Effect of the Marcus Theory on Photosynthesis

Effect of the Marcus Theory on Photosynthesis

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As far as I know, the Marcus Theory explains the rates of electron transfers in reactions as a function of differences in free energy between the product/reactant's potential well.

Furthermore, there is the so called inverted region which is often said to be important to explain effects as the photosynthesis. Sadly, I do not see the connection here. The inverted region seems to reduce the transfer rate in the backwards reaction but not in the forwards reaction which creates a net reaction flux. But how can this be explained by the Marcus Theory? I tried to read several sources which claimed to talk about this online, but apparently missed the crucial point.

15.5: Marcus Theory for Electron Transfer

  • Contributed by Andrei Tokmakoff
  • Professor (Chemistry) at University of Chicago

The displaced harmonic oscillator (DHO) formalism and the Energy Gap Hamiltonian have been used extensively in describing charge transport reactions, such as electron and proton transfer. Here we describe the rates of electron transfer between weakly coupled donor and acceptor states when the potential energy depends on a nuclear coordinate, i.e., nonadiabatic electron transfer. These results reflect the findings of Marcus&rsquo theory of electron transfer.

We can represent the problem as calculating the transfer or reaction rate for the transfer of an electron from a donor to an acceptor

This reaction is mediated by a nuclear coordinate (q). This need not be, and generally isn&rsquot, a simple vibrational coordinate. For electron transfer in solution, we most commonly consider electron transfer to progress along a solvent rearrangement coordinate in which solvent reorganizes its configuration so that dipoles or charges help to stabilize the extra negative charge at the acceptor site. This type of collective coordinate is illustrated below.

The external response of the medium along the electron transfer coordinate is referred to as &ldquoouter shell&rdquo electron transfer, whereas the influence of internal vibrational modes that promote ET is called &ldquoinner shell&rdquo. The influence of collective solvent rearrangements or intramolecular vibrations can be captured with the use of an electronic transition coupled to a harmonic bath.

Normally we associate the rates of electron transfer with the free-energy along the electron transfer coordinate (q). Pictures such as the ones above that illustrate states of the system with electron localized on the donor or acceptor electrons hopping from donor to acceptor are conceptually represented through diabatic energy surfaces. The electronic coupling (J) that results in transfer mixes these diabatic states in the crossing region. From this adiabatic surface, the rate of transfer for the forward reaction is related to the flux across the barrier. From classical transition state theory we can associate the rate with the free energy barrier using

[k _ = A exp left( - Delta G^ / k _ T ight)]

If the coupling is weak, we can describe the rates of transfer between donor and acceptor in the diabatic basis with perturbation theory. This accounts for nonadiabatic effects and tunneling through the barrier.

To begin we consider a simple classical derivation for the free-energy barrier and the rate of electron transfer from donor to acceptor states for the case of weakly coupled diabatic states. First we assume that the free energy or potential of mean force for the initial and final state,

[mathrm ( mathrm ) = - mathrm _ > mathrm ln mathrm

( mathrm )]

is well represented by two parabolas.

To find the barrier height (Delta G^), we first find the crossing point (dC) where

Substituting Equations ef <14.58a>and ef <14.58b>into Equation ef

[ frac <1> <2>m omega _ <0>^ <2>left( d _ - d _ ight)^ <2>= Delta G^ + frac <1> <2>m omega _ <0>^ <2>left( d _ - d _ ight)^ <2>]

and solving for (d_C) gives

The last expression comes from the definition of the reorganization energy ((lambda)), which is the energy to be dissipated on the acceptor surface if the electron is transferred at (d_D),

Then, the free energy barrier to the transfer (Delta G^) is

[egin Delta G^ & = G _ left( d _ ight) - G _ left( d _ ight) & = frac <1> <2>m omega _ <0>^ <2>left( d _ - d _ ight)^ <2> & = frac <1> <4 lambda>left[ Delta G^ + lambda ight]^ <2>end.]

So the Arrhenius rate constant is for electron transfer via activated barrier crossing is

This curve qualitatively reproduced observations of a maximum electron transfer rate under the conditions (- Delta G^ = lambda), which occurs in the barrierless case when the acceptor parabola crosses the donor state energy minimum.

