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I'm reading a paper about yeast culture and in the methods, it says:
Then $5$ ml of sterile $M/15 KH_2PO_4$, was added to the slant,
What is the meaning of $M/15$?
Penicillium: Description, Structure and Reproduction
Penicillium is a saprophytic fungus, com­monly known as blue or green mold. According to Raper and Thom (1949), the genus includes 1 36 species, distributed throughout the world. They are present in soil, in air, on decaying fruits, vegetables, meat, etc.
The “wonder drug” penicillin was first dis­covered by Sir Alexander Fleming at Sant Mary’s Hospital, London, in 1929 during his work with a bacterium Staphylococcus aureus responsible for boil, carbuncle, sepsis in wounds and burns etc., get contaminated with mold spore (Penicillium notatum) which after proper growth causes death of 5. aureus showing lytic zone around itself.
He isolated and called this anti­microbial compound as Penicillin. Later Raper and Alexander (1945) selected a strain of P. crysogenum, more efficient than P. notatum, in the production of penicillin. The importance of Penicillium is mentioned in the Table 4.6.
Vegetative Structure of Penicillium:
The vegetative body is mycelial (Fig. 4.42A, B). The mycelium is profusely branched with septate hyphae, composed of thin-walled cells containing one to many nuclei (Fig. 4.42C). Each septum has a central pore, through which cyto­plasmic continuity is maintained.
Some mycelia grow deeper into the substratum to absorb food material and others remain on the substrate and grow a mycelial felt. The reserve food is present in the form of oil globules.
Reproduction in Penicillium:
Penicillium reproduces by vegetative, asexual and sexual means.
1. Vegetative reproduction:
It takes place by accidental breaking of vegetative mycelium into two or more fragments. Each fragment then grows individually like the mother mycelium.
2. Asexual Reproduction:
Asexual repro­duction takes place by unicellular, uninucleate, nonmotile spores, the conidia formed on conidiophore (Fig. 4.43).
The conidiophore develops as an erect branch from any cell of the vegetative mycelium. The conidiophore may be unbranched (P. spinulosum, P. thomii) or becomes variously branched (P. expansum). The branch of the conidiophore (Fig. 4.44B) is known as ramus (plural rami) which further becomes branched known as metulae. A number of flask-shaped phialid or sterigmata develops at the tip of each metulae.
Each sterigmata develops at its tip a number of conidia arranged basipetally (younger one near the mother and older one away from it). In species (P. spinulosum) with unbranched coni­diophore, the sterigmata develops at the tip of conidiophore. Rarely (P. claviforme) many conidiophores become aggregated to form a club- shaped fructification called coremium, which develops conidia known as coremiospores.
During the development of conidium, the tip of the sterigma swells up and its nucleus divides mitotically into two nuclei, of which one migrates into the swollen tip and by partition wall the swollen region cuts off from the mother and forms the uninucleate conidium.
The tip of the sterigma swells up again and following the same procedure second conidium is formed, which pushes the first one towards the outer side. This process repeats several times and thus a chain of conidia is formed.
The conidia (Fig. 4.44C) are oval, elliptical or globose in structure having smooth, rough, echinulate outer surface and of various colou­rations like green, yellow, blue etc.
After maturation, the conidia get detached from the mother and are dispersed by wind. On suitable substratum, they germinate (Fig. 4.44D) by developing germ tube. The nucleus undergoes repeated mitotic division and all nuclei enter into the germ tube. The septa formation continues with the elongation of germ tube and finally a new septate branched mycelium develops.
3. Sexual Reproduction:
Sexual reproduction has been studied only in few species (Fig. 4.44). It shows great variation from isogamy (P. bacillosporum), oogamy (P. vermiculatum) to somatogamy (P. brefeldianum). Most of the species are homothallic, except a few like P. luteum are heterothallic. Ascocarps are rarely formed. Based on the ascocarps, different genera can be assigned as Europenicillium, Talaromyces and Carpenteles.
The genus Talaromyces consists of 15 species. All the species of Talaro­myces studied are homothallic. The account of sexual reproduction deals with Talaromyces vermiculatus (= Penicillium vermiculatum) was described by Dangeard (1907). This spedes shows oogamous type of sexual reproduction. The female and male sex organs are ascogonium and antheridium’, respectively.
