nature. 1994;367(6464):614–21.View ArticleGoogle Scholar
- Giuffra E, Cugini D, Croce R, Bassi R. Reconstitution and pigment-binding properties of recombinant CP29. Eur J Biochem. 1996;238(1):112–20.View ArticleGoogle Scholar
- Kim BL, Schafer NP, Wolynes PG. Predictive energy landscapes for folding α-helical transmembrane proteins. Proc Natl Acad Sci. 2014;111(30):11031–6.View ArticleGoogle Scholar
- Fersht A. Structure and mechanism in protein science: a guide to enzyme catalysis and protein folding. New York: W.H. Freeman, 1998. xxi, 631.Google Scholar
- Kosinski J, Mosalaganti S, von Appen A, Teimer R, DiGuilio AL, Wan W, et al. Molecular architecture of the inner ring scaffold of the human nuclear pore complex. Science. 2016;352(6283):363–5.View ArticleGoogle Scholar
- Fan M, Li M, Liu Z, Cao P, Pan X, Zhang H, et al. Crystal structures of the PsbS protein essential for photoprotection in plants. Nat Struct Mol Biol. 2015;22(9):729–35.View ArticleGoogle Scholar
- Situ AJ, Kang S-M, Frey BB, An W, Kim C, Ulmer TS. Membrane anchoring of α-helical proteins: role of tryptophan. J Phys Chem B. 2018;122(3):1185–94.View ArticleGoogle Scholar
- Vinothkumar KR, Henderson R. Structures of membrane proteins. Q Rev Biophys. 2010;43(1):65–158.View ArticleGoogle Scholar
- Callebaut I, Labesse G, Durand P, Poupon A, Canard L, Chomilier J, et al. Deciphering protein sequence information through hydrophobic cluster analysis (HCA): current status and perspectives. Cell Mol Life Sci. 1997;53(8):621–45.Google Scholar
- Gaboriaud C, Bissery V, Benchetrit T, Mornon JP. Hydrophobic cluster-analysis - An efficient new way to compare and analyze amino-acid-sequences. Febs Letters. 1987;224(1):149–55.Google Scholar
- Seo A, Jackson JL, Schuster JV, Vardar-Ulu D. Using UV-absorbance of intrinsic dithiothreitol (DTT) during RP-HPLC as a measure of experimental redox potential in vitro. Anal Bioanal Chem. 2013;405(19):6379–84.View ArticleGoogle Scholar
- Cammarata KV, Schmidt GW. In vitro reconstitution of a light-harvesting gene product: deletion mutagenesis and analyses of pigment binding. Biochemistry. 1992;31(10):2779–89.View ArticleGoogle Scholar
- Staleva H, Komenda J, Shukla MK, Slouf V, Kana R, Polivka T, et al. Mechanism of photoprotection in the cyanobacterial ancestor of plant antenna proteins. Nat Chem Biol. 2015;11(4):287–91.View ArticleGoogle Scholar
- Hassan PA, Rana S, Verma G. Making sense of Brownian motion: colloid characterization by dynamic light scattering. Langmuir ACS J Surf Colloids. 2015;31(1):3–12.View ArticleGoogle Scholar
- Hansen PC, O’Leary DP. The use of the L-curve in the regularization of discrete ill-posed problems. J Sci Comput. 1993;14(6):1487–503.Google Scholar
- Lawson CL, Hanson RJ. Solving least squares problems. Philadelphia: Society for Industrial & Applied Mathematics; 1995.View ArticleGoogle Scholar
- Ruf H. Effects of experimental errors in dynamic light scattering data on the results from regularized inversions. In: Buckin V, editor. Trends in colloid and interface science XIV. Berlin: Springer; 2000. p. 255–8.View ArticleGoogle Scholar
- ISO22412. Particle size analysis: dynamic light scattering (DLS). 2017.Google Scholar
- Twomey S. Introduction to the mathematics of inversion of remote sensing and indirect measurements. New York: Dover; 1997.Google Scholar
- Jerabek-Willemsen M, Wienken CJ, Braun D, Baaske P, Duhr S. Molecular interaction studies using microscale thermophoresis. Assay Drug Dev Technol. 2011;9(4):342–53.View ArticleGoogle Scholar