We expect that we can more accurately describe nonadiabatic electron transfer using the DHO or Energy Gap Hamiltonian, which will include the possibility of tunneling through the barrier when donor and acceptor wavefunctions overlap. We start by writing the transfer rates in terms of the potential energy as before. We recognize that when we calculate thermally averaged transfer rates that this is equivalent to describing the diabatic free energy surfaces. The Hamiltonian is

[H _ <0>= | D angle H _ langle D | + | A angle H _ langle A | label<14.62>]

Here (| D angle) and (| A angle) refer to the potential where the electron is either on the donor or acceptor, respectively. Also remember that (| D angle) refers to the vibronic states

These are represented through the same harmonic potential, displaced from one another vertically in energy by

and horizontally along the reaction coordinate (q):

Here we are using reduced variables for the momenta, coordinates, and displacements of the harmonic oscillator. The diabatic surfaces can be expressed as product states in the electronic and nuclear configurations: (| D angle = | d , n angle). The interaction between the surfaces is assigned a coupling (J)

[V = J [ | d angle langle a | + | a angle langle d | ] label<14.65>]

We have made the Condon approximation, implying that the transfer matrix element that describes the electronic interaction has no dependence on nuclear coordinate. Typically this electronic coupling is expected to drop off exponentially with the separation between donor and acceptor orbitals

[J = J _ <0>exp left( - eta _ left( R - R _ <0> ight) ight) label<14.66>]

Here (eta_E) is the parameter governing the distance dependence of the overlap integral. For our purposes, even though this is a function of donor-acceptor separation (R), we take this to vary slowly over the displacements investigated here, and therefore be independent of the nuclear coordinate ((Q)).

Marcus evaluated the perturbation theory expression for the transfer rate by calculating Franck-Condon factors for the overlap of donor and acceptor surfaces, in a manner similar to our treatment of the DHO electronic absorption spectrum. Similarly, we can proceed to calculate the rates of electron transfer using the Golden Rule expression for the transfer of amplitude between two states

[w _ = frac <1>> int _ <- infty>^ <+ infty>d t leftlangle V _ (t) V _ ( 0 ) ight angle label<14.67>]

[V _ (t) = e^ t / hbar> V e^ <- i H _ <0>t / hbar>,]

we write the electron transfer rate in the DHO eigenstate form as

This form emphasizes that the electron transfer rate is governed by the overlap of vibrational wavepackets on the donor and acceptor potential energy surfaces.

Alternatively, we can cast this in the form of the Energy Gap Hamiltonian. This carries with is a dynamical picture of the electron transfer event. The energy of the two states have time-dependent (fluctuating) energies as a result of their interaction with the environment. Occasionally the energy of the donor and acceptor states coincide that is the energy gap between them is zero. At this point transfer becomes efficient. By integrating over the correlation function for these energy gap fluctuations, we characterize the statistics for barrier crossing, and therefore forward electron transfer.

Similar to before, we define a donor-acceptor energy gap Hamiltonian

[F (t) = leftlangle exp _ <+>left[ - frac int _ <0>^ d t^ H _ left( t^ ight) ight] ight angle label<14.71>]

These expressions and application of the cumulant expansio n to equation allow s us to express the transfer rate in terms of the lineshape function and correlation function

[F (t) = exp left[ frac <- i> leftlangle H _ ight angle t - g (t) ight] label<14.73>]

[g (t) = int _ <0>^ d au _ <2>int _ <0>^< au _ <2>> d au _ <1>C _ left( au _ <2>- au _ <1> ight) label<14.74>]

[C _ (t) = frac <1>> leftlangle delta H _ (t) delta H _ ( 0 ) ight angle label<14.75>]

[leftlangle H _ ight angle = lambda label<14.76>]

The lineshape function can also be written as a sum of many coupled nuclear coordinates, (q_). This expression is commonly applied to the vibronic (inner shell) contributions to the transfer rate:

Substituting the expression for a single harmonic mode into the Golden Rule rate expression gives

[egin w _ &= frac <| J |^<2>> > int _ <- infty>^ <+ infty>d t e^ <- i Delta E t / hbar - g (t)>label <4.78>[4pt] &= frac <| J |^<2>> > int _ <- infty>^ <+ infty>d t e^ <- i ( Delta E + lambda ) t / hbar>exp left[ D left( operatorname left( eta hbar omega _ <0>/ 2 ight) left( cos omega _ <0>t - 1 ight) - i sin omega _ <0>t ight) ight] label <14.78>end]

This expression is very similar to the one that we evaluated for the absorption lineshape of the Displaced Harmonic Oscillator model. A detailed evaluation of this vibronically mediated transfer rate is given in Jortner.