The ascogonium develops from any cell of the vegetative filament as an erect uninucleate and unicellular body (Fig. 4.44E). The nucleus then undergoes repeated mitotic divisions and produces 32 or 64 nuclei (Fig. 4.44F).
The antheridium develops simultaneously with the ascogonium from any neighbouring hypha (Fig. 4.44F). It is also an uninucleate and unicellu­lar branch which coils around the ascogonium. The apical region of antheridial branch cuts off by septum and forms a short, somewhat inflated uni­cellular and uninucleate antheridium (Fig. 4.44G).
After maturation of both ascogonium and antheridium, the tip of the antheridium bends and touches the ascogonial wall. The common wall at the point of contact dissoves and the two cytoplasm then intermixed.
The nucleus of the .antheridium does not migrate (Fig. 4.44H) into the ascogonium (Dangeard, 1907). Later, the pairing of nuclei into the ascogonium takes place by the ascogonial nuclei only. The ascogonium then divides by partition wall into many binucle­ate cells, arrange uniseriately (Fig. 4.44H).
Some of the binucleate cells of the ascogo­nium projects out by the formation of multicellu­lar ascogenous branched hyphae, whose cells are also dikaryotic (Fig. 4.441). The apical cells of the dikaryotic mycelia swell up and function as an ascus mother cells (Fig. 4.44J).
Both the nuclei of ascus mother cell undergo karyogamy and form diploid (2n) nucleus (Fig. 4.44K). The nucleus then undergoes first meiosis, then mito­sis, results in the formation of 8 nuclei those after accumulating some cytoplasm form 8 ascospores (Fig. 4.44L).
With the development of ascogonium and antheridium, many sterile hyphae gradually entangle with them and finally after the forma­tion of ascospores, the total structure becomes a round fruit body i.e., cleistothecium (Fig. 4.44M). The asci arrange irregularly inside the cleistothecium. The ascospores may be globose, elliptical or lenticular in shape with smooth, echinucleate, pitted (Fig. 4.44N) or branched outer wall like a pully-wheel in lateral view.
The ascospores are released by the dis­solution of ascus and cleistothecium wall. The ascospore germinates on a suitable substratum by developing germ tube (Fig. 4.440) and ulti­mately into a mycelium like the mother.
Dot notation for property access in Objective-C is a message send, just as bracket notation. That is, given this:
The last two lines will compile exactly the same. The only thing that changes this is if a property has a getter and/or setter attribute specified however, all it does is change what message gets sent, not whether a message is sent:
Both of the last two lines will compile identically.
Check out article from Cocoa is My Girlfriend. The gist of it, is that there is no performance penalty of using one over the other.
However, the notation does make it more difficult to see what is happening with your variables and what your variables are.
The only time you'll see a performance difference is if you do not mark a property as "nonatomic". Then @synthesize will automatically add synchronization code around the setting of your property, keeping it thread safe - but slower to set and access.
Thus mostly you probably want to define a property like:
@property (nonatomic, retain) NSString *myProp
Personally I find the dot notation generally useful from the standpoint of you not having to think about writing correct setter methods, which is not completely trivial even for nonatomic setters because you must also remember to release the old value properly. Using template code helps but you can always make mistakes and it's generally repetitious code that clutters up classes.
A pattern to be aware of: if you define the setter yourself (instead of letting @synthesize create it) and start having other side effects of setting a value you should probably make the setter a normal method instead of calling using the property notation.
Semantically using properties appears to be direct access to the actual value to the caller and anything that varies from that should thus be done via sending a message, not accessing a property (even though they are really both sending messages).
3. The old cast iron washbacks
In the 19th and 20th century some distilleries looked for alternatives. They wanted to use materials that are easier to clean and effect a longer operational life span. Cast iron was the answer of these centuries and in a few distilleries you still can see some of these heavy washbacks.