To get a feeling for the dependence of (k) on (q), we can look at the classical limit (hbar omega ll k T). This corresponds to the case where one is describing the case of a low frequency &ldquosolvent mode&rdquo or &ldquoouter sphere&rdquo effect on the electron transfer. Now, we neglect the imaginary part of (g(t)) and take the limit

[operatorname ( eta hbar omega / 2 ) ightarrow 2 / eta hbar omega]

Note that the high temperature limit also means the low frequency limit for (omega _ <0>). This means that we can expand

[cos omega _ <0>t approx 1 - left( omega _ <0>t ight)^ <2>/ 2,]

where (lambda = D hbar omega _ <0>). Note that the activation barrier (Delta E^) for displaced harmonic oscillators is (Delta E^ = Delta E + lambda). For a thermally averaged rate it is proper to associate the average energy gap with the standard free energy of reaction,

Therefore, this expression is equivalent to the classical Marcus&rsquo result for the electron transfer rate

where the pre-exponential is

This expression shows the nonlinear behavior expected for the dependence of the electron transfer rate on the driving force for the forward transfer, i.e., the reaction free energy. This is unusual because we generally think in terms of a linear free energy relationship between the rate of a reaction and the equilibrium constant:

This leads to the thinking that the rate should increase as we increase the driving free energy for the reaction (-Delta G^<0>). This behavior only hold for a small region in (Delta G^<0>). Instead, eq. shows that the ET rate will increase with (-Delta G^<0>), until a maximum rate is observed for (-Delta G^<0>=lambda) and the rate then decreases. This decrease of k with increased (-Delta G^<0>) is known as the &ldquoinverted regime&rdquo. The inverted behavior means that extra vibrational excitation is needed to reach the curve crossing as the acceptor well is lowered. The high temperature behavior for coupling to a low frequency mode (left(100 mathrm<

K> ight)) is shown at right, in addition to a cartoon that indicates the shift of the curve crossing at (Delta G^<0>) in increased.

Particularly in intramolecular ET, it is common that one wants to separately account for the influence of a high frequency intramolecular vibration (inner sphere ET) that is not in the classical limit that applies to the low frequency classical solvent response. If an additional mode of frequency (omega _ <0>) and a rate in the form of Equation ef <14.81>is added to the low frequency mode, Jortner has given an expression for the rate as:

Here (lambda _ <0>) is the solvation reorganization energy. For this case, the same inverted regime exists although the simple Gaussian dependence of (k) on (Delta G^<0>) no longer exists. The asymmetry here exists because tunneling sees a narrower barrier in the inverted regime than in the normal regime. Examples of the rates obtained with eq. are plotted in the figure below (T= 300 K).

As with electronic spectroscopy, a more general and effective way of accounting for the nuclear motions that mediate the electron transfer process is to describe the coupling weighted density of states as a spectral density. Then we can use coupling to a harmonic bath to describe solvent and/or vibrational contributions of arbitrary form to the transfer event using

[g (t) = int _ <0>^ d omega, ho ( omega ) left[ operatorname left( frac <eta hbar omega> <2> ight) ( 1 - cos omega t ) + i ( sin omega t - omega t ) ight] label<14.85>]

Hidden Allee effect in photosynthetic organisms

In ecology and population biology, logistic equation is widely applied for simulating the population of organisms. By combining the logistic model with the low-density effect called Allee effect, several variations of mathematical expressions have been proposed. The upper half of the work was dedicated to establish a novel equation for highly flexible density effect model with Allee threshold. Allee effect has been rarely observed in microorganisms with asexual reproduction despite of theoretical studies. According to the exploitation ecosystem hypotheses, plants are believed to be insensitive to Allee effect. Taken together, knowledge on the existence of low-density effect in photosynthetic microorganisms is required for redefining the ecological theories emphasizing the photosynthetic organisms as the basis for food chains. Therefore, in the lower half of the present article, we report on the possible Allee effect in photo-autotrophic organisms, namely, green paramecia, and cyanobacteria. Optically monitored growth of green paramecia was shown to be regulated by Allee-like weak low-density effect under photo-autotrophic and photo-heterotrophic conditions. Insensitiveness of wild type cyanobacteria (Synechocystis sp. Strain PCC6803) to low-density effect was confirmed, as consistent with our empirical knowledge. In contrast, a mutant line of PCC6803 impaired with a photosynthesis-related pxcA gene was shown to be sensitive to typical Allee's low-density effect (i.e. this line of cells failed to propagate at low cellular density while cells start logarithmic growth at relatively higher inoculating density). This is the first observation that single-gene mutation in an autotrophic organism alters the sensitivity to Allee effect.