Cast iron Washbacks at Alt a Bhaine
Background information and search criteria
A patent is a legal document describing technical information. This review is based on “patent families” that combine specifications describing the same basic invention. Contrary to other reviews on this topic ( Gélinas 2009 2010a 2010b ), these related patents are presented according to the earliest filing date, not the publication date. This helped to determine priority of related inventions, trace back the original inventors, and better judge technology trends and inventors’ incentives according to time. During the preparation of this review, it was found that in countries such as Germany and Austria, there were large delays between filing dates and publication dates, sometimes more than 5 y, especially during the World War I and II periods around 1914 to 1918 and 1939 to 1945.
In several patent offices, priority of inventions disclosed in specifications filed after 1900 was generally checked before the acceptance and publication of patents. However, in Great Britain (GB), specifications of nonaccepted patents were published until 1883 but the complete specification of one nonaccepted GB patent issued in 1924 was found (GB 192085). GB patents with an application date earlier than 1916 were identified both by the year of application (rather than year of publication) and by serial number afterwards, a new and continuously numbered sequence was introduced ( Rimmer and Van Dulken 1992 ).
This review did not attempt to give a full account of yeast technology because patents represent only a fraction of total inventions. This has been covered elsewhere ( Reed and Nagodawithana 1991 Gélinas 2006 ). Patents were rather seen as privileged and timely evidence of the evolution of interests and concerns in the yeast manufacturing industry, especially in the years 1900 to 2009. This work also completes the review of patents published before 1900 ( Gélinas 2010a ). Most of the patents were obtained through search in data bases, such as [email protected] and Depatis. Some French patents were ordered through INPI (Institut Natl. de la Propriété Intellectuelle, Paris). More details on the methodology are given in Gélinas (2010a) . Near the completion of this review, it was possible to get access to a book published by Wagner (1936) that includes a brief abstract of many patents issued prior to 1936 on baker's yeast.
The expression of recombinant proteins, especially using bacterial vectors and hosts, is a mature technology. With the appropriate cDNA and PCR methods, expression plasmids can be rapidly produced. Following sequence determination of the constructs, plasmids are transformed into expression hosts, single colonies picked, and fermentation performed. With E. coli, a 2-liter fermentation using complex media will generate
50 to 80 g (wet weight of cells). Assuming modest protein expression (2% to 5% of the total cellular protein), between 100 and 300 mg of recombinant protein is available in the cells. The problem is, of course, how to isolate it in an active form. Soluble proteins can be recovered with good yields (㹐%), and insoluble proteins, which must undergo a denaturation and folding cycle, can be recovered with more modest yields (5% to 20%). Hence, using small-scale fermentations and laboratory-scale processing equipment, proteins (or subdomains thereof) can usually be produced in sufficient quantities (10 to 100 mg) to initiate most studies including detailed structural determinations. Some strategies for achieving high-level expression of genes in E. coli have been reviewed by Markrides (1996) and Baneyx (1999) and are also discussed in Unit 5.24.
Some of the above characteristics also hold true for the production of proteins using yeast and baculovirus eukaryotic expression systems, although more effort and expertise is required to construct the vectors and, with the baculovirus system, produce cells for processing. A yeast expression system may be a wise choice for proteins that form insoluble inclusions in bacteria, and for the production of membrane-associated proteins (Cereghino and Clegg, 1999 UNITS 5.6𠄵.8). The baculovirus system has proven very useful for producing phosphorylated proteins and glycoproteins (Kost, 1999 UNITS 5.4𠄵.5) and for the co-expression of interacting proteins. The construction of stable mammalian protein expression vectors requires considerably more time and effort but may be the only approach for producing complex multidomain proteins (UNITS 5.9𠄵.10). Cells growing to cell densities of 1𠄵 휐 9 cells/ml can be expected to typically secrete 㸐 mg/liter of product. Alternatively, transient gene expression systems using various viral vectors (e.g., vaccinia virus UNITS 5.12𠄵.15), can be used to produce lesser amounts of protein, which is useful for feasibility studies. It is of interest to note that the large-scale transient expression systems in mammalian cells are being actively developed by biotechnology companies (Wurm and Bernard, 1999).
The choice of a host system for the production of recombinant proteins is discussed in unit 5.16 and is also concisely summarized by Brondyke (2009). Also, there is a special issue on the production of recombinant proteins in the journal Biotechnology Advances (Sanchez and Demin, 2012). In this issue there are excellent overviews of protein expression and production using E.coli (Chen, 2012) yeast (Celik and Calik, 2012) insect cell and the baculovirus system (Drugmand et al 2012) mammalian cells (Zhu, 2012) cell free systems (Carlson et al., 2012) and plant cells (Xu et al., 2012).
As mentioned by Chen (2012), for many investigators the initial choice is often Escherichia coli which remains the preferred system for laboratory investigations and initial development in commercial activities and is a benchmark for comparison among the other various expression platforms. This is due to such factors as ease of genetic manipulation, availability of optimized expression plasmids, and ease of growth. This unit presents an overview of recombinant protein purification with special emphasis on proteins expressed in E. coli. Practical aspects and strategies are stressed throughout, and wherever possible, the discussion is cross-referenced to the example protocols described in the rest of Chapter 6.
The first section deals with information pertinent to protein purification that can be derived from translation of the cDNA sequence. This is followed by a brief discussion of some of the common problems associated with bacterial protein expression (see also UNIT 5.1). Planning a protein purification strategy requires that the solubility of the expression product be determined it is also useful to establish the location of the protein in the cell𠅎.g., cytoplasm or periplasm. This unit includes flow charts that summarize approaches for establishing solubility and localization of bacterially produced proteins (see also UNIT 5.2).
Purification strategies for both soluble and insoluble proteins are reviewed and summarized in flow charts (see also Chapter 1). Many of the individual purification steps, especially those involving chromatography, are covered in detail in Chapters 8 and 9, and elsewhere (Scopes, 1994 Janson, 2011). The methodologies and approaches described here are essentially suitable for laboratory-scale operations. Large-scale methodologies have been previously reviewed (Asenjo and Patrick 1990 Thatcher, 1996 Sofer and Hagel, 1997).
A section on glycoproteins produced in bacteria in the nonglycosylated state is included to emphasize that, although they may not be useful for in vivo studies, such proteins are well suited for structural studies. The final sections deal with protein handling, scale and aims of purification, and specialized equipment needed for recombinant protein purification and characterization.
How the Scientific Method Works
Clearly, the scientific method is a powerful tool, but it does have its limitations. These limitations are based on the fact that a hypothesis must be testable and falsifiable and that experiments and observations be repeatable. This places certain topics beyond the reach of the scientific method. Science cannot prove or refute the existence of God or any other supernatural entity. Sometimes, scientific principles are used to try to lend credibility to certain nonscientific ideas, such as intelligent design. Intelligent design is the assertion that certain aspects of the origin of the universe and life can be explained only in the context of an intelligent, divine power. Proponents of intelligent design try to pass this concept off as a scientific theory to make it more palatable to developers of public school curriculums. But intelligent design is not science because the existence of a divine being cannot be tested with an experiment.
Science is also incapable of making value judgments. It cannot say global warming is bad, for example. It can study the causes and effects of global warming and report on those results, but it cannot assert that driving SUVs is wrong or that people who haven't replaced their regular light bulbs with compact fluorescent bulbs are irresponsible. Occasionally, certain organizations use scientific data to advance their causes. This blurs the line between science and morality and encourages the creation of "pseudo-science," which tries to legitimize a product or idea with a claim that has not been subjected to rigorous testing.
And yet, used properly, the scientific method is one of the most valuable tools humans have ever created. It helps us solve everyday problems around the house and, at the same time, helps us understand profound questions about the world and universe in which we live.
Most of the time, two competing theories can’t exist to describe one phenomenon. But in the case of light, one theory is not enough. Many experiments support the notion that light behaves like a longitudinal wave. Taken collectively, these experiments have given rise to the wave theory of light. Other experiments, however, support the notion that light behaves as a particle. Instead of throwing out one theory and keeping the other, physicists maintain a wave/particle duality to describe the behavior of light.
Classification of Microorganism | Microbiology
The following points highlight the three main system of classifications of microorganism. The system of classifications are: 1. Five-Kingdom System of Classifications 2. Eight Kingdom System of Classi­fication 3. Three Domain System of Classification.