Keywords: Allee effect cyanobacteria green paramecia logistic equation photosynthesis.

© 2020 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.

Rudolph A. Marcus

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Rudolph A. Marcus, (born July 21, 1923, Montreal, Que., Can.), Canadian-born American chemist, winner of the 1992 Nobel Prize for Chemistry for his work on the theory of electron-transfer reactions in chemical systems. The Marcus theory shed light on diverse and fundamental phenomena such as photosynthesis, cell metabolism, and simple corrosion.

Marcus received his doctorate from McGill University, Montreal, in 1946. From 1951 he worked at the Polytechnic Institute of Brooklyn. In 1964 he joined the faculty of the University of Illinois, leaving in 1978 for the California Institute of Technology.

Marcus began studying electron-transfer reactions in the 1950s. In a series of papers published between 1956 and 1965, he investigated the role of surrounding solvent molecules in determining the rate of r edox reactions—oxidation and reduction reactions in which the reactants exchange electrons—in solution. Marcus determined that subtle changes occur in the molecular structure of the reactants and the solvent molecules around them these changes influence the ability of electrons to move between the molecules. He further established that the relationship between the driving force of an electron-transfer reaction and the reaction’s rate is described by a parabola. Thus, as more driving force is applied to a reaction, its rate at first increases but then begins to decrease. This insight aroused considerable skepticism until it was confirmed experimentally in the 1980s.

Marcus also did important work in areas such as transition-state theory, the theory of unimolecular reactions, and the theory of collisions and bound states.

Quantum effects observed in photosynthesis

The figure shows the photosynthetic complex of light-harvesting green sulfur bacteria the green and yellow circles highlight the two molecules simultaneously excited. Credit: dr. Thomas la Cour Jansen/University of Groningen

Molecules that are involved in photosynthesis exhibit the same quantum effects as non-living matter, concludes an international team of scientists including University of Groningen theoretical physicist Thomas la Cour Jansen. This is the first time that quantum mechanical behavior was proven to exist in biological systems that are involved in photosynthesis. The interpretation of these quantum effects in photosynthesis may help in the development of nature-inspired light-harvesting devices. The results were published in Nature Chemistry on 21 May.

For several years now, there has been a debate about quantum effects in biological systems. The basic idea is that electrons in can be in two states at once, until they are observed. This may be compared to the thought experiment known as Schrödinger's Cat. The cat is locked in a box with a vial of a toxic substance. If the cap of the vial is locked with a quantum system, it may simultaneously be open or closed, so the cat is in a mixture of the states "dead" and "alive," until we open the box and observe the system. This is precisely the apparent behavior of electrons.

In earlier research, scientists had already found signals suggesting that light-harvesting molecules in bacteria may be excited into two states simultaneously. In itself this proved the involvement of quantum mechanical effects, however in those experiments, that excited state supposedly lasted more than 1 picosecond (0.000 000 000 001 second). This is much longer than one would expect on the basis of quantum mechanical theory.

Jansen and his colleagues show in their publication that this earlier observation is wrong. "We have shown that the quantum effects they reported were simply regular vibrations of the molecules." Therefore, the team continued the search. "We wondered if we might be able to observe that Schrödinger cat situation."

They used different polarizations of light to perform measurements in light-harvesting green sulfur bacteria. The bacteria have a photosynthetic complex, made up of seven light sensitive molecules. A photon will excite two of those molecules, but the energy is superimposed on both. So just like the cat is dead or alive, one or the other molecule is excited by the photon. "In the case of such a superposition, spectroscopy should show a specific oscillating signal," explains Jansen. "And that is indeed what we saw. Furthermore, we found quantum effects that lasted precisely as long as one would expect based on theory and proved that these belong to energy superimposed on two molecules simultaneously." Jansen concludes that biological systems exhibit the same quantum effects as non-biological systems.