1. Five-Kingdom System of Classifications:
Later, prokaryotic and eukaryotic organisms were distinguished on the basis of cell anatomy, and the concept of a bacterium as a prokaryotic organism was established in microbiology in 1962 by Stamir and Van Niel. In 1969, Whittaker proposed a five kingdom system consisting of kingdom of plantae, fungi, animalia, protista and monera (Fig. 2.3) for all organisms on the basis of their energy- yielding systems and cell anatomy.
Microorganisms with the common characterstics described above are distributed in the kingdoms of monera, protista, fungi and a part of plants. Recently, evolutionary relationships of living organisms have been defined on the basis of ribosomal RNA sequences and other data.
The kingdom Monera of prokaryoteae includes all prokaryotic microorganisms. Protista consists of unicellular or multicellular eukaryotic organisms but true tissues are lacking. The kingdom Fungi contains eukaryotic and multinucleate organisms.
The members have absorptive mode of nutrition. Animalia contains multicellular animals devoid of cell wall. Ingestion is the mode of nutrition. The kingdom Plantae includes multicellular eukaryotes. Their mode of nutrition is the photosynthesis.
2. Eight Kingdom System of Classi­fication:
Cavalier-Smith (1987, 1993) classi­fied protists into eight kingdoms on the basis of ultrastructure of cell and genetic organisations (rRNA sequencing and other data). He divided all organisms into two empires (Bacteria and Eukaryota) (Fig. 2.4). The empire Bacteria includes two kingdoms (Eubacteria and Archaeobacteria). The empire Eukaryota contains six kingdoms (Archezoa, Protozoa, Plantae, Chromista, Fungi and Animalia).
The kingdom Chromista includes diatoms, brown algae, crypto-monads and oomycetes. The members of Chromista are photosynthetic and have their chromoplast within the lumen of endoplasmic reticulum but not in cytoplasm.
3. Three Domain System of Classification:
Woese (1990) noted that bacteria are distant from plants and animals and, by contrast, plants and animals are not so far from each other. Therefore, they established a new superior concept of domains over the kingdom, and proposed three domains, Bacteria, Archaea and Eukarya in 1991 (Fig. 2.5).
Fig. 2.5 : Universal phylogenetic tree derived from comparative sequencing of 16S or 18S ribosomal RNA.
The domains Archaea and Eukarya are distinctly related to each other. Eukarya includes the organisms which possess glycerol fatty acyl-diester as membrane lipids and eukaryotic rRNA. The domain Bacteria consists of such members which have membrane lipids as diacyl glycerol diesters and eubacterial rRNA.
The mem­ber of domain Archaea consists of isoprenoid glycerol diester (or diglycerol tetraether) lipids in their membrane and archebacterial rRNA.
In a modern sense, bacteria, cyanobacteria, actinomycetes, etc. are dis­tributed in the domain bacteria methanogens extremely thermophilic organisms, extremely halophilic organisms, etc. are in the domain Archaea and molds, yeasts, basidiomycetes, algae and protozoa, etc. in the domain Eukarya. Microorganisms are regarded as collections of evolutionary different organisms.
Move it to a safe spot
Once the bottle filled up completely, we moved the whole yeast sugar experriment to the sink. The bubbles were slow-moving, and there was nothing to worry ourselves with, but N enjoyed pulling the balloon off and watching the foam slowly pour over the bottle’s top.
Materials and methods
The maximum likelihood fit procedure (Figure 2D) was implemented in MATLAB and the source code is available at https://github.com/gerland-group/PHO5_on-off-slide_models.
Maximum likelihood fits
Depending on the stage of the analysis, we optimized the parameter values, that is, the rate values of the processes within a given model, r → , by maximizing the sum of log10 likelihood values: L I ( r → ) in stage 1, L I ( r → ) + L I I ( r → ) in stage 2 and L I ( r → ) + L I I ( r → ) + L I I I ( r → ) in stage 3. Note that the optimal r → can differ between different stages. We ignored additive constants to the log likelihood, so that after including the next data set into the fit, a perfect agreement between model and the additional data set, already with the values r → from the previous stage, would lead to the same log likelihood value as before. In all stages we used the MATLAB fmincon function to find the parameter values r → that maximize the likelihood.