The observation techniques developed for this research project may be applied to different systems, both biological and non-biological. Jansen is happy with the results. "This is an interesting observation for anyone who is interested in the fascinating world of quantum mechanics. Moreover, the results may play a role in the development of new systems, such as the storage of solar energy or the development of quantum computers."

2.2 Marcus Theory of Electron Transfer

The first generally accepted theory of ET was developed by Rudolph A. Marcus to address outer-sphere electron transfer and was based on a transition-state theory approach. The Marcus theory of electron transfer was then extended to include inner-sphere electron transfer by Noel Hush and Marcus. The resultant theory, called Marcus-Hush theory , has guided most discussions of electron transfer ever since. Both theories are, however, semiclassical in nature, although they have been extended to fully quantum mechanical treatments by Joshua Jortner , Alexender M. Kuznetsov , and others proceeding from Fermi's Golden Rule and following earlier work in non-radiative transitions . Furthermore, theories have been put forward to take into account the effects of vibronic coupling on electron transfer in particular, the PKS theory of electron transfer . A ccording to the Franck–Condon principle, electronic transitions are so fast that they can be regarded as taking place in a stationary nuclear framework. This principle also applies to an electron transfer process in which an electron migrates from one energy surface, representing the dependence of the energy of DA on its geometry, to another representing the energy of D+A−. We can represent the potential energy (and the Gibbs energy) surfaces of the two complexes (the reactant complex, DA, and the product complex, D+A−) by the parabolas characteristic of harmonic oscillators, with the displacement coordinate corresponding to the changing geometries (Fig. 24.27). This coordinate represents a collective mode of the donor, acceptor, and solvent. According to the Franck–Condon principle, the nuclei do not have time to move when the system passes from the reactant to the product surface as a result of the transfer of an electron. Therefore, electron transfer can occur only after thermal fluctuations bring the geometry of DA to q* in Fig. 24.27, the value of the nuclear coordinate at which the two parabolas intersect. The factor κν is a measure of the probability that the system will convert from reactants (DA) to products (D+A−) at q* by electron transfer within the thermally excited DA complex. To understand the process, we must turn our attention to the effect that the rearrangement of nuclear coordinates has on electronic energy levels of DA and D+A− for a given distance r between D and A (Fig. 24.28). Initially, the electron to be transferred occupies the HOMO of D, and the overall energy of DA is lower than that of D+A− (Fig. 24.28a). As the nuclei rearrange to a configuration represented by q* in Fig. 24.28b, the highest occupied electronic level of DA and the lowest unoccupied electronic level of D+A− become degenerate and electron transfer becomes energetically feasible.

Blackman&rsquos Law and Photosynthesis | Botany

Sachs in 1860 for the first time propounded the concept of the three cardinal points. According to this concept, there is a minimum, optimum and maximum for each factor in relation to photosynthesis.

This way, with any given species there may be a minimum temperature below which no photosynthesis takes place, an optimum temperature at which the highest rate takes place and a maximum temperature beyond which no photosynthesis will take place.

In the twentieth century Blackman (1905) proposed his principle of limiting factors. According to this principle the rate of photosynthesis controlled by several factors is only as rapid as the slowest factor permits.

He claimed that, if all other factors are kept constant the factor under consideration will affect the rate of photosynthesis, starting at a minimum below which no photosynthesis takes place and ending with an optimum at which a horizontal would be established, that is, the rate would remain constant despite further increases in that factor. At this point some other factor becomes limiting.

The explanation of Blackman’s principle can best be presented in terms of the illustration given by Blackman himself. It is to be assumed that light intensity supplied to a leaf is just sufficient to utilize 5 mg of carbon dioxide per hour in photosynthesis. As the carbon dioxide supply is increased the rate of photosynthesis is also increased until 5 mg of carbon dioxide enters the leaf per hour.

Any further increase in the supply of carbon dioxide will have no influence upon the rate of photosynthesis. Light has now become the limiting factor and further increase in the rate of photosynthesis can be brought about only by an increase in the intensity of light.

These results are indicated graphically. Here the effects of three different light intensities have been shown on the rate of photosynthesis under increasing concentrations of carbon dioxide.

Under low light intensity, the rate of photosynthesis increasing concentrations of carbon dioxide. Concentration is raised until B is reached where further increase in carbon dioxide concentration is not accompanied by any increase in the rate of photosynthesis.

The rate of photosynthesis becomes constant along the line BC. Any further increase in the supply of carbon dioxide will have no effect single upon the rate of photosynthesis, because light intensity has now become the limiting factor. If light intensity is now further increased, the rate of photosynthesis also increases until light again becomes a limiting factor.

Here light becomes the limiting factor at the point C and there is another sharp break in the rate of photosynthesis along the line CF. Further increase in light intensity causes an increase in the rate of photosynthesis along the line CD with a Proportional increase in carbon dioxide concentration.

The rate of photosynthesis becomes constant along the line DE where light again becomes limiting factor. At the points B, C and D the increase in the rate of photosynthesis stops abruptly because one or the other factors becomes limiting.

Light and carbon dioxide are not the only factors which can be limiting in the process of photosynthesis other factors of photosynthesis can also become limiting under certain conditions.

It becomes clear from the above discussion that when photosynthesis is under the influence of several factors simultaneously, an increase in that factor and the limiting factor will bring about an increase in the rate of photosynthesis.

The Process of Photosynthesis

The process of photosynthesis occurs when green plants use the energy of light to convert carbon dioxide (CO2) and water (H2O) into carbohydrates. Light energy is absorbed by chlorophyll, a photosynthetic pigment of the plant, while air containing carbon dioxide and oxygen enters the plant through the leaf stomata. An extremely important by-product of photosynthesis is oxygen, on which most organisms depend.

Glucose, a carbohydrate processed during photosynthesis, is mostly used by plants as an energy source to build leaves, flowers, fruits, and seeds. Molecules of glucose later combine with each other to form more complex carbohydrates such as starch and cellulose. The cellulose is the structural material used in plant cell walls. Photosynthesis provides the basic energy source for virtually all organisms.

We can express the overall reaction of photosynthesis as:


Euglena are unicellular protists in the genus Euglena. These organisms were classified in the phylum Euglenophyta with algae due to their photosynthetic ability. Scientists now believe that they are not algae but have gained their photosynthetic capabilities through an endosymbiotic relationship with green algae. As such, Euglena have been placed in the phylum Euglenozoa.

Science Practice Challenge Questions

On a hot, dry day, plants close their stomata to conserve water. Explain the connection between the oxidation of water in photosystem II of the light-dependent reactions and the synthesis of glyceraldehyde-3-phosphate (G3PA) in the light-independent reactions. Predict the effect of closed stomata on the synthesis of G3PA and justify the prediction.

The emergence of photosynthetic organisms is recorded in layers of sedimentary rock known as a banded iron formation. Dark-colored and iron-rich bands composed of hematite (Fe2O3) and magnetite (Fe3O4) only a few millimeters thick alternate with light-colored and iron-poor shale or chert. Hematite and magnetite can form precipitates from water that has a high concentration of dissolved oxygen. Shale and chert can form under conditions that have high concentrations of carbonates (CO3 -2 ). These banded iron formations appeared 3.7 billion years ago (and became less common 1.8 billion years ago). Justify the claim that these sedimentary rock formations reveal early Earth conditions.

The following diagram summarizes the light reactions of photosynthesis.

The diagram shows light-dependent reactions of photosynthesis, including the reaction centers, electron transport chains, and the overall reactions within each of these. The free energy per electron is shown for the oxidation-reduction reactions. The free change of the captured radiant energy is shown.

  1. In the overall mass balance equation for the light reactions shown above, identify the source of electrons for the synthesis of NADPH.
  2. Calculate the number of electrons transferred in this reaction.
  3. Using the free energies per electron displayed, calculate the free energy change of the light-dependent reactions.
  4. Given that the free energy change for the hydrolysis of ATP is -31.5 kJ/mole and the free energy change for the formation of NADPH from NADP + is 18 kJ/mole, calculate the total production of free energy for the light reactions.
  5. Using this definition of energy efficiency, calculate the efficiency of the light reaction of photosynthesis: energy efficiency = free energy produced/energy input.