With the rate parameter notation introduced in Figure 2, we have for the example of Figure 3A:
Let Q ( r → σ ) be the transition rate matrix of the Markov process defined by the model for promoter state σ , where r → σ denotes the vector containing the regulated parameter value(s) of promoter state σ and all constitutive parameter values. A non-diagonal entry Q i j ( r → σ ) is the rate to go from configuration i to configuration j and is non-zero only for valid assembly, disassembly and sliding reactions and then given by the entry of r → σ which holds the parameter value of the process that governs this reaction in the given model. If sliding reactions are not governed by any sliding process within the model, their rate is set to zero. Diagonal entries are given by Q i i ( r → σ ) = - ∑ j ≠ i Q i j ( r → σ ) . In the example of Figure 3A, the transition rate matrix in the activated state is given by (with ' … ' representing the diagonal entries)
The steady state distribution p i σ of Q ( r → σ ) is the solution of p j σ = ∑ i p i σ Q i j ( r → σ ) = 0 .
Then L I ( r → ) can be calculated using the multinomial distribution,
with n i σ being the number of observations of the corresponding promoter configurations (Figure 1—source data 1).
For each model, we used 100 different sets of initial parameter values to ensure a robust maximum. To calculate the steady state distribution of a given model for fixed parameter values, we used the state reduction algorithm (Sheskin, 1985 Grassmann et al., 1985 Shanbhag and Rao, 2003). Alternatively, the Matrix-Tree theorem can be used to find the steady state distributions of Markov processes (Wong and Gunawardena, 2020). We limited the range of parameter values to [ 10 - 2 10 2 ] , with one being the rate value of the global assembly process for the activated state. A wider range of [ 10 - 3 10 3 ] did not affect the results. In 3.6% of all models the 100 tries found at least two different maximal likelihood values, which were always extremely low. In 2.4% of all models, the found maximum likelihood parameter values were not unique. In both cases, none of these problematic models were among models with relatively high maximal likelihoods.
In stage 2, the sum of L I ( r → ) and L I I ( r → ) is optimized. Assuming the experimental fold changes are normally distributed the log10 likelihood of a model to reproduce the new data up to an additive constant is given by
with f s m mean and f s m var being mean and variance, respectively, of the measured accessibility fold changes in active state of sticky N-3 mutant m at nucleosome site s (two for N-2 and 3 for N-3), f s ( r → , κ → m ) being the corresponding model fold change, and κ → m being the values of the rate prefactors of sticky mutant m .
To obtain f s ( r → , κ → m ) for each model, we calculated a modified transition rate matrix for each mutant using the non-diagonal part of the transition rate matrix Q ( r → act ) and multiplied it component-wise with the matrix W ( κ → m ) containing the prefactor values κ → m for the affected reactions for mutant m (and one otherwise). Using the modified transition rate matrices, we calculated the mutant steady state distributions and finally the corresponding fold ratios of accessibilities at N-2 and N-3.
We used four prefactors per sticky N-3 mutant, one for each group of reactions, assembly at N-3, disassembly at N-3, sliding from N-3 to N-2 and from N-2 to N-3 (Figure 2—figure supplement 5), respectively, leading to κ → m = ( κ a 3 m , κ d 3 m , κ s 23 m , κ s 32 m ) ⊤ . The off-diagonal part of W ( κ → m ) is then given by
where the diagonal does not matter due the component-wise multiplication with the non-diagonal part of Q ( r → act ) in order to obtain the non-diagonal part of the mutant rate transition matrices. Thus, L I I depends only on r → act . Note that the exact values of prefactors found during optimization depended on their initial condition, as their best values were often sloppy or not unique, but still resulted in the maximum likelihood.
For stage 3, L I I I has two contributions, one for each histone H3 exchange experiment:
Strictly speaking L I I I depends only on r → rep , since all the histone H3 exchange experiments were done in the repressed state. For the first contribution, to fit the data from Rufiange et al., 2007, we used
with g mean and g var being the mean and variance, respectively, of the measured log2 ratios of Flag amounts at N-1 over N-2 (Flag-H3 MNase-ChIP in Rufiange et al., 2007, ratio values 0.591 and 0.483 for replicate 1 and 2, respectively) and g ( r → , t ′ ) the corresponding log2 ratio of the model (see Materials and methods section: H3 histone exchange model) for measurement time t ′ = 2 h (not corrected for the lag time).