Algae can be used for food and fuel. To maximize profit from algae production under artificial light, researchers proposed an experiment to determine the dependence of the efficiency of the process used to grow the algae on light intensity (“brightness”) that will be purchased from the electric company.

The algae will be grown on a flat sheet that will be continuously washed with dissolved carbon dioxide and nutrients. Light-emitting diodes (LEDs) will be used to illuminate the growth sheet. Photodiodes placed above and below the sheet will be used to detect light transmitted through and reflected from the algal mat. The intensity of light can be varied, and the algae can be removed, filtered, and dried. The amount of stored energy in the algal mats can be determined by calorimetry.

A. Identify a useful definition of efficiency for this study and justify your choice.

B. Frequencies of light emitted by the LEDs will not be variables but must be specified for the construction of the apparatus. Identify the frequencies of light that should be used in the experiment and justify your choice.

C. Evaluate the claim that the experiment is based on the assumption that there is an upper limit on the intensity of light used to support growth of algae. Predict a possible effect on algal growth if light with too great an intensity is used and justify the prediction.

D. Design an experiment by describing a procedure that can be used to determine the relationship between light intensity and efficiency.

The classical theory of evolution is based on a gradual transformation, the accumulation of many random mutations that are selected. The biological evidence for evolution is overwhelming, particularly when one considers what has not changed: core conserved characteristics.

A. Describe three conserved characteristics common to both chloroplasts and mitochondria.

Some hypotheses that have been proposed to account for biological diversity are saltatory, involving sudden changes, rather than gradualist. In defense of the classical gradualist theory of evolution, nearly all biologists in the late 1960s rejected the theory of endosymbiosis as presented by Lynn Margulis in 1967.

B. Suppose that you want to disprove the theory of endosymbiosis.

Explain how the following evidence could disprove the theory:

i. a “transitional species” with cellular features that are intermediate cells with and without mitochondria

ii. a “transitional organelle” with some features, such as compartmentalized metabolic processes, but not other features, such as DNA

Explain how the following evidence supports the theory of endosymbiosis:

iii. bacteria live within your intestines, but you still have a separate identity

iv. no one has directly observed the fusion of two organisms in which a single organism results

Discovering the carbon-fixation reactions (or light-independent reactions) of photosynthesis earned Melvin Calvin a Nobel Prize in 1961. The isolation and identification of the products of algae exposed to 14 C revealed the path of carbon in photosynthesis. 14 C was fed to the algal culture in the form of bicarbonate ion (HCO3 - ). To agitate the culture, air, which contains CO2, was bubbled through the system, so there were two sources of carbon.

Since Calvin’s experiment, research has focused on the way carbon from a solution containing bicarbonate ions is absorbed by algae. In aqueous solution, the bicarbonate anion (HCO3 - ) is in equilibrium with dissolved CO2 as shown in the equation below:

H + + H C O 3 − ← → H 2 O + C O 2 H + + H C O 3 − ← → H 2 O + C O 2

In a later experiment, Larsson and Axelsson (1999) used acetazolamide (AZ), a carbonate anhydrase inhibitor, to inhibit enzymes that convert bicarbonate into carbon dioxide. They also used disulfonate (DIDS), an inhibitor of the transport of anions, such as the bicarbonate ion, through the plasma membrane.

A. Pose a scientific question that can be pursued with AZ and DIDS in terms of the path of carbon in photosynthesis.

B. The plasma membrane is permeable to the nonpolar, uncharged carbon dioxide molecule. However, the concentration of carbon dioxide in solution can be very small. Explain how the enzyme carbonate anhydrase can increase the availability of carbon dioxide to the cell.

C. Larsson and Axelsson conducted experiments in which the growth medium was fixed at two different pH levels and determined the effects of AZ and DIDS on the rate of photosynthesis by measuring oxygen concentrations at various times. The results are shown in the two graphs below. The arrows indicate the time points during which HCO3 - , AZ, and DIDS were added to each system.

In which system, A or B, is there a strong reliance on the bicarbonate ion as the mechanism of carbon uptake by the cell? Justify your answer using the data.

D. If both systems are dosed with the same concentrations of bicarbonate ion, in which system, A or B, is the pH higher? Justify your answer using the data and the bicarbonate-carbon dioxide equilibrium equation.

Watch the video: Marcus Theory I (October 2022).