For the second contribution, let h j mean denote the measured normalized mean log2 ratios of Flag amount over Myc amount at N-1, with j = 1 , 2 , 3 , 4 indicating the four different time points. We obtained h → mean = ( - 0.417 , 1.24 , 1.87 , 2.60 ) ⊤ from Dion et al., 2007 as follows: we recalculated the normalization constant of each time point using the measured mean log2 Myc/Flag signal ratios as described (supplementary material of Dion et al., 2007 using the whole-genome commercial microarrays (Agilent) data with the nucleosome pool parameters as in the section above) and then took the normalized results of the probe at the N-1 position of the PHO5 promoter (chr2:431049–431108). Unfortunately, neighboring probes were only in linker regions between promoter nucleosome positions. As mentioned in Dion et al., 2007 and corroborated by our own calculations, the values h j mean have large uncertainties, mostly due to an additive sloppy global normalization constant leading to systematic errors, while the differences between time points were determined with reasonable accuracy. Thus, we decided to fit the measured values only after a transformation that eliminates the sloppy global normalization constant by choosing the average over the four time points as a reference: h
j mean = h j mean - 1 / 4 ∑ k = 1 4 h k mean . Let C be the resulting covariance matrix after this linear transformation, assuming an independent estimated experimental standard deviation of 0.4 before the transformation. This estimate was informed by the standard deviation of the Rufiange et al., 2007 data as well as from perturbations of the nucleosome pool parameters when recalculating the normalization constants. The corresponding normalized values of the model are denoted by h
j ( r → ) , calculated from the log2 ratios of Flag amount over Myc amount at N-1, h ( r → , t j ) (see Materials and methods section: H3 histone exchange model), using the same transformation, with t j denoting the measurement time points. Since the four measurements at different time points were linearly mapped to always have an average of zero, the estimated density follows a degenerate multivariate normal distribution with the covariance matrix C . Thus the log10 likelihood can be calculated with
where C + is the Moore-Penrose inverse (pseudoinverse) of C .
H3 histone exchange model
To obtain the Flag and Myc amounts in a given model with given parameter values and then determine g ( r → , t ′ ) and h ( r → , t j ) , we used the histone pool and nucleosome turnover models in Dion et al., 2007 and assumed that the Myc H3 and Flag H3 amounts in the histone pool are given by M ( t ) = α M β M and
where we used the production rates α F = 50 / min , α M = 10 / min , the degradation rates β F = 0.01 / min , β M = 0.03 / min and the lag time t 0 = 15 min which were fitted in Dion et al., 2007. For t > t 0 , the probability that a newly assembled nucleosome contains a Flag H3 is given by
In Dion et al., 2007, the conditional probability that a given nucleosome at site l at time t contains a Flag H3 then fulfills the ordinary differential equation
with λ l being an effective turnover rate at probe position l . In our case, the dynamics of the three promoter nucleosomes are coupled, determined by the transition rate matrix Q ( r → σ ) of a given regulated on-off-slide model. At this stage, we included different nucleosome types (i.e. Flag and Myc) into the model, replacing the eight promoter configurations by all 27 possibilities to arrange no, a Flag or a Myc nucleosome at each of the three sites. Based on Q ( r → σ ) and P + ( t | N ) , we define an extended Flag/Myc transition rate matrix E ( r → σ , P + ( t | N ) ) . Each ‘new’ assembly reaction rate in E ( r → σ , P + ( t | N ) ) is given by the corresponding ‘old’ assembly rate in Q ( r → σ ) times either P + ( t | N ) or 1 - P + ( t | N ) , for a new Flag or Myc nucleosome, respectively. To find the corresponding ‘old’ reaction any extended Flag/Myc configuration is projected to one of the eight normal nucleosome configurations simply by ignoring the Flag/Myc tag information. For example, denoting Flag- and Myc-tagged nucleosomes with ‘F’ and ‘M’, respectively, an assembly reaction from the state (F, M, 0) to the state (F, M, M) in the extended model corresponds to an assembly reaction from state (1, 1, 0) to the state (1, 1, 1) in the normal model, and its reaction rate is multiplied by 1 - P + ( t | N ) in the extended model, since the new nucleosome is Myc-tagged. The rates of sliding and disassembly of Flag or Myc nucleosomes are assumed to be equal to the corresponding normal sliding and disassembly rates. The probability of extended configuration i at time t is the i -th entry of q → * ( t ) , the solution of
where σ is fixed in the repressed state, in which all histone exchange experiments took place. The log2 ratios of Flag at N-1 over Flag at N-2 amount, g ( r → , t ) , and Flag over Myc amounts at N-1, h ( r → , t ) , of each model then correspond to log2 ratios of sums of q i * ( t ) over suitable configurations i with Flag or Myc nucleosomes at the wanted sites.
In order to determine how sloppy the found best parameter values for a given model are, we performed a simple sensitivity analysis, by calculating the log10 likelihood L I + L I I + L I I I along certain directions from the best fit point in logarithmic parameter space. We found that an approximation of the real likelihood function by a second-order Taylor expansion at the best fit point worked only in a small area, as expected in a highly non-linear setting, but too small to determine parameter sloppiness properly.
As a compromise between properly scanning the parameter space and computational feasibility, we chose a small number of test directions: each fitted parameter value individually, the eigenvectors of the numerical Hessian of the likelihood function at the best fit, as well as the numerical gradient, which can be non-zero if the best fit point lies on the boundary. We ignored the boundary during the sensitivity analysis, to also take into account sloppiness that 'reaches over’ the boundary. Along these directions, we tested in exponentially increasing steps from the best fit position which positions in parameter space lead to a decrease of the likelihood by ≈ 50 % , that is, a log10 likelihood ratio change of ≈ 0.30 , which is of similar order as the log10 likelihood differences within our group of satisfactory models. We then obtained 'error bars’ for each parameter by taking the largest deviation of the log10 parameter value at the 50% likelihood level from the best value found in all tested directions (Figure 4—source data 1 and Figure 4—source data 2).
Effective chromatin opening and closing rates
The effective trajectory in time of the regulated process rate from the value of the repressed state to the value of the activated state depends on how fast the cell senses the phosphate starvation and subsequent signal processes. To obtain a reasonable upper bound for the chromatin opening rate, we assumed the regulation happens instantaneously, that is, the activated rate value of the regulated processes applies immediately at the change of the medium for a population in repressed state. Then the promoter configuration distribution decays exponentially toward the activated steady state with a rate well approximated by the negative eigenvalue of the transition rate matrix closest (but not equal) to zero, taking into account the fitted time scale. This ‘effective chromatin opening rate’ is an upper bound of how fast a given model can switch to the activated state. Conversely, we did the same calculations for the ‘effective chromatin closing rate’, which is an upper bound of how fast a given model can switch to the repressed state.
Sticky N-3 experiments
Strains 'sticky N-3 mutant 1’ and 'sticky N-3 mutant 2’ used for restriction enzyme accessibility assays were generated by transformation of linear fragments of plasmids ECS53 and ECS56, respectively, into the wild type strain BY4741 as described for the 'periodicity mutants’ in Small et al., 2014. For the sticky N-3 mutant 1, the sequence GTTTTCTCATGTAAGCGGACGTCGTC inside the PHO5 promoter was replaced with GTTTTCTTATGTAAGCTTACGTCGTC . For sticky N-3 mutant 2, GCGCAAATATGTCAACGTATTTGGAAG was replaced with GCGCAAATATGTCAAAGTATTTGGAAG . Strains were grown in YPDA medium to logarithmic phase for repressive (+Pi) and shifted from logarithmic phase to phosphate-free YNB medium (Formedia) over night for inducing (-Pi) conditions. Nuclei preparation, restriction enzyme digestion, DNA purification, secondary digest, agarose gel electrophoresis, Southern blotting, hybridization, and Phosphorimager analysis were as in Musladin et al., 2014. Secondary digest was with HaeIII for both ClaI and HhaI digests probing N-2 or N-3, respectively. The probe for both ClaI and HhaI digests corresponded to the ApaI-BamHI restriction fragment upstream of N-